Eulerian and Lagrangian approaches to multidimensional condensation and collection
NASA Astrophysics Data System (ADS)
Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.
2017-06-01
Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.Plain Language SummaryThe bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 μm ˜ 40 μm [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> schemes in detail to tackle with the turbulence-generated collection.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DPPTP9094H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DPPTP9094H"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Plasma Jet Modeling for the Plasma Liner Experiment</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Hatcher, Richard; Cassibry, Jason; Stanic, Milos; Loverich, John; Hakim, Ammar</p>
<p>2011-10-01</p>
<p>The Plasma Liner Experiment (PLX) aims to demonstrate the feasibility of using spherically-convergent plasma jets to from an imploding plasma liner. Our group has modified two hydrodynamic simulation codes to include radiative loss, tabular equations of state (EOS), and thermal transport. Nautilus, created by TechX Corporation, is a finite-difference <span class="hlt">Eulerian</span> code which solves the MHD equations <span class="hlt">formulated</span> as systems of hyperbolic conservation laws. The other is SPHC, a smoothed particle hydrodynamics code produced by Stellingwerf Consulting. Use of the <span class="hlt">Lagrangian</span> fluid particle approach of SPH is motivated by the ability to accurately track jet interfaces, the plasma vacuum boundary, and mixing of various layers, but <span class="hlt">Eulerian</span> codes have been in development for much longer and have better shock capturing. We validate these codes against experimental measurements of jet propagation, expansion, and merging of two jets. Precursor jets are observed to form at the jet interface. Conditions that govern evolution of two and more merging jets are explored.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F"><span>Uncertainty quantification in <span class="hlt">Eulerian-Lagrangian</span> models for particle-laden flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs</p>
<p>2017-11-01</p>
<p>A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based <span class="hlt">Eulerian-Lagrangian</span> model, which traces individual particles in their <span class="hlt">Lagrangian</span> frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear <span class="hlt">Eulerian-Lagrangian</span> systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016OcMod..97...27F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016OcMod..97...27F"><span>A LES-based <span class="hlt">Eulerian-Lagrangian</span> approach to predict the dynamics of bubble plumes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.</p>
<p>2016-01-01</p>
<p>An approach for <span class="hlt">Eulerian-Lagrangian</span> large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1247151','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1247151"><span>Adaptive reconnection-based arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> method</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bo, Wurigen; Shashkov, Mikhail</p>
<p></p>
<p>We present a new adaptive Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit <span class="hlt">Lagrangian</span> phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the <span class="hlt">Lagrangian</span> solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1247151-adaptive-reconnection-based-arbitrary-lagrangian-eulerian-method','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1247151-adaptive-reconnection-based-arbitrary-lagrangian-eulerian-method"><span>Adaptive reconnection-based arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> method</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Bo, Wurigen; Shashkov, Mikhail</p>
<p>2015-07-21</p>
<p>We present a new adaptive Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit <span class="hlt">Lagrangian</span> phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the <span class="hlt">Lagrangian</span> solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......215H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......215H"><span><span class="hlt">Eulerian</span> <span class="hlt">Formulation</span> of Spatially Constrained Elastic Rods</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Huynen, Alexandre</p>
<p></p>
<p>Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation <span class="hlt">formulates</span> a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the <span class="hlt">Eulerian</span> framework of the constraint. The methodical exploration of both types of elementary problems leads to specific <span class="hlt">formulations</span> of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed <span class="hlt">Eulerian</span> reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21279359','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21279359"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Chen, Zhan; Baker, Nathan A; Wei, G W</p>
<p>2011-12-01</p>
<p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of our differential geometry based solvation models. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for the purpose of</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p>
<p>2010-01-01</p>
<p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of our differential geometry based solvation model. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>AN <span class="hlt">EULERIAN-LAGRANGIAN</span> LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include <span class="hlt">Eulerian-Lagrangian</span> methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....53.9040S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....53.9040S"><span>A <span class="hlt">Lagrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi</p>
<p>2017-11-01</p>
<p>Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a <span class="hlt">Lagrangian</span> framework, while in others an <span class="hlt">Eulerian</span> might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a <span class="hlt">Lagrangian</span> closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a <span class="hlt">LAgrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the <span class="hlt">Lagrangian</span> Spatial Markov model and maps concentrations to an <span class="hlt">Eulerian</span> grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the <span class="hlt">Eulerian</span> reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.; ...</p>
<p>2017-05-09</p>
<p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The <span class="hlt">formulation</span> is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting <span class="hlt">formulation</span> of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1360930','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1360930"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.</p>
<p></p>
<p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The <span class="hlt">formulation</span> is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting <span class="hlt">formulation</span> of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70011338','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70011338"><span>Euler-<span class="hlt">Lagrangian</span> computation for estuarine hydrodynamics</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Cheng, Ralph T.</p>
<p>1983-01-01</p>
<p>The transport of conservative and suspended matter in fluid flows is a phenomenon of <span class="hlt">Lagrangian</span> nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an <span class="hlt">Eulerian</span> <span class="hlt">formulation</span> for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an <span class="hlt">Eulerian</span> reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> computational techniques.</p>
</li>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IJMPS..4260159F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IJMPS..4260159F"><span>a Marker-Based <span class="hlt">Eulerian-Lagrangian</span> Method for Multiphase Flow with Supersonic Combustion Applications</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fan, Xiaofeng; Wang, Jiangfeng</p>
<p>2016-06-01</p>
<p>The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an <span class="hlt">Eulerian-Lagrangian</span> computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (<span class="hlt">Eulerian</span>) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (<span class="hlt">Lagrangian</span>) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based <span class="hlt">Eulerian-Lagrangian</span> method is effective and reliable.</p>
</li>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z"><span>Scalable Methods for <span class="hlt">Eulerian-Lagrangian</span> Simulation Applied to Compressible Multiphase Flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zwick, David; Hackl, Jason; Balachandar, S.</p>
<p>2017-11-01</p>
<p>Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the <span class="hlt">Eulerian-Lagrangian</span> method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for <span class="hlt">Eulerian-Lagrangian</span> simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>Extension of rezoned <span class="hlt">Eulerian-Lagrangian</span> method to astrophysical plasma applications</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Song, M. T.; Wu, S. T.; Dryer, Murray</p>
<p>1993-01-01</p>
<p>The rezoned <span class="hlt">Eulerian-Lagrangian</span> procedure developed by Brackbill and Pracht (1973), which is limited to simple configurations of the magnetic fields, is modified in order to make it applicable to astrophysical plasma. For this purpose, two specific methods are introduced, which make it possible to determine the initial field topology for which no analytical expressions are available. Numerical examples illustrating these methods are presented.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1995JCoPh.122..291L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1995JCoPh.122..291L"><span>A Shock-Adaptive Godunov Scheme Based on the Generalised <span class="hlt">Lagrangian</span> <span class="hlt">Formulation</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lepage, C. Y.; Hui, W. H.</p>
<p>1995-12-01</p>
<p>Application of the Godunov scheme to the Euler equations of gas dynamics based on the <span class="hlt">Eulerian</span> <span class="hlt">formulation</span> of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O( h), where h is the cell width. Based on the generalised <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> (GLF) of Hui et al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slipline—itself a streamline—is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation <span class="hlt">formulation</span> of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA542504','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA542504"><span>Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2010-09-30</p>
<p>simulating violent free - surface flows , and show the importance of wave breaking in energy transport...using <span class="hlt">Eulerian</span> simulation . 3 IMPACT/APPLICATION This project aims at developing an advanced simulation tool for multi-fluids free - surface flows that...several <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for free - surface turbulence and wave simulation . The WIND–SNOW is used to simulate 1 Report</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164423','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164423"><span>On <span class="hlt">Lagrangian</span> residual currents with applications in south San Francisco Bay, California</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Cheng, Ralph T.; Casulli, Vincenzo</p>
<p>1982-01-01</p>
<p>The <span class="hlt">Lagrangian</span> residual circulation has often been introduced as the sum of the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift. Unfortunately, this definition of the <span class="hlt">Lagrangian</span> residual circulation is conceptually incorrect because both the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift are <span class="hlt">Eulerian</span> variables. In this paper a classification of various residual variables are reviewed and properly defined. The <span class="hlt">Lagrangian</span> residual circulation is then studied by means of a two-stage <span class="hlt">formulation</span> of a computer model. The tidal circulation is first computed in a conventional <span class="hlt">Eulerian</span> way, and then the <span class="hlt">Lagrangian</span> residual circulation is determined by a method patterned after the method of markers and cells. To demonstrate properties of the <span class="hlt">Lagrangian</span> residual circulation, application of this approach in South San Francisco Bay, California, is considered. With the aid of the model results, properties of the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residual circulation are examined. It can be concluded that estimation of the <span class="hlt">Lagrangian</span> residual circulation from <span class="hlt">Eulerian</span> data may lead to unacceptable error, particularly in a tidal estuary where the tidal excursion is of the same order of magnitude as the length scale of the basin. A direction calculation of the <span class="hlt">Lagrangian</span> residual circulation must be made and has been shown to be feasible.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..1511185C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..1511185C"><span>A <span class="hlt">lagrangian-eulerian</span> description of debris transport by a tsunami in the Lisbon waterfront</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.</p>
<p>2013-04-01</p>
<p>Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (<span class="hlt">eulerian</span>) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two <span class="hlt">formulations</span> were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (<span class="hlt">lagrangian</span>) <span class="hlt">formulation</span> where solid bodies are tracked between two time-steps once the flow field is determined by the <span class="hlt">eulerian</span> solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>An <span class="hlt">Eulerian/Lagrangian</span> method for computing blade/vortex impingement</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Steinhoff, John; Senge, Heinrich; Yonghu, Wenren</p>
<p>1991-01-01</p>
<p>A combined <span class="hlt">Eulerian/Lagrangian</span> approach to calculating helicopter rotor flows with concentrated vortices is described. The method computes a general evolving vorticity distribution without any significant numerical diffusion. Concentrated vortices can be accurately propagated over long distances on relatively coarse grids with cores only several grid cells wide. The method is demonstrated for a blade/vortex impingement case in 2D and 3D where a vortex is cut by a rotor blade, and the results are compared to previous 2D calculations involving a fifth-order Navier-Stokes solver on a finer grid.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019"><span>Acoustic streaming: an arbitrary Lagrangian–<span class="hlt">Eulerian</span> perspective</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco</p>
<p>2017-01-01</p>
<p>We analyse acoustic streaming flows using an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) perspective. The <span class="hlt">formulation</span> stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, <span class="hlt">formulated</span> in terms of the fluid displacement at the fast scale, and a second-order problem, <span class="hlt">formulated</span> in terms of the <span class="hlt">Lagrangian</span> flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the <span class="hlt">Lagrangian</span> velocity, the <span class="hlt">formulation</span> does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is <span class="hlt">formulated</span> in terms of the displacement field, our <span class="hlt">formulation</span> is directly applicable to more complex fluid–structure interaction problems in microacoustofluidic devices. After the formulation’s exposition, we present numerical results that illustrate the advantages of the <span class="hlt">formulation</span> with respect to current approaches. PMID:29051631</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29060488','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29060488"><span>Serial fusion of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approaches for accurate heart-rate estimation using face videos.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Gupta, Puneet; Bhowmick, Brojeshwar; Pal, Arpan</p>
<p>2017-07-01</p>
<p>Camera-equipped devices are ubiquitous and proliferating in the day-to-day life. Accurate heart rate (HR) estimation from the face videos acquired from the low cost cameras in a non-contact manner, can be used in many real-world scenarios and hence, require rigorous exploration. This paper has presented an accurate and near real-time HR estimation system using these face videos. It is based on the phenomenon that the color and motion variations in the face video are closely related to the heart beat. The variations also contain the noise due to facial expressions, respiration, eye blinking and environmental factors which are handled by the proposed system. Neither <span class="hlt">Eulerian</span> nor <span class="hlt">Lagrangian</span> temporal signals can provide accurate HR in all the cases. The cases where <span class="hlt">Eulerian</span> temporal signals perform spuriously are determined using a novel poorness measure and then both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> temporal signals are employed for better HR estimation. Such a fusion is referred as serial fusion. Experimental results reveal that the error introduced in the proposed algorithm is 1.8±3.6 which is significantly lower than the existing well known systems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70033100','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70033100"><span><span class="hlt">Eulerian-Lagrangian</span> numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Cox, T.J.; Runkel, R.L.</p>
<p>2008-01-01</p>
<p>Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, <span class="hlt">Eulerian</span> numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking <span class="hlt">Lagrangian</span> control volumes across a fixed (<span class="hlt">Eulerian</span>) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative <span class="hlt">Eulerian</span> numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the <span class="hlt">Lagrangian</span> scheme performs better than the <span class="hlt">Eulerian</span> scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative <span class="hlt">Eulerian</span> scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative <span class="hlt">Eulerian</span> scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1419712','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1419712"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Parameterization of the Oceanic Mixed Layer using Large Eddy Simulation and MPAS-Ocean</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Van Roekel, Luke</p>
<p></p>
<p>We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that <span class="hlt">Eulerian-Lagrangian</span> effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and <span class="hlt">Lagrangian</span> particles will be utilized to better represent the movement of water into and out of the mixed layer.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture <span class="hlt">formulation</span> based on a single inverse deformation gradient tensor field</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...</p>
<p>2017-12-31</p>
<p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1423820','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1423820"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture <span class="hlt">formulation</span> based on a single inverse deformation gradient tensor field</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.</p>
<p></p>
<p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.351..422P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.351..422P"><span>An adaptive reconstruction for <span class="hlt">Lagrangian</span>, direct-forcing, immersed-boundary methods</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Posa, Antonio; Vanella, Marcos; Balaras, Elias</p>
<p>2017-12-01</p>
<p><span class="hlt">Lagrangian</span>, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the <span class="hlt">Lagrangian</span> grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of <span class="hlt">Lagrangian</span> IB, and <span class="hlt">Eulerian</span> grids. With this approach, the density of surface <span class="hlt">Lagrangian</span> markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying <span class="hlt">Eulerian</span> grid. The markers are not stored and the <span class="hlt">Lagrangian</span> data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction <span class="hlt">formulation</span>, but it can be adapted to any <span class="hlt">Lagrangian</span>, direct-forcing <span class="hlt">formulation</span>. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392"><span>Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Techniques for the Mesh Representation</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick</p>
<p>2016-01-01</p>
<p>In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary <span class="hlt">Lagrangian-Eulerian</span>) or an <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>. The majority of the reported 3D heart valve FSI simulations are performed with the <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an <span class="hlt">Eulerian</span>-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE <span class="hlt">formulation</span>, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996dmu..conf..543B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996dmu..conf..543B"><span><span class="hlt">Lagrangian</span> Perturbation Approach to the Formation of Large-scale Structure</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Buchert, Thomas</p>
<p></p>
<p>The present lecture notes address three columns on which the <span class="hlt">Lagrangian</span> perturbation approach to cosmological dynamics is based: 1. the <span class="hlt">formulation</span> of a <span class="hlt">Lagrangian</span> theory of self-gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of <span class="hlt">Eulerian</span> fields from the <span class="hlt">Lagrangian</span> picture, and 3. a precise definition of a Newtonian cosmology framework in which <span class="hlt">Lagrangian</span> perturbation solutions can be studied. While the first is a discussion of the basic equations obtained by transforming the <span class="hlt">Eulerian</span> evolution and field equations to the <span class="hlt">Lagrangian</span> picture, the second exemplifies how the <span class="hlt">Lagrangian</span> theory determines the evolution of <span class="hlt">Eulerian</span> fields including kinematical variables like expansion, vorticity, as well as the shear and tidal tensors. The third column is based on a specification of initial and boundary conditions, and in particular on the identification of the average flow of an inhomogeneous cosmology with a `Hubble-flow'. Here, we also look at the limits of the <span class="hlt">Lagrangian</span> perturbation approach as inferred from comparisons with N-body simulations and illustrate some striking properties of the solutions.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1270630','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1270630"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p>
<p></p>
<p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be <span class="hlt">formulated</span> in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu</p>
<p></p>
<p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be <span class="hlt">formulated</span> in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. All the perturbative models fare better than linear theory.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p>
<p>2015-09-02</p>
<p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be <span class="hlt">formulated</span> in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1613316G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1613316G"><span><span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Gotovac, Hrvoje; Srzic, Veljko</p>
<p>2014-05-01</p>
<p>Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different <span class="hlt">Eulerian</span>, <span class="hlt">Lagrangian</span> and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACP....12.8979P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACP....12.8979P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p>
<p>2012-10-01</p>
<p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70018031','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70018031"><span>A finite-volume <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method for solution of the advection-dispersion equation</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Healy, R.W.; Russell, T.F.</p>
<p>1993-01-01</p>
<p>A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM <span class="hlt">formulations</span>, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on <span class="hlt">Lagrangian</span> space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/15013474','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/15013474"><span>Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Anderson, R W; Pember, R B; Elliott, N S</p>
<p>2001-10-22</p>
<p>A new method that combines staggered grid Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid <span class="hlt">Lagrangian</span> integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by <span class="hlt">Lagrangian</span> methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970001872','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970001872"><span>An Extended <span class="hlt">Lagrangian</span> Method</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Liou, Meng-Sing</p>
<p>1995-01-01</p>
<p>A unique <span class="hlt">formulation</span> of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method,' is interesting from both theoretical and numerical points of view. The <span class="hlt">formulation</span> offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. The present method and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations <span class="hlt">formulated</span> a priori. Unlike the <span class="hlt">Lagrangian</span> method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1993MsT.........23L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1993MsT.........23L"><span>A second-order shock-adaptive Godunov scheme based on the generalized <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lepage, Claude</p>
<p></p>
<p>Application of the Godunov scheme to the Euler equations of gas dynamics, based on the <span class="hlt">Eulerian</span> <span class="hlt">formulation</span> of flow, smears discontinuities (especially sliplines) over several computational cells, while the accuracy in the smooth flow regions is of the order of a function of the cell width. Based on the generalized <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> (GLF), the Godunov scheme yields far superior results. By the use of coordinate streamlines in the GLF, the slipline (itself a streamline) is resolved crisply. Infinite shock resolution is achieved through the splitting of shock cells, while the accuracy in the smooth flow regions is improved using a nonconservative <span class="hlt">formulation</span> of the governing equations coupled to a second order extension of the Godunov scheme. Furthermore, GLF requires no grid generation for boundary value problems and the simple structure of the solution to the Riemann problem in the GLF is exploited in the numerical implementation of the shock adaptive scheme. Numerical experiments reveal high efficiency and unprecedented resolution of shock and slipline discontinuities.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACPD...12.1267P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACPD...12.1267P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p>
<p>2012-01-01</p>
<p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015OcDyn..65..679R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015OcDyn..65..679R"><span>Comparison of HF radar measurements with <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> surface currents</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Röhrs, Johannes; Sperrevik, Ann Kristin; Christensen, Kai Håkon; Broström, Göran; Breivik, Øyvind</p>
<p>2015-05-01</p>
<p>High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. <span class="hlt">Eulerian</span> current measurements from a high-resolution acoustic Doppler current profiler and <span class="hlt">Lagrangian</span> measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the <span class="hlt">Eulerian</span> current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26456304','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26456304"><span>The Trapping Index: How to integrate the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approach for the computation of the transport time scales of semi-enclosed basins.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Cucco, Andrea; Umgiesser, Georg</p>
<p>2015-09-15</p>
<p>In this work, we investigated if the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an <span class="hlt">Eulerian</span> only or from a <span class="hlt">Lagrangian</span> only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CTM....16..435J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CTM....16..435J"><span>Comparisons of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Jaishree, J.; Haworth, D. C.</p>
<p>2012-06-01</p>
<p>Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, <span class="hlt">Lagrangian</span> particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, <span class="hlt">Lagrangian</span> particle PDF methods are computationally intensive and are not readily integrated into conventional <span class="hlt">Eulerian</span> computational fluid dynamics (CFD) codes. <span class="hlt">Eulerian</span> field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid <span class="hlt">Lagrangian</span> particle/<span class="hlt">Eulerian</span> mesh (LPEM) method, a stochastic <span class="hlt">Eulerian</span> field (SEF) method and a deterministic <span class="hlt">Eulerian</span> field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 <span class="hlt">Eulerian</span> fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930017014','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930017014"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Liou, Meng-Sing</p>
<p>1992-01-01</p>
<p>A unique <span class="hlt">formulation</span> of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The <span class="hlt">formulation</span> offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. Unlike the <span class="hlt">Lagrangian</span> method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950017213','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950017213"><span>A Generalized <span class="hlt">Eulerian-Lagrangian</span> Analysis, with Application to Liquid Flows with Vapor Bubbles</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Dejong, Frederik J.; Meyyappan, Meyya</p>
<p>1993-01-01</p>
<p>Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined <span class="hlt">Eulerian-Lagrangian</span> technique, in which <span class="hlt">Eulerian</span> conservation equations are solved for the liquid phase, while <span class="hlt">Lagrangian</span> equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the <span class="hlt">Lagrangian</span> analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S"><span>Insights into the physico-chemical evolution of pyrogenic organic carbon emissions from biomass burning using coupled <span class="hlt">Lagrangian-Eulerian</span> simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Suciu, L. G.; Griffin, R. J.; Masiello, C. A.</p>
<p>2017-12-01</p>
<p>Wildfires and prescribed burning are important sources of particulate and gaseous pyrogenic organic carbon (PyOC) emissions to the atmosphere. These emissions impact atmospheric chemistry, air quality and climate, but the spatial and temporal variabilities of these impacts are poorly understood, primarily because small and fresh fire plumes are not well predicted by three-dimensional <span class="hlt">Eulerian</span> chemical transport models due to their coarser grid size. Generally, this results in underestimation of downwind deposition of PyOC, hydroxyl radical reactivity, secondary organic aerosol formation and ozone (O3) production. However, such models are very good for simulation of multiple atmospheric processes that could affect the lifetimes of PyOC emissions over large spatiotemporal scales. Finer resolution models, such as <span class="hlt">Lagrangian</span> reactive plumes models (or plume-in-grid), could be used to trace fresh emissions at the sub-grid level of the <span class="hlt">Eulerian</span> model. Moreover, <span class="hlt">Lagrangian</span> plume models need background chemistry predicted by the <span class="hlt">Eulerian</span> models to accurately simulate the interactions of the plume material with the background air during plume aging. Therefore, by coupling the two models, the physico-chemical evolution of the biomass burning plumes can be tracked from local to regional scales. In this study, we focus on the physico-chemical changes of PyOC emissions from sub-grid to grid levels using an existing chemical mechanism. We hypothesize that finer scale <span class="hlt">Lagrangian-Eulerian</span> simulations of several prescribed burns in the U.S. will allow more accurate downwind predictions (validated by airborne observations from smoke plumes) of PyOC emissions (i.e., submicron particulate matter, organic aerosols, refractory black carbon) as well as O3 and other trace gases. Simulation results could be used to optimize the implementation of additional PyOC speciation in the existing chemical mechanism.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26754057','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26754057"><span>Modified Mixed <span class="hlt">Lagrangian-Eulerian</span> Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Suk, Heejun</p>
<p>2016-07-01</p>
<p>MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the <span class="hlt">Lagrangian</span> concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the <span class="hlt">Lagrangian</span> concentration on the Cauchy boundary. The proposed method combines the numerical <span class="hlt">formulations</span> of two different schemes, the finite element method (FEM) and the <span class="hlt">Eulerian-Lagrangian</span> method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M"><span>A cavitation model based on <span class="hlt">Eulerian</span> stochastic fields</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Magagnato, F.; Dumond, J.</p>
<p>2013-12-01</p>
<p>Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on <span class="hlt">Lagrangian</span> "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel <span class="hlt">formulation</span> called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.268..154K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.268..154K"><span>Compatible, total energy conserving and symmetry preserving arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in 2D rz - Cylindrical coordinates</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail</p>
<p>2014-07-01</p>
<p>We present a new discretization for 2D arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic <span class="hlt">Lagrangian</span> hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the <span class="hlt">Lagrangian</span> equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; <span class="hlt">formulated</span> for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for <span class="hlt">Lagrangian</span> equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary <span class="hlt">Lagrangian-Eulerian</span> algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JHEP...07..061G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JHEP...07..061G"><span>Parent <span class="hlt">formulation</span> at the <span class="hlt">Lagrangian</span> level</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Grigoriev, Maxim</p>
<p>2011-07-01</p>
<p>The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of <span class="hlt">Lagrangian</span> systems. It is shown that for diffeomorphism-invariant theories the parent <span class="hlt">formulation</span> takes the form of an AKSZ-type sigma model. The proposed <span class="hlt">formulation</span> can be also seen as a <span class="hlt">Lagrangian</span> version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV-BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang-Mills theory, and gravity.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JCoPh.229.8231C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JCoPh.229.8231C"><span>Differential geometry based solvation model I: <span class="hlt">Eulerian</span> <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p>
<p>2010-11-01</p>
<p>This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the surface energy into an <span class="hlt">Eulerian</span> <span class="hlt">formulation</span> so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2951687','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2951687"><span>Differential geometry based solvation model I: <span class="hlt">Eulerian</span> <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p>
<p>2010-01-01</p>
<p>This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the surface energy into an <span class="hlt">Eulerian</span> <span class="hlt">formulation</span> so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Liou, Meng-Sing</p>
<p>1993-01-01</p>
<p>A unique <span class="hlt">formulation</span> of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The <span class="hlt">formulation</span> offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015WRR....51.1916W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015WRR....51.1916W"><span>Variational <span class="hlt">Lagrangian</span> data assimilation in open channel networks</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.</p>
<p>2015-04-01</p>
<p>This article presents a data assimilation method in a tidal system, where data from both <span class="hlt">Lagrangian</span> drifters and <span class="hlt">Eulerian</span> flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be <span class="hlt">formulated</span> as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of <span class="hlt">Lagrangian</span> data, a time series of positions as the sensors moved through the water. Measurements were also taken from <span class="hlt">Eulerian</span> sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AtmEn.184..304D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AtmEn.184..304D"><span><span class="hlt">Eulerian-Lagrangian</span> CFD modelling of pesticide dust emissions from maize planters</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Devarrewaere, Wouter; Foqué, Dieter; Nicolai, Bart; Nuyttens, David; Verboven, Pieter</p>
<p>2018-07-01</p>
<p>An <span class="hlt">Eulerian-Lagrangian</span> 3D computational fluid dynamics (CFD) model of pesticide dust drift from precision vacuum planters in field conditions was developed. Tractor and planter models were positioned in an atmospheric computational domain, representing the field and its edges. Physicochemical properties of dust abraded from maize seeds (particle size, shape, porosity, density, a.i. content), dust emission rates and exhaust air velocity values at the planter fan outlets were measured experimentally and implemented in the model. The wind profile, the airflow pattern around the machines and the dust dispersion were computed. Various maize sowing scenarios with different wind conditions, dust properties, planter designs and vacuum pressures were simulated. Dust particle trajectories were calculated by means of <span class="hlt">Lagrangian</span> particle tracking, considering nonspherical particle drag, gravity and turbulent dispersion. The dust dispersion model was previously validated with wind tunnel data. In this study, simulated pesticide concentrations in the air and on the soil in the different sowing scenarios were compared and discussed. The model predictions were similar to experimental literature data in terms of concentrations and drift distance. Pesticide exposure levels to bees during flight and foraging were estimated from the simulated concentrations. The proposed CFD model can be used in risk assessment studies and in the evaluation of dust drift mitigation measures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..1818317B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1818317B"><span><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> description of bed-load particle kinematics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio</p>
<p>2016-04-01</p>
<p>The motion of bed-load sediment particles transported by a flow can be analyzed within a <span class="hlt">Lagrangian</span> or an <span class="hlt">Eulerian</span> framework. In the former case, we consider the particles as individual objects in motion and we study their kinematic properties. The latter approach is instead referred to suitably chosen control volumes. Quantities describing sediment motion in the two frameworks are different, and the relationships among the two approaches are not straightforward. In this work, we intend to discuss the kinematic properties of sediment transport: first, a set of quantities is univocally defined; then, relationships among different representations are explored. Proof-of-concept results presented in the study are from a recent experiment involving weak bed-load sediment transport, where the moving particles were released over a fixed rough bed. The bulk flow velocity was 1.4 times the critical value for incipient particle motion, and particles were mostly moving by rolling and sliding, with limited saltation. The particle motion was filmed from the top and the measurements were conducted by image-based methods, obtaining extensive samples of virtually-instantaneous quantities.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf','USGSPUBS'); return false;" href="http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf"><span>A three-dimensional finite-volume <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) for solute-transport modeling</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.</p>
<p>2000-01-01</p>
<p>This report documents the U.S. Geological Survey <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral <span class="hlt">formulation</span> of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit <span class="hlt">formulation</span>. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/12779582','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/12779582"><span><span class="hlt">Lagrangian</span> averages, averaged <span class="hlt">Lagrangians</span>, and the mean effects of fluctuations in fluid dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Holm, Darryl D.</p>
<p>2002-06-01</p>
<p>We begin by placing the generalized <span class="hlt">Lagrangian</span> mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged <span class="hlt">Lagrangian</span>. This is the <span class="hlt">Lagrangian</span> averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a <span class="hlt">Lagrangian</span> trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the <span class="hlt">Eulerian</span> mean fluid quantities by the fluctuating displacements of the <span class="hlt">Lagrangian</span> trajectories in terms of their <span class="hlt">Eulerian</span> second moments. The derivation of the glm equations uses the linearized relations between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> fluctuations, in the tradition of <span class="hlt">Lagrangian</span> stability analysis for fluids. The glm derivation also uses the method of averaged <span class="hlt">Lagrangians</span>, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the <span class="hlt">Lagrangian</span> statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for <span class="hlt">Lagrangian</span> averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164425','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164425"><span>On tide-induced <span class="hlt">Lagrangian</span> residual current and residual transport: 1. <span class="hlt">Lagrangian</span> residual current</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi</p>
<p>1986-01-01</p>
<p>Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a <span class="hlt">Lagrangian</span> mean velocity than an <span class="hlt">Eulerian</span> mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents. When k is small, the first-order <span class="hlt">Lagrangian</span> residual is shown to be the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes drift. The <span class="hlt">Lagrangian</span> residual drift velocity or the second-order <span class="hlt">Lagrangian</span> residual current has been shown to be dependent on the phase of tidal current. The <span class="hlt">Lagrangian</span> drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the <span class="hlt">Lagrangian</span> residual current.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD37005K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD37005K"><span>Investigation of erosion behavior in different pipe-fitting using <span class="hlt">Eulerian-Lagrangian</span> approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kulkarni, Harshwardhan; Khadamkar, Hrushikesh; Mathpati, Channamallikarjun</p>
<p>2017-11-01</p>
<p>Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled <span class="hlt">Eulerian-Lagrangian</span> approach is used to solve the liquid solid (water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50% open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number (10k, 25k, 50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of <span class="hlt">Lagrangian</span> library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/ED119999.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/ED119999.pdf"><span>The Case for Including <span class="hlt">Eulerian</span> Kinematics in Undergraduate Dynamics.</span></a></p>
<p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p>
<p>Uram, Earl M.</p>
<p></p>
<p>A <span class="hlt">Eulerian</span> framework is proposed as an alternative to the <span class="hlt">Lagrangian</span> framework usually used in undergraduate dynamics courses. An attempt to introduce <span class="hlt">Eulerian</span> kinematics into a dynamics course is discussed. (LMH)</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method for subsonic flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Liou, Meng-Sing; Loh, Ching Y.</p>
<p>1992-01-01</p>
<p>It is well known that fluid motion can be specified by either the <span class="hlt">Eulerian</span> of <span class="hlt">Lagrangian</span> description. Most of Computational Fluid Dynamics (CFD) developments over the last three decades have been based on the <span class="hlt">Eulerian</span> description and considerable progress has been made. In particular, the upwind methods, inspired and guided by the work of Gudonov, have met with many successes in dealing with complex flows, especially where discontinuities exist. However, this shock capturing property has proven to be accurate only when the discontinuity is aligned with one of the grid lines since most upwind methods are strictly <span class="hlt">formulated</span> in 1-D framework and only formally extended to multi-dimensions. Consequently, the attractive property of crisp resolution of these discontinuities is lost and research on genuine multi-dimensional approach has just been undertaken by several leading researchers. Nevertheless they are still based on the <span class="hlt">Eulerian</span> description.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MMTB...48.1248L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MMTB...48.1248L"><span>Modeling of Quasi-Four-Phase Flow in Continuous Casting Mold Using Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan</p>
<p>2017-04-01</p>
<p><span class="hlt">Lagrangian</span> tracking model combined with <span class="hlt">Eulerian</span> multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The <span class="hlt">Eulerian</span> approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the <span class="hlt">Lagrangian</span> way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/ h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/ h is larger than 0.4.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JGRC..122.5445S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGRC..122.5445S"><span>Impact of data assimilation on <span class="hlt">Eulerian</span> versus <span class="hlt">Lagrangian</span> estimates of upper ocean transport</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sperrevik, Ann Kristin; Röhrs, Johannes; Christensen, Kai Hâkon</p>
<p>2017-07-01</p>
<p>Using four-dimensional variational analysis, we produce an estimate of the state of a coastal region in Northern Norway during the late winter and spring in 1984. We use satellite sea surface temperature and in situ observations from a series of intensive field campaigns, and obtain a more realistic distribution of water masses both in the horizontal and the vertical than a pure downscaling approach can achieve. Although the distribution of <span class="hlt">Eulerian</span> surface current speeds are similar, we find that they are more variable and less dependent on model bathymetry in our reanalysis compared to a hindcast produced using the same modeling system. <span class="hlt">Lagrangian</span> drift currents on the other hand are significantly changed, with overall higher kinetic energy levels in the reanalysis than in the hindcast, particularly in the superinertial frequency band.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvD..97h4048D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvD..97h4048D"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the general relativistic Poynting-Robertson effect</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio</p>
<p>2018-04-01</p>
<p>We propose the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDA37008R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDA37008R"><span>GPU acceleration of <span class="hlt">Eulerian-Lagrangian</span> particle-laden turbulent flow simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Richter, David; Sweet, James; Thain, Douglas</p>
<p>2017-11-01</p>
<p>The <span class="hlt">Lagrangian</span> point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the <span class="hlt">Eulerian</span> flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian"><span>The piecewise-linear predictor-corrector code - A <span class="hlt">Lagrangian</span>-remap method for astrophysical flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Lufkin, Eric A.; Hawley, John F.</p>
<p>1993-01-01</p>
<p>We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing <span class="hlt">Eulerian</span> schemes in its use of operator-splitting and artificial viscosity, except that we solve the <span class="hlt">Lagrangian</span> equations of motion with a predictor-corrector and then remap onto a fixed <span class="hlt">Eulerian</span> grid. The remap is <span class="hlt">formulated</span> to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector <span class="hlt">Lagrangian</span>-remap code has great flexibility for application to a variety of astrophysical problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130010995','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130010995"><span>Ice Accretion Modeling using an <span class="hlt">Eulerian</span> Approach for Droplet Impingement</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.</p>
<p>2012-01-01</p>
<p>A three-dimensional <span class="hlt">Eulerian</span> analysis has been developed for modeling droplet impingement on lifting bodes. The <span class="hlt">Eulerian</span> model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the <span class="hlt">Eulerian</span> approach is more efficient because the <span class="hlt">Lagrangian</span> approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the <span class="hlt">Lagrangian</span> approach used in an industry standard analysis called LEWICE.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F"><span>Wake modeling in complex terrain using a hybrid <span class="hlt">Eulerian-Lagrangian</span> Split Solver</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind</p>
<p>2016-09-01</p>
<p>Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid <span class="hlt">Eulerian</span>- <span class="hlt">Lagrangian</span> approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19029589','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19029589"><span>Simulation of atmospheric dispersion of radionuclides using an <span class="hlt">Eulerian-Lagrangian</span> modelling system.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N</p>
<p>2008-12-01</p>
<p>In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a <span class="hlt">Lagrangian</span> stochastic particle model (LSPM) coupled with an <span class="hlt">Eulerian</span> regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a <span class="hlt">Lagrangian</span> stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Wolfram, Phillip J.; Ringler, Todd D.</p>
<p>2017-08-14</p>
<p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1412853','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1412853"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wolfram, Phillip J.; Ringler, Todd D.</p>
<p></p>
<p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26317686','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26317686"><span>Particle transport in the human respiratory tract: <span class="hlt">formulation</span> of a nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> transport and implementation of the Wind-Kessel algorithm for an oral delivery.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kannan, Ravishekar; Guo, Peng; Przekwas, Andrzej</p>
<p>2016-06-01</p>
<p>This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational finite volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's finite volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> <span class="hlt">formulation</span> to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a finite number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes"><span>A point-centered arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> hydrodynamic approach for tetrahedral meshes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...</p>
<p>2015-02-24</p>
<p>We present a three dimensional (3D) arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D"><span>Bayesian <span class="hlt">Lagrangian</span> Data Assimilation and Drifter Deployment Strategies</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Dutt, A.; Lermusiaux, P. F. J.</p>
<p>2017-12-01</p>
<p>Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). <span class="hlt">Lagrangian</span> Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such <span class="hlt">Lagrangian</span> transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint <span class="hlt">Eulerian-Lagrangian</span> Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of <span class="hlt">Eulerian</span> variables (e.g. velocity, temperature, salinity, etc.) and <span class="hlt">Lagrangian</span> variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017BoLMe.165..251D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017BoLMe.165..251D"><span>Water-Channel Estimation of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio</p>
<p>2017-11-01</p>
<p><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the <span class="hlt">Eulerian</span> (TE) and <span class="hlt">Lagrangian</span> (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width ( W) to the height ( H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the <span class="hlt">Eulerian</span> time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the <span class="hlt">Lagrangian</span> time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2) and also for T_u^L when AR = 1. In contrast, for AR = 2, T_u^L follows Raupach's law only above z=2H. Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1. It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H, irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0). It is</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M"><span>An <span class="hlt">Eulerian-Lagrangian</span> description for fluvial coarse sediment transport: theory and verification with low-cost inertial sensors.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Maniatis, Georgios</p>
<p>2017-04-01</p>
<p>Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (<span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span>) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general <span class="hlt">Eulerian-Lagrangian</span> (E-L) model. This approach accounts for inertial characteristics of particles in a <span class="hlt">Lagrangian</span> (particle fixed) frame, and for the hydrodynamics in an independent <span class="hlt">Eulerian</span> frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDG18003H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDG18003H"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for vortex tracking in 2D and 3D flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Huang, Yangzi; Green, Melissa</p>
<p>2014-11-01</p>
<p>Coherent structures are a key component of unsteady flows in shear layers. Improvement of experimental techniques has led to larger amounts of data and requires of automated procedures for vortex tracking. Many vortex criteria are <span class="hlt">Eulerian</span>, and identify the structures by an instantaneous local swirling motion in the field, which are indicated by closed or spiral streamlines or pathlines in a reference frame. Alternatively, a <span class="hlt">Lagrangian</span> Coherent Structures (LCS) analysis is a <span class="hlt">Lagrangian</span> method based on the quantities calculated along fluid particle trajectories. In the current work, vortex detection is demonstrated on data from the simulation of two cases: a 2D flow with a flat plate undergoing a 45 ° pitch-up maneuver and a 3D wall-bounded turbulence channel flow. Vortices are visualized and tracked by their centers and boundaries using Γ1, the Q criterion, and LCS saddle points. In the cases of 2D flow, saddle points trace showed a rapid acceleration of the structure which indicates the shedding from the plate. For channel flow, saddle points trace shows that average structure convection speed exhibits a similar trend as a function of wall-normal distance as the mean velocity profile, and leads to statistical quantities of vortex dynamics. Dr. Jeff Eldredge and his research group at UCLA are gratefully acknowledged for sharing the database of simulation for the current research. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1429778-arbitrary-lagrangianeulerian-finite-element-formulation-poroelasticity-problem-stemming-from-mixture-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1429778-arbitrary-lagrangianeulerian-finite-element-formulation-poroelasticity-problem-stemming-from-mixture-theory"><span>An arbitrary Lagrangian–<span class="hlt">Eulerian</span> finite element <span class="hlt">formulation</span> for a poroelasticity problem stemming from mixture theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Costanzo, Francesco; Miller, Scott T.</p>
<p>2017-05-22</p>
<p>In this paper, a finite element <span class="hlt">formulation</span> is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The <span class="hlt">formulation</span> is based on the adoption of an arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the <span class="hlt">formulation</span> is discussed, and numerical results demonstrate agreement with the theory.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1429778','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1429778"><span>An arbitrary Lagrangian–<span class="hlt">Eulerian</span> finite element <span class="hlt">formulation</span> for a poroelasticity problem stemming from mixture theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Costanzo, Francesco; Miller, Scott T.</p>
<p></p>
<p>In this paper, a finite element <span class="hlt">formulation</span> is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The <span class="hlt">formulation</span> is based on the adoption of an arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the <span class="hlt">formulation</span> is discussed, and numerical results demonstrate agreement with the theory.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDM31008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDM31008C"><span>Evaluation of particle-based flow characteristics using novel <span class="hlt">Eulerian</span> indices</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cho, Youngmoon; Kang, Seongwon</p>
<p>2017-11-01</p>
<p>The main objective of this study is to evaluate flow characteristics in complex particle-laden flows efficiently using novel <span class="hlt">Eulerian</span> indices. For flows with a large number of particles, a <span class="hlt">Lagrangian</span> approach leads to accurate yet inefficient prediction in many engineering problems. We propose a technique based on <span class="hlt">Eulerian</span> transport equation and ensemble-averaged particle properties, which enables efficient evaluation of various particle-based flow characteristics such as the residence time, accumulated travel distance, mean radial force, etc. As a verification study, we compare the developed <span class="hlt">Eulerian</span> indices with those using <span class="hlt">Lagrangian</span> approaches for laminar flows with and without a swirling motion and density ratio. The results show satisfactory agreement between two approaches. The accumulated travel distance is modified to analyze flow motions inside IC engines and, when applied to flow bench cases, it can predict swirling and tumbling motions successfully. For flows inside a cyclone separator, the mean radial force is applied to predict the separation of particles and is shown to have a high correlation to the separation efficiency for various working conditions. In conclusion, the proposed <span class="hlt">Eulerian</span> indices are shown to be useful tools to analyze complex particle-based flow characteristics. Corresponding author.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/5455999-lagrangian-formulation-penny-shaped-perkins-kern-geometry-models','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/5455999-lagrangian-formulation-penny-shaped-perkins-kern-geometry-models"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for penny-shaped and Perkins-Kern geometry models</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Lee, W.S.</p>
<p>1989-09-01</p>
<p>This paper discusses basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models developed with a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> combined with a virtual-work analysis. The <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> yields a pair of nonlinear equations in R/sub f/ or L/sub f/ and b/sub f/, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved numerically. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, canmore » be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28989316','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28989316"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Cotter, C J; Gottwald, G A; Holm, D D</p>
<p>2017-09-01</p>
<p>In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>A new <span class="hlt">Lagrangian</span> random choice method for steady two-dimensional supersonic/hypersonic flow</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Loh, C. Y.; Hui, W. H.</p>
<p>1991-01-01</p>
<p>Glimm's (1965) random choice method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>. The method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing <span class="hlt">Eulerian</span> methods. Many computed examples are given.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018GMD....11..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018GMD....11..103G"><span><span class="hlt">Lagrangian</span> condensation microphysics with Twomey CCN activation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna</p>
<p>2018-01-01</p>
<p>We report the development of a novel <span class="hlt">Lagrangian</span> microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional <span class="hlt">Eulerian</span> method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses <span class="hlt">Lagrangian</span> <q>super-droplets</q> to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the <span class="hlt">Lagrangian</span> warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in <span class="hlt">Eulerian</span> bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other <span class="hlt">formulation</span> of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A"><span>Compressibility Effects on Particle-Fluid Interaction Force for <span class="hlt">Eulerian-Eulerian</span> Simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Akiki, Georges; Francois, Marianne; Zhang, Duan</p>
<p>2017-11-01</p>
<p>Particle-fluid interaction forces are essential in modeling multiphase flows. Several models can be found in the literature based on empirical, numerical, and experimental results from various simplified flow conditions. Some of these models also account for finite Mach number effects. Using these models is relatively straightforward with <span class="hlt">Eulerian-Lagrangian</span> calculations if the model for the total force on particles is used. In <span class="hlt">Eulerian-Eulerian</span> simulations, however, there is the pressure gradient terms in the momentum equation for particles. For low Mach number flows, the pressure gradient force is negligible if the particle density is much greater than that of the fluid. For supersonic flows where a standing shock is present, even for a steady and uniform flow, it is unclear whether the significant pressure-gradient force should to be separated out from the particle force model. To answer this conceptual question, we perform single-sphere fully-resolved DNS simulations for a wide range of Mach numbers. We then examine whether the total force obtained from the DNS can be categorized into well-established models, such as the quasi-steady, added-mass, pressure-gradient, and history forces. Work sponsored by Advanced Simulation and Computing (ASC) program of NNSA and LDRD-CNLS of LANL.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A"><span>Chaos in an <span class="hlt">Eulerian</span> Based Model of Sickle Cell Blood Flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Apori, Akwasi; Harris, Wesley</p>
<p>2001-11-01</p>
<p>A novel <span class="hlt">Eulerian</span> model describing the manifestation of sickle cell blood flow in the capillaries has been <span class="hlt">formulated</span> to study the apparently chaotic onset of sickle cell crises. This <span class="hlt">Eulerian</span> model was based on extending previous models of sickle cell blood flow which were limited due to their <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Cotter, C. J.</p>
<p>2017-01-01</p>
<p>In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo; ...</p>
<p>2017-09-01</p>
<p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo</p>
<p></p>
<p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p>
</li>
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<ol class="result-class" start="121">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910001565','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910001565"><span>A combined <span class="hlt">Eulerian-Lagrangian</span> two-phase analysis of the SSME HPOTP nozzle plug trajectories</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Garcia, Robert; Mcconnaughey, P. K.; Dejong, F. J.; Sabnis, J. S.; Pribik, D.</p>
<p>1989-01-01</p>
<p>As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs <span class="hlt">Lagrangian</span> tracking of the particle through the <span class="hlt">Eulerian</span> flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T"><span>Modeling possible spreadings of a buoyant surface plume with <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> approaches at different resolutions using flow syntheses from 1992-2007 - a Gulf of Mexico study</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tulloch, R.; Hill, C. N.; Jahn, O.</p>
<p>2010-12-01</p>
<p>We present results from an ensemble of BP oil spill simulations. The oil spill slick is modeled as a buoyant surface plume that is transported by ocean currents modulated, in some experiments, by surface winds. Ocean currents are taken from ECCO2 project (see http://ecco2.org ) observationally constrained state estimates spanning 1992-2007. In this work we (i) explore the role of increased resolution of ocean eddies, (ii) compare inferences from particle based, <span class="hlt">lagrangian</span>, approaches with <span class="hlt">eulerian</span>, field based, approaches and (ii) examine the impact of differential response of oil particles and water to normal and extreme, hurricane derived, wind stress. We focus on three main questions. Is the simulated response to an oil spill markedly different for different years, depending on ocean circulation and wind forcing? Does the simulated response depend heavily on resolution and are <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> estimates comparable? We start from two regional configurations of the MIT General Circulation Model (MITgcm - see http://mitgcm.org ) at 16km and 4km resolutions respectively, both covering the Gulf of Mexico and western North Atlantic regions. The simulations are driven at open boundaries with momentum and hydrographic fields from ECCO2 observationally constrained global circulation estimates. The time dependent surface flow fields from these simulations are used to transport a dye that can optionally decay over time (approximating biological breakdown) and to transport <span class="hlt">lagrangian</span> particles. Using these experiments we examine the robustness of conclusions regarding the fate of a buoyant slick, injected at a single point. In conclusion we discuss how future drilling operations could use similar approaches to better anticipate outcomes of accidents both in this region and elsewhere.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGRC..123..759C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGRC..123..759C"><span>Nitrate Sources, Supply, and Phytoplankton Growth in the Great Australian Bight: An <span class="hlt">Eulerian-Lagrangian</span> Modeling Approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cetina-Heredia, Paulina; van Sebille, Erik; Matear, Richard J.; Roughan, Moninya</p>
<p>2018-02-01</p>
<p>The Great Australian Bight (GAB), a coastal sea bordered by the Pacific, Southern, and Indian Oceans, sustains one of the largest fisheries in Australia but the geographical origin of nutrients that maintain its productivity is not fully known. We use 12 years of modeled data from a coupled hydrodynamic and biogeochemical model and an <span class="hlt">Eulerian-Lagrangian</span> approach to quantify nitrate supply to the GAB and the region between the GAB and the Subantarctic Australian Front (GAB-SAFn), identify phytoplankton growth within the GAB, and ascertain the source of nitrate that fuels it. We find that nitrate concentrations have a decorrelation timescale of ˜60 days; since most of the water from surrounding oceans takes longer than 60 days to reach the GAB, 23% and 75% of nitrate used by phytoplankton to grow are sourced within the GAB and from the GAB-SAFn, respectively. Thus, most of the nitrate is recycled locally. Although nitrate concentrations and fluxes into the GAB are greater below 100 m than above, 79% of the nitrate fueling phytoplankton growth is sourced from above 100 m. Our findings suggest that topographical uplift and stratification erosion are key mechanisms delivering nutrients from below the nutricline into the euphotic zone and triggering large phytoplankton growth. We find annual and semiannual periodicities in phytoplankton growth, peaking in the austral spring and autumn when the mixed layer deepens leading to a subsurface maximum of phytoplankton growth. This study highlights the importance of examining phytoplankton growth at depth and the utility of <span class="hlt">Lagrangian</span> approaches.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AtmEn..45..839O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AtmEn..45..839O"><span>Development and evaluation of GRAL-C dispersion model, a hybrid <span class="hlt">Eulerian-Lagrangian</span> approach capturing NO-NO 2-O 3 chemistry</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Oettl, Dietmar; Uhrner, Ulrich</p>
<p>2011-02-01</p>
<p>Based on two recent publications using <span class="hlt">Lagrangian</span> dispersion models to simulate NO-NO 2-O 3 chemistry for industrial plumes, a similar modified approach was implemented using GRAL-C ( Graz <span class="hlt">Lagrangian</span> Model with Chemistry) and tested on two urban applications. In the hybrid dispersion model GRAL-C, the transport and turbulent diffusion of primary species such as NO and NO 2 are treated in a <span class="hlt">Lagrangian</span> framework while those of O 3 are treated in an <span class="hlt">Eulerian</span> framework. GRAL-C was employed on a one year street canyon simulation in Berlin and on a four-day simulation during a winter season in Graz, the second biggest city in Austria. In contrast to Middleton D.R., Jones A.R., Redington A.L., Thomson D.J., Sokhi R.S., Luhana L., Fisher B.E.A. (2008. <span class="hlt">Lagrangian</span> modelling of plume chemistry for secondary pollutants in large industrial plumes. Atmospheric Environment 42, 415-427) and Alessandrini S., Ferrero E. (2008. A <span class="hlt">Lagrangian</span> model with chemical reactions: application in real atmosphere. Proceedings of the 12th Int. Conf. on Harmonization within atmospheric dispersion modelling for regulatory purposes. Croatian Meteorological Journal, 43, ISSN: 1330-0083, 235-239) the treatment of ozone was modified in order to facilitate urban scale simulations encompassing dense road networks. For the street canyon application, modelled daily mean NO x/NO 2 concentrations deviated by +0.4%/-15% from observations, while the correlations for NO x and NO 2 were 0.67 and 0.76 respectively. NO 2 concentrations were underestimated in summer, but were captured well for other seasons. In Graz a fair agreement for NO x and NO 2 was obtained between observed and modelled values for NO x and NO 2. Simulated diurnal cycles of NO 2 and O 3 matched observations reasonably well, although O 3 was underestimated during the day. A possible explanation here might lie in the non-consideration of volatile organic compounds (VOCs) chemistry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/934850','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/934850"><span><span class="hlt">Lagrangian</span> continuum dynamics in ALEGRA.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wong, Michael K. W.; Love, Edward</p>
<p></p>
<p>Alegra is an ALE (Arbitrary <span class="hlt">Lagrangian-Eulerian</span>) multi-material finite element code that emphasizes large deformations and strong shock physics. The <span class="hlt">Lagrangian</span> continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CompM..51..865C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CompM..51..865C"><span>A two-field modified <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for robust simulations of extrinsic cohesive zone models</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cazes, F.; Coret, M.; Combescure, A.</p>
<p>2013-06-01</p>
<p>This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field <span class="hlt">Lagrangian</span> weak <span class="hlt">formulation</span> in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this <span class="hlt">formulation</span> cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed <span class="hlt">formulations</span> to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal"><span><span class="hlt">Lagrangian</span> or <span class="hlt">Eulerian</span>; real or Fourier? Not all approaches to large-scale structure are created equal</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Tassev, Svetlin, E-mail: tassev@astro.princeton.edu</p>
<p></p>
<p>We present a pedagogical systematic investigation of the accuracy of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theorymore » to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by <span class="hlt">Eulerian</span> Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1911392T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1911392T"><span>Mass and tracer transport within oceanic <span class="hlt">Lagrangian</span> coherent vortices as diagnosed in a global mesoscale eddying climate model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tarshish, Nathaniel; Abernathey, Ryan; Dufour, Carolina; Frenger, Ivy; Griffies, Stephen</p>
<p>2017-04-01</p>
<p>Transient ocean mesoscale fluctuations play a central role in the global climate system, transporting climate relevant tracers such as heat and carbon. In satellite observations and numerical simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on <span class="hlt">Eulerian</span> identification methods, in which vortices are identified by selecting closed contours of <span class="hlt">Eulerian</span> fields (e.g. sea surface height, or the Okubo-Weiss parameter) that satisfy geometric criteria and anomaly thresholds. In contrast, recent studies employ <span class="hlt">Lagrangian</span> analysis of virtual particle trajectories initialized within the selected <span class="hlt">Eulerian</span> contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the <span class="hlt">Eulerian</span> field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> analyses for the detection of vortices. To do so, we use GFDL's CM2.6 coupled climate model with 5-10km horizontal grid spacing. We identify coherent vortices in CM2.6 by implementing the Rotationally Coherent <span class="hlt">Lagrangian</span> Vortex (RCLV) framework, which recently emerged from dynamical systems theory. This approach involves the numerical advection of millions of <span class="hlt">Lagrangian</span> particles and guarantees material coherence by construction. We compute the statistics, spatial distribution, and lifetimes of coherent vortices in addition to calculating the associated mass and tracer transports. We offer compelling evidence that <span class="hlt">Eulerian</span> vortex methods are poorly suited to answer questions of mass and tracer transport.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1413605S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1413605S"><span>An online-coupled NWP/ACT model with conserved <span class="hlt">Lagrangian</span> levels</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sørensen, B.; Kaas, E.; Lauritzen, P. H.</p>
<p>2012-04-01</p>
<p>Numerical weather and climate modelling is under constant development. Semi-implicit semi-<span class="hlt">Lagrangian</span> (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-<span class="hlt">Lagrangian</span> schemes with quasi-<span class="hlt">Lagrangian</span> vertical coordinates the <span class="hlt">Lagrangian</span> levels are remapped to <span class="hlt">Eulerian</span> model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-<span class="hlt">Lagrangian</span> advection method is introduced, it combines an inherently mass conserving 2D semi-<span class="hlt">Lagrangian</span> scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully <span class="hlt">Lagrangian</span> vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the <span class="hlt">Lagrangian</span> levels suffer from traditional <span class="hlt">Lagrangian</span> limitations caused by the convergence and divergence of the flow, remappings to the <span class="hlt">Eulerian</span> model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AtmEn.170....1P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AtmEn.170....1P"><span>Improved quantification of CO2 emission at Campi Flegrei by combined <span class="hlt">Lagrangian</span> Stochastic and <span class="hlt">Eulerian</span> dispersion modelling</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pedone, Maria; Granieri, Domenico; Moretti, Roberto; Fedele, Alessandro; Troise, Claudia; Somma, Renato; De Natale, Giuseppe</p>
<p>2017-12-01</p>
<p>This study investigates fumarolic CO2 emissions at Campi Flegrei (Southern Italy) and their dispersion in the lowest atmospheric boundary layer. We innovatively utilize a <span class="hlt">Lagrangian</span> Stochastic dispersion model (WindTrax) combined with an <span class="hlt">Eulerian</span> model (DISGAS) to diagnose the dispersion of diluted gas plumes over large and complex topographic domains. New measurements of CO2 concentrations acquired in February and October 2014 in the area of Pisciarelli and Solfatara, the two major fumarolic fields of Campi Flegrei caldera, and simultaneous measurements of meteorological parameters are used to: 1) test the ability of WindTrax to calculate the fumarolic CO2 flux from the investigated sources, and 2) perform predictive numerical simulations to resolve the mutual interference between the CO2 emissions of the two adjacent areas. This novel approach allows us to a) better quantify the CO2 emission of the fumarolic source, b) discriminate ;true; CO2 contributions for each source, and c) understand the potential impact of the composite CO2 plume (Pisciarelli ;plus; Solfatara) on the highly populated areas inside the Campi Flegrei caldera.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770023699','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770023699"><span>Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an <span class="hlt">Eulerian-Lagrangian</span> marker particle technique</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Pavish, D. L.; Spaulding, M. L.</p>
<p>1977-01-01</p>
<p>A computer coded <span class="hlt">Lagrangian</span> marker particle in <span class="hlt">Eulerian</span> finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013698','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013698"><span>Near-Surface Monsoonal Circulation of the Vietnam East Sea from <span class="hlt">Lagrangian</span> Drifters</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2015-09-30</p>
<p>Sea from <span class="hlt">Lagrangian</span> Drifters Luca Centurioni Scripps Institution of Oceanography 9500 Gilman Drive Mail Code 0213 La Jolla, California 92103...Contribute to the study of coastal and open ocean current systems in sparsely sampled regions such us the South China Sea (SCS), using a <span class="hlt">Lagrangian</span> ...We intend to make new <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> observations to measure the seasonal circulation 1) in the coastal waters of Vietnam and 2) in the SCS</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70016855','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70016855"><span>Solution of the advection-dispersion equation by a finite-volume <span class="hlt">eulerian-lagrangian</span> local adjoint method</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Healy, R.W.; Russell, T.F.</p>
<p>1992-01-01</p>
<p>A finite-volume <span class="hlt">Eulerian-Lagrangian</span> local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016Chaos..26j3102H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016Chaos..26j3102H"><span>Level set <span class="hlt">formulation</span> of two-dimensional <span class="hlt">Lagrangian</span> vortex detection methods</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Hadjighasem, Alireza; Haller, George</p>
<p>2016-10-01</p>
<p>We propose here the use of the variational level set methodology to capture <span class="hlt">Lagrangian</span> vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches that seek material vortex boundaries as extremum solutions of variational problems. We demonstrate the performance of this technique for two different variational <span class="hlt">formulations</span> built upon different notions of coherence. The first <span class="hlt">formulation</span> uses an energy functional that penalizes the deviation of a closed material line from piecewise uniform stretching [Haller and Beron-Vera, J. Fluid Mech. 731, R4 (2013)]. The second energy function is derived for a graph-based approach to vortex boundary detection [Hadjighasem et al., Phys. Rev. E 93, 063107 (2016)]. Our level-set <span class="hlt">formulation</span> captures an a priori unknown number of vortices simultaneously at relatively low computational cost. We illustrate the approach by identifying vortices from different coherence principles in several examples.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003STIN...0316602M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003STIN...0316602M"><span>Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Melis, Matthew E.</p>
<p>2003-01-01</p>
<p>Explicit finite element techniques employing an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030016601','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030016601"><span>Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary <span class="hlt">Lagrangian-eulerian</span> Approach</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Melis, Matthew E.</p>
<p>2003-01-01</p>
<p>Explicit finite element techniques employing an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G"><span>Well-balanced Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael</p>
<p>2018-06-01</p>
<p>In this work, we present a novel second-order accurate well-balanced arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have <span class="hlt">formulated</span> a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.346..449B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.346..449B"><span>Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Boscheri, Walter; Dumbser, Michael</p>
<p>2017-10-01</p>
<p>We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) schemes, where a space-time conservation <span class="hlt">formulation</span> of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhFl...28f1901S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28f1901S"><span>An unstructured mesh arbitrary <span class="hlt">Lagrangian-Eulerian</span> unsteady incompressible flow solver and its application to insect flight aerodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Su, Xiaohui; Cao, Yuanwei; Zhao, Yong</p>
<p>2016-06-01</p>
<p>In this paper, an unstructured mesh Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CompM..50..805L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CompM..50..805L"><span>A coupled PFEM-<span class="hlt">Eulerian</span> approach for the solution of porous FSI problems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Larese, A.; Rossi, R.; Oñate, E.; Idelsohn, S. R.</p>
<p>2012-12-01</p>
<p>This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a <span class="hlt">Lagrangian</span> model for the structural behavior and an <span class="hlt">Eulerian</span> approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an <span class="hlt">Eulerian</span> fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.</p>
</li>
</ol>
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<ol class="result-class" start="141">
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. II - The spinning sphere</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Van Dommelen, Leon L.</p>
<p>1990-01-01</p>
<p>A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A <span class="hlt">Lagrangian</span> numerical scheme is developed which gives results in good agreement with <span class="hlt">Eulerian</span> computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the <span class="hlt">Eulerian</span> structure, including the presence of logarithmic terms. Further, while the <span class="hlt">Eulerian</span> computations broke down at the first occurrence of separation, it is found that the <span class="hlt">Lagrangian</span> computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.275..484B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.275..484B"><span>A direct Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Boscheri, Walter; Dumbser, Michael</p>
<p>2014-10-01</p>
<p>In this paper we present a new family of high order accurate Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final <span class="hlt">Lagrangian</span> finite volume scheme is based directly on a space-time conservation <span class="hlt">formulation</span> of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26753780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26753780"><span>Geometric effects in microfluidics on heterogeneous cell stress using an <span class="hlt">Eulerian-Lagrangian</span> approach.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F</p>
<p>2016-02-07</p>
<p>The response of individual cells at the micro-scale in cell mechanics is important in understanding how they are affected by changing environments. To control cell stresses, microfluidics can be implemented since there is tremendous control over the geometry of the devices. Designing microfluidic devices to induce and manipulate stress levels on biological cells can be aided by computational modeling approaches. Such approaches serve as an efficient precursor to fabricating various microfluidic geometries that induce predictable levels of stress on biological cells, based on their mechanical properties. Here, a three-dimensional, multiphase computational fluid dynamics (CFD) modeling approach was implemented for soft biological materials. The computational model incorporates the physics of the particle dynamics, fluid dynamics and solid mechanics, which allows us to study how stresses affect the cells. By using an <span class="hlt">Eulerian-Lagrangian</span> approach to treat the fluid domain as a continuum in the microfluidics, we are conducting studies of the cells' movement and the stresses applied to the cell. As a result of our studies, we were able to determine that a channel with periodically alternating columns of obstacles was capable of stressing cells at the highest rate, and that microfluidic systems can be engineered to impose heterogenous cell stresses through geometric configuring. We found that when using controlled geometries of the microfluidics channels with staggered obstructions, we could increase the maximum cell stress by nearly 200 times over cells flowing through microfluidic channels with no obstructions. Incorporating computational modeling in the design of microfluidic configurations for controllable cell stressing could help in the design of microfludic devices for stressing cells such as cell homogenizers.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C"><span>On modeling heterogeneous coastal sediment transport - A numerical study using multiphase <span class="hlt">Eulerian</span> and Euler-<span class="hlt">Lagrangian</span> approaches</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cheng, Z.; Yu, X.; Hsu, T. J.; Calantoni, J.; Chauchat, J.</p>
<p>2016-02-01</p>
<p>Regional scale coastal evolution models do not explicitly resolve wave-driven sediment transport and must rely on bedload/suspended modules that utilize empirical assumptions. Under extreme wave events or in regions of high sediment heterogeneity, these empirical bedload/suspended load modules may need to be reevaluated with detailed observation and more sophisticated small-scale models. In the past decade, significant research efforts have been devoted to modeling sediment transport using multiphase <span class="hlt">Eulerian</span> or Euler-<span class="hlt">Lagrangian</span> approaches. Recently, an open-source multi-dimensional Reynolds-averaged two-phase sediment transport model, SedFOAM is developed by the authors and it has been adopted by many researchers to study momentary bed failure, granular rheology in sheet flow and scour around structures. In this abstract, we further report our recent progress made in extending the model with 3D turbulence-resolving capability and to model the sediment phase with the Discrete Element method (DEM). Adopting the large-eddy simulation methodology, we validate the 3D model with measured fine sediment transport is oscillatory sheet flow and demonstrate that the model is able to resolve sediment burst events during flow reversals. To better resolve the intergranular interactions and to model heterogeneous properties of sediment (e.g., mixed grain sizes and grain shape), we use an Euler-<span class="hlt">Lagrangian</span> solver called CFDEM, which couples OpenFOAM for the fluid phase and LIGGGHTS for the particle phase. We improve the model by better enforcing conservation of mass in the pressure solver. The modified CFDEM solver is validated with measured oscillatory sheet flow data for coarse sand and we demonstrated that the model can reproduce the well-known armoring effects. We show that under Stokes second-order wave forcing, the armoring effect is more significant during the energetic positive peak, and hence the net onshore transport is reduced. Preliminary results modeling the shape</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25127407','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25127407"><span>Dynamic analysis of a needle insertion for soft materials: Arbitrary <span class="hlt">Lagrangian-Eulerian</span>-based three-dimensional finite element analysis.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Yamaguchi, Satoshi; Tsutsui, Kihei; Satake, Koji; Morikawa, Shigehiro; Shirai, Yoshiaki; Tanaka, Hiromi T</p>
<p>2014-10-01</p>
<p>Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030052220','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030052220"><span>A Vertically <span class="hlt">Lagrangian</span> Finite-Volume Dynamical Core for Global Models</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Lin, Shian-Jiann</p>
<p>2003-01-01</p>
<p>A finite-volume dynamical core with a terrain-following <span class="hlt">Lagrangian</span> control-volume discretization is described. The vertically <span class="hlt">Lagrangian</span> discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-<span class="hlt">Lagrangian</span>-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-<span class="hlt">Lagrangian</span> algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the <span class="hlt">Lagrangian</span> dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating <span class="hlt">Lagrangian</span> control-volume to an <span class="hlt">Eulerian</span> terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the <span class="hlt">Lagrangian</span> surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014ACP....14.5477H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014ACP....14.5477H"><span>Technical Note: Adjoint <span class="hlt">formulation</span> of the TOMCAT atmospheric transport scheme in the <span class="hlt">Eulerian</span> backtracking framework (RETRO-TOM)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Haines, P. E.; Esler, J. G.; Carver, G. D.</p>
<p>2014-06-01</p>
<p>A new methodology for the <span class="hlt">formulation</span> of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM. The <span class="hlt">Eulerian</span> backtracking method is used, allowing the forward advection scheme (Prather's second-order moments) to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time symmetric, suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" <span class="hlt">formulation</span> with the accuracy of an "adjoint of finite difference" <span class="hlt">formulation</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014ACPD...14.1481H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014ACPD...14.1481H"><span>Technical Note: Adjoint <span class="hlt">formulation</span> of the TOMCAT atmospheric transport scheme in the <span class="hlt">Eulerian</span> backtracking framework (RETRO-TOM)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Haines, P. E.; Esler, J. G.; Carver, G. D.</p>
<p>2014-01-01</p>
<p>A new methodology for the <span class="hlt">formulation</span> of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model RETRO-TOM. The <span class="hlt">Eulerian</span> backtracking method is used, allowing the forward advection scheme (Prather's second-order moments), to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time-symmetric suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux-limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" <span class="hlt">formulation</span> with the accuracy of an "adjoint of finite difference" <span class="hlt">formulation</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164424','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164424"><span>On tide-induced <span class="hlt">Lagrangian</span> residual current and residual transport: 2. Residual transport with application in south San Francisco Bay, California</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi</p>
<p>1986-01-01</p>
<p>The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current-induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide-induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection-dispersion equation in which the convective velocity is the <span class="hlt">Eulerian</span> residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long-term transport phenomena are closely related to the <span class="hlt">Lagrangian</span> residual current or the <span class="hlt">Lagrangian</span> residual transport. In this paper a new <span class="hlt">formulation</span> of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection-dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first-order <span class="hlt">Lagrangian</span> residual current (the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes drift). The remaining dispersion terms are important only in higher-order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70020645','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70020645"><span>Solution of the advection-dispersion equation in two dimensions by a finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Healy, R.W.; Russell, T.F.</p>
<p>1998-01-01</p>
<p>We extend the finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AdWR..113..141E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AdWR..113..141E"><span>Shear and shearless <span class="hlt">Lagrangian</span> structures in compound channels</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Enrile, F.; Besio, G.; Stocchino, A.</p>
<p>2018-03-01</p>
<p>Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a <span class="hlt">Lagrangian</span> analysis based on nonlinear dynamical system theory. Two-dimensional free surface <span class="hlt">Eulerian</span> experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called <span class="hlt">Lagrangian</span> Coherent Structures. <span class="hlt">Lagrangian</span> structures are recognized as the key features that govern particle trajectories. We seek for two particular class of <span class="hlt">Lagrangian</span> structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear <span class="hlt">Lagrangian</span> Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless <span class="hlt">Lagrangian</span> Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these <span class="hlt">Lagrangian</span> Structures tends to fade in deep flow conditions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y"><span><span class="hlt">Lagrangian</span> statistics in compressible isotropic homogeneous turbulence</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi</p>
<p>2011-11-01</p>
<p>In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the <span class="hlt">Lagrangian</span> point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the <span class="hlt">Eulerian</span> field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a <span class="hlt">Lagrangian</span> module for tracking the tracers and recording the data. The <span class="hlt">Lagrangian</span> probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The <span class="hlt">Lagrangian</span> structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface"><span><span class="hlt">Lagrangian</span> flows within reflecting internal waves at a horizontal free-slip surface</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.</p>
<p></p>
<p>In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider <span class="hlt">Lagrangian</span> flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking <span class="hlt">Lagrangian</span> fluid particles in direct numerical simulation (DNS) datasets of the <span class="hlt">Eulerian</span> flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that <span class="hlt">Eulerian</span> mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero <span class="hlt">Lagrangian</span> mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean <span class="hlt">Lagrangian</span> flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean <span class="hlt">Lagrangian</span> drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA062335','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA062335"><span>Incorporation of the NAG-FRAG Model for Ductile and Brittle Fracture into Help, a 2D Multimaterial <span class="hlt">Eulerian</span> Program</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>1978-09-01</p>
<p>Models HELP Ductile Material HEMP Brittle Material PUFF Iron Aluminum <span class="hlt">Eulerian</span> Codea Tap«.r«»H Flyor Pl^«-» rmp«^» tO. ABITRACT (Conllmjm M r«v... HEMP ) code with those obtained by the <span class="hlt">Eulerian</span> (HELP) code 5.3 Relative void volume of damage regions at three times after impact in the 1145...plate calculation 5.5 Relative void volume of material in the 1145 aluminum target at 1.46 us after impact as computed by the <span class="hlt">Lagrangian</span> ( HEMP</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CNSNS..20..516I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CNSNS..20..516I"><span>Transport induced by mean-eddy interaction: I. Theory, and relation to <span class="hlt">Lagrangian</span> lobe dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ide, Kayo; Wiggins, Stephen</p>
<p>2015-02-01</p>
<p>In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods. The (<span class="hlt">Eulerian</span>) boundaries across which we consider (<span class="hlt">Lagrangian</span>) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of <span class="hlt">Lagrangian</span> transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the <span class="hlt">Lagrangian</span> lobes. We contrast the similarities and differences between the TIME and <span class="hlt">Lagrangian</span> lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the <span class="hlt">Lagrangian</span> transport theory is made.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016TCry...10.1513R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016TCry...10.1513R"><span>Arctic sea-ice diffusion from observed and simulated <span class="hlt">Lagrangian</span> trajectories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Rampal, Pierre; Bouillon, Sylvain; Bergh, Jon; Ólason, Einar</p>
<p>2016-07-01</p>
<p>We characterize sea-ice drift by applying a <span class="hlt">Lagrangian</span> diffusion analysis to buoy trajectories from the International Arctic Buoy Programme (IABP) dataset and from two different models: the standalone <span class="hlt">Lagrangian</span> sea-ice model neXtSIM and the <span class="hlt">Eulerian</span> coupled ice-ocean model used for the TOPAZ reanalysis. By applying the diffusion analysis to the IABP buoy trajectories over the period 1979-2011, we confirm that sea-ice diffusion follows two distinct regimes (ballistic and Brownian) and we provide accurate values for the diffusivity and integral timescale that could be used in <span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span> passive tracers models to simulate the transport and diffusion of particles moving with the ice. We discuss how these values are linked to the evolution of the fluctuating displacements variance and how this information could be used to define the size of the search area around the position predicted by the mean drift. By comparing observed and simulated sea-ice trajectories for three consecutive winter seasons (2007-2011), we show how the characteristics of the simulated motion may differ from or agree well with observations. This comparison illustrates the usefulness of first applying a diffusion analysis to evaluate the output of modeling systems that include a sea-ice model before using these in, e.g., oil spill trajectory models or, more generally, to simulate the transport of passive tracers in sea ice.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960049629','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960049629"><span>Atomization simulations using an <span class="hlt">Eulerian-VOF-Lagrangian</span> method</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Chen, C. P.</p>
<p>1994-01-01</p>
<p>This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a <span class="hlt">Lagrangian</span> tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A"><span><span class="hlt">Lagrangian</span> theory of structure formation in relativistic cosmology. IV. <span class="hlt">Lagrangian</span> approach to gravitational waves</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander</p>
<p>2017-12-01</p>
<p>The relativistic generalization of the Newtonian <span class="hlt">Lagrangian</span> perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of <span class="hlt">Lagrangian</span>-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the <span class="hlt">Lagrangian</span> perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to <span class="hlt">Eulerian</span> background coordinates with truncation of nonlinear terms.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics"><span>Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Barlow, Andrew; Klima, Matej; Shashkov, Mikhail</p>
<p>2018-04-02</p>
<p>In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) methods. This includes a new <span class="hlt">formulation</span> of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the <span class="hlt">Lagrangian</span> stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics"><span>Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Barlow, Andrew; Klima, Matej; Shashkov, Mikhail</p>
<p></p>
<p>In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) methods. This includes a new <span class="hlt">formulation</span> of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the <span class="hlt">Lagrangian</span> stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029"><span><span class="hlt">Lagrangian</span> transport properties of pulmonary interfacial flows</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.</p>
<p>2012-01-01</p>
<p>Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of <span class="hlt">Lagrangian</span> coherent structures (LCSs) and their effects on transport. The <span class="hlt">Lagrangian</span> perspective of these techniques reveals flow characteristics that are not readily apparent by observing <span class="hlt">Eulerian</span> measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The <span class="hlt">Lagrangian</span> analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the <span class="hlt">Eulerian</span> frame. PMID:23049141</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Crowley, W.P.</p>
<p>1992-06-17</p>
<p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode`s and pde`s. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Crowley, W.P.</p>
<p>1992-06-17</p>
<p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode's and pde's. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24277435','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24277435"><span>Source apportion of atmospheric particulate matter: a joint <span class="hlt">Eulerian/Lagrangian</span> approach.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Riccio, A; Chianese, E; Agrillo, G; Esposito, C; Ferrara, L; Tirimberio, G</p>
<p>2014-12-01</p>
<p>PM2.5 samples were collected during an annual monitoring campaign (January 2012-January 2013) in the urban area of Naples, one of the major cities in Southern Italy. Samples were collected by means of a standard gravimetric sampler (Tecora Echo model) and characterized from a chemical point of view by ion chromatography. As a result, 143 samples together with their ionic composition have been collected. We extend traditional source apportionment techniques, usually based on multivariate factor analysis, interpreting the chemical analysis results within a <span class="hlt">Lagrangian</span> framework. The Hybrid Single-Particle <span class="hlt">Lagrangian</span> Integrated Trajectory Model (HYSPLIT) model was used, providing linkages to the source regions in the upwind areas. Results were analyzed in order to quantify the relative weight of different source types/areas. Model results suggested that PM concentrations are strongly affected not only by local emissions but also by transboundary emissions, especially from the Eastern and Northern European countries and African Saharan dust episodes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B"><span><span class="hlt">Eulerian</span> velocity reconstruction in ideal atmospheric dynamics using potential vorticity and potential temperature</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Blender, R.</p>
<p>2009-04-01</p>
<p>An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the <span class="hlt">Lagrangian</span> tracers Q, Î&,cedil; and ? determine the <span class="hlt">Eulerian</span> velocity field, the reconstruction combines the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains finite. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/wri/1986/4145/report.pdf','USGSPUBS'); return false;" href="https://pubs.usgs.gov/wri/1986/4145/report.pdf"><span>Users manual for a one-dimensional <span class="hlt">Lagrangian</span> transport model</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Schoellhamer, D.H.; Jobson, H.E.</p>
<p>1986-01-01</p>
<p>A Users Manual for the <span class="hlt">Lagrangian</span> Transport Model (LTM) is presented. The LTM uses <span class="hlt">Lagrangian</span> calculations that are based on a reference frame moving with the river flow. The <span class="hlt">Lagrangian</span> reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used <span class="hlt">Eulerian</span> reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.348..493T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.348..493T"><span>An updated <span class="hlt">Lagrangian</span> particle hydrodynamics (ULPH) for Newtonian fluids</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tu, Qingsong; Li, Shaofan</p>
<p>2017-11-01</p>
<p>In this work, we have developed an updated <span class="hlt">Lagrangian</span> particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics <span class="hlt">formulation</span> proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not <span class="hlt">formulated</span> with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update <span class="hlt">Lagrangian</span> particle hydrodynamics <span class="hlt">formulation</span> converges to the conventional local fluid mechanics <span class="hlt">formulation</span>; (2) the non-local updated <span class="hlt">Lagrangian</span> particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the <span class="hlt">formulation</span>, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C"><span>Laboratory experiment on the 3D tide-induced <span class="hlt">Lagrangian</span> residual current using the PIV technique</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chen, Yang; Jiang, Wensheng; Chen, Xu; Wang, Tao; Bian, Changwei</p>
<p>2017-12-01</p>
<p>The 3D structure of the tide-induced <span class="hlt">Lagrangian</span> residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced <span class="hlt">Lagrangian</span> residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the <span class="hlt">Lagrangian</span> residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents shows that the <span class="hlt">Eulerian</span> residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19730006017','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19730006017"><span><span class="hlt">Lagrangian</span> description of warm plasmas</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kim, H.</p>
<p>1970-01-01</p>
<p>Efforts are described to extend the averaged <span class="hlt">Lagrangian</span> method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic <span class="hlt">Lagrangian</span> is <span class="hlt">formulated</span> rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic <span class="hlt">Lagrangian</span>. In the first of these, the <span class="hlt">Lagrangian</span> is obtained by velocity integration of the exact microscopic <span class="hlt">Lagrangian</span>. In the second, the expanded hydrodynamic <span class="hlt">Lagrangian</span> is obtained directly from the expanded microscopic <span class="hlt">Lagrangian</span>. As applications of the microscopic <span class="hlt">Lagrangian</span>, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.358..173F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.358..173F"><span>Enhancement of a 2D front-tracking algorithm with a non-uniform distribution of <span class="hlt">Lagrangian</span> markers</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Febres, Mijail; Legendre, Dominique</p>
<p>2018-04-01</p>
<p>The 2D front tracking method is enhanced to control the development of spurious velocities for non-uniform distributions of markers. The hybrid <span class="hlt">formulation</span> of Shin et al. (2005) [7] is considered. A new tangent calculation is proposed for the calculation of the tension force at markers. A new reconstruction method is also proposed to manage non-uniform distributions of markers. We show that for both the static and the translating spherical drop test case the spurious currents are reduced to the machine precision. We also show that the ratio of the <span class="hlt">Lagrangian</span> grid size Δs over the <span class="hlt">Eulerian</span> grid size Δx has to satisfy Δs / Δx > 0.2 for ensuring such low level of spurious velocity. The method is found to provide very good agreement with benchmark test cases from the literature.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1412096D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1412096D"><span>Mean <span class="hlt">Lagrangian</span> drift in continental shelf waves</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Drivdal, M.; Weber, J. E. H.</p>
<p>2012-04-01</p>
<p>The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW's) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E¯ over the shelf region, the radiation stress tensor component S¯11 for CSW's is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW's, the ratio ¯S11/¯E depends strongly on the wave number. The mean <span class="hlt">Lagrangian</span> flow forced by the radiation stress can be subdivided into a Stokes drift and a mean <span class="hlt">Eulerian</span> drift current. The magnitude of the latter depends on the ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW's show that the Stokes drift and the friction-dependent wave-induced mean <span class="hlt">Eulerian</span> current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW's they are approximately in phase. In both cases the mean <span class="hlt">Lagrangian</span> current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the <span class="hlt">Eulerian</span> mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW's that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deep water drilling accidents.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhyA..506..350S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhyA..506..350S"><span>A new <span class="hlt">Eulerian</span> model for viscous and heat conducting compressible flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Svärd, Magnus</p>
<p>2018-09-01</p>
<p>In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the <span class="hlt">Lagrangian</span> derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely <span class="hlt">Eulerian</span> framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhFl...26k3303M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhFl...26k3303M"><span>Guidelines for the <span class="hlt">formulation</span> of <span class="hlt">Lagrangian</span> stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Minier, Jean-Pierre; Chibbaro, Sergio; Pope, Stephen B.</p>
<p>2014-11-01</p>
<p>In this paper, we establish a set of criteria which are applied to discuss various <span class="hlt">formulations</span> under which <span class="hlt">Lagrangian</span> stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of <span class="hlt">Lagrangian</span> stochastic models. A central issue is to put forward reliable requirements which must be met by <span class="hlt">Lagrangian</span> stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their <span class="hlt">formulation</span> since advantages and disadvantages of different <span class="hlt">formulations</span> are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these <span class="hlt">Lagrangian</span> stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22393117','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22393117"><span><span class="hlt">Eulerian-Lagrangian</span> analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Umeyama, Motohiko</p>
<p>2012-04-13</p>
<p>This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an <span class="hlt">Eulerian</span> scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the <span class="hlt">Eulerian</span> velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhA...49g5501W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhA...49g5501W"><span>Vorticity and symplecticity in multi-symplectic, <span class="hlt">Lagrangian</span> gas dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Webb, G. M.; Anco, S. C.</p>
<p>2016-02-01</p>
<p>The <span class="hlt">Lagrangian</span>, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the <span class="hlt">Lagrangian</span> fluid labels, m i (the <span class="hlt">Lagrangian</span> mass coordinates) and time t are the independent variables, and in which the <span class="hlt">Eulerian</span> position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the <span class="hlt">Lagrangian</span> map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the <span class="hlt">Lagrangian</span> map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The <span class="hlt">Lagrangian</span> is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the <span class="hlt">Lagrangian</span> energy conservation law with respect to the <span class="hlt">Lagrangian</span> mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.329...48D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.329...48D"><span>A semi-<span class="hlt">Lagrangian</span> transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Doisneau, François; Arienti, Marco; Oefelein, Joseph C.</p>
<p>2017-01-01</p>
<p>For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the <span class="hlt">Eulerian</span> formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-<span class="hlt">Lagrangian</span> schemes, developed for Gas Dynamics. We show how semi-<span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of <span class="hlt">Eulerian</span> fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622237-semi-lagrangian-transport-method-kinetic-problems-application-dense-dilute-polydisperse-reacting-spray-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622237-semi-lagrangian-transport-method-kinetic-problems-application-dense-dilute-polydisperse-reacting-spray-flows"><span>A semi-<span class="hlt">Lagrangian</span> transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Doisneau, François, E-mail: fdoisne@sandia.gov; Arienti, Marco, E-mail: marient@sandia.gov; Oefelein, Joseph C., E-mail: oefelei@sandia.gov</p>
<p></p>
<p>For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the <span class="hlt">Eulerian</span> formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-<span class="hlt">Lagrangian</span> schemes, developed for Gas Dynamics. We show how semi-<span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barelymore » influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of <span class="hlt">Eulerian</span> fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PhRvA..81b2112K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PhRvA..81b2112K"><span>Functional integral for non-<span class="hlt">Lagrangian</span> systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kochan, Denis</p>
<p>2010-02-01</p>
<p>A functional integral <span class="hlt">formulation</span> of quantum mechanics for non-<span class="hlt">Lagrangian</span> systems is presented. The approach, which we call “stringy quantization,” is based solely on classical equations of motion and is free of any ambiguity arising from <span class="hlt">Lagrangian</span> and/or Hamiltonian <span class="hlt">formulation</span> of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -κq˙A. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29347330','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29347330"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> and symmetrical description of liquid dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Trachenko, K</p>
<p>2017-12-01</p>
<p>Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field <span class="hlt">Lagrangian</span> of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The <span class="hlt">Lagrangian</span> predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvE..96f2134T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvE..96f2134T"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> and symmetrical description of liquid dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Trachenko, K.</p>
<p>2017-12-01</p>
<p>Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k -space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field <span class="hlt">Lagrangian</span> of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The <span class="hlt">Lagrangian</span> predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k -space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.</p>
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<ol class="result-class" start="181">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JCoPh.237..251S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JCoPh.237..251S"><span>A cell-centered <span class="hlt">Lagrangian</span> finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.</p>
<p>2013-03-01</p>
<p>A finite volume cell-centered <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> hydrocodes in addition to analytical and experimental results are made to validate the current approach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L"><span>A Skill Score of Trajectory Model Evaluation Using Reinitialized Series of Normalized Cumulative <span class="hlt">Lagrangian</span> Separation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Liu, Y.; Weisberg, R. H.</p>
<p>2017-12-01</p>
<p>The <span class="hlt">Lagrangian</span> separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative <span class="hlt">Lagrangian</span> separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the <span class="hlt">Lagrangian</span> separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional <span class="hlt">Eulerian</span>-based velocity nor a <span class="hlt">Lagrangian</span>-based probability density function may be estimated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JChPh.147e4103N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JChPh.147e4103N"><span>Next generation extended <span class="hlt">Lagrangian</span> first principles molecular dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Niklasson, Anders M. N.</p>
<p>2017-08-01</p>
<p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is <span class="hlt">formulated</span> for general Hohenberg-Kohn density-functional theory and compared with the extended <span class="hlt">Lagrangian</span> framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent <span class="hlt">formulations</span> of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this <span class="hlt">formulation</span> provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28789552','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28789552"><span>Next generation extended <span class="hlt">Lagrangian</span> first principles molecular dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Niklasson, Anders M N</p>
<p>2017-08-07</p>
<p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is <span class="hlt">formulated</span> for general Hohenberg-Kohn density-functional theory and compared with the extended <span class="hlt">Lagrangian</span> framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent <span class="hlt">formulations</span> of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this <span class="hlt">formulation</span> provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26611112','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26611112"><span>Updated <span class="hlt">Lagrangian</span> finite element <span class="hlt">formulations</span> of various biological soft tissue non-linear material models: a comprehensive procedure and review.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Townsend, Molly T; Sarigul-Klijn, Nesrin</p>
<p>2016-01-01</p>
<p>Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to <span class="hlt">formulate</span>. This paper strives to offer the updated <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26026433','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26026433"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of irreversible thermodynamics and the second law of thermodynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Glavatskiy, K S</p>
<p>2015-05-28</p>
<p>We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a <span class="hlt">Lagrangian</span>, which depends on the properties of the normal and the so-called "mirror-image" system. The <span class="hlt">Lagrangian</span> is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the <span class="hlt">Lagrangian</span>. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23944559','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23944559"><span><span class="hlt">Lagrangian</span> coherent structures separate dynamically distinct regions in fluid flows.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kelley, Douglas H; Allshouse, Michael R; Ouellette, Nicholas T</p>
<p>2013-07-01</p>
<p>Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this <span class="hlt">Lagrangian</span>-averaged flux is nearly unchanged from its <span class="hlt">Eulerian</span> counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of <span class="hlt">Lagrangian</span> coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24d2702V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24d2702V"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR code</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; Molvig, K.; Simakov, A. N.; Haines, B. M.</p>
<p>2017-04-01</p>
<p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22415860-lagrangian-formulation-irreversible-thermodynamics-second-law-thermodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22415860-lagrangian-formulation-irreversible-thermodynamics-second-law-thermodynamics"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of irreversible thermodynamics and the second law of thermodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Glavatskiy, K. S.</p>
<p></p>
<p>We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a <span class="hlt">Lagrangian</span>, which depends on the properties of the normal and the so-called “mirror-image” system. The <span class="hlt">Lagrangian</span> is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the <span class="hlt">Lagrangian</span>. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such thatmore » there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26679833','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26679833"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices--How numerical implementation affects the results.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Marom, Gil; Bluestein, Danny</p>
<p>2016-01-01</p>
<p>This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices - How numerical implementation affects the results</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Marom, Gil; Bluestein, Danny</p>
<p>2016-01-01</p>
<p>Summary This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed. PMID:26679833</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S"><span>Evaluation of a <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> air quality model using perfluorocarbon tracers released in Texas for the BRAVO haze study</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Schichtel, Bret A.; Barna, Michael G.; Gebhart, Kristi A.; Malm, William C.</p>
<p></p>
<p>The Big Bend Regional Aerosol and Visibility Observational (BRAVO) study was designed to determine the sources of haze at Big Bend National Park, Texas, using a combination of source and receptor models. BRAVO included an intensive monitoring campaign from July to October 1999 that included the release of perfluorocarbon tracers from four locations at distances 230-750 km from Big Bend and measured at 24 sites. The tracer measurements near Big Bend were used to evaluate the dispersion mechanisms in the REMSAD <span class="hlt">Eulerian</span> model and the CAPITA Monte Carlo (CMC) <span class="hlt">Lagrangian</span> model used in BRAVO. Both models used 36 km MM5 wind fields as input. The CMC model also used a combination of routinely available 80 and 190 km wind fields from the National Weather Service's National Centers for Environmental Prediction (NCEP) as input. A model's performance is limited by inherent uncertainties due to errors in the tracer concentrations and a model's inability to simulate sub-resolution variability. A range in the inherent uncertainty was estimated by comparing tracer data at nearby monitoring sites. It was found that the REMSAD and CMC models, using the MM5 wind field, produced performance statistics generally within this inherent uncertainty. The CMC simulation using the NCEP wind fields could reproduce the timing of tracer impacts at Big Bend, but not the concentration values, due to a systematic underestimation. It appears that the underestimation was partly due to excessive vertical dilution from high mixing depths. The model simulations were more sensitive to the input wind fields than the models' different dispersion mechanisms. Comparisons of REMSAD to CMC tracer simulations using the MM5 wind fields had correlations between 0.75 and 0.82, depending on the tracer, but the tracer simulations using the two wind fields in the CMC model had correlations between 0.37 and 0.5.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26874478','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26874478"><span>A view on coupled cluster perturbation theory using a bivariational <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul</p>
<p>2016-02-14</p>
<p>We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC <span class="hlt">Lagrangian</span> (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930046859&hterms=mixed+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmixed%2Bmethods','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930046859&hterms=mixed+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmixed%2Bmethods"><span>Noniterative implicit method for tracking particles in mixed <span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">formulations</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Shih, T. I.-P.; Dasgupta, A.</p>
<p>1993-01-01</p>
<p>The existing implicit methods for the current initial value problems (IVPs) concerning particle-laden flows are complicated and iterative in nature. This paper presents a noniterative implicit method which can be used with pressure-based as well as with density-based algorithms. The method is illustrated by analyzing a dilute dispersion of noninteracting solid particles in an isothermal flow in a passage bounded by one straight wall and one wavy wall, in which all particles are spherical and have a finite velociy relative to the continuum phase at the inflow boundary.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22403195-guidelines-formulation-lagrangian-stochastic-models-particle-simulations-single-phase-dispersed-two-phase-turbulent-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22403195-guidelines-formulation-lagrangian-stochastic-models-particle-simulations-single-phase-dispersed-two-phase-turbulent-flows"><span>Guidelines for the <span class="hlt">formulation</span> of <span class="hlt">Lagrangian</span> stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Minier, Jean-Pierre, E-mail: Jean-Pierre.Minier@edf.fr; Chibbaro, Sergio; Pope, Stephen B.</p>
<p></p>
<p>In this paper, we establish a set of criteria which are applied to discuss various <span class="hlt">formulations</span> under which <span class="hlt">Lagrangian</span> stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of <span class="hlt">Lagrangian</span> stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangianmore » stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their <span class="hlt">formulation</span> since advantages and disadvantages of different <span class="hlt">formulations</span> are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these <span class="hlt">Lagrangian</span> stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1989umas.reptQ....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1989umas.reptQ....O"><span><span class="hlt">Lagrangian</span> turbulence near walls: Structures and mixing in admissible model flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ottino, J. M.</p>
<p>1989-05-01</p>
<p>The general objective of work during this period was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: a perturbed Kelvin cat eyes flow, and prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: production flows capable of producing complex distributions of vorticity, and constructed flow fields, based on solutions of the Navier Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR code</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; ...</p>
<p>2017-04-04</p>
<p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions tomore » flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26826855','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26826855"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Rivera, Michael K; Ecke, Robert E</p>
<p>2016-01-01</p>
<p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1351187','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1351187"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Rivera, Michael K.; Ecke, Robert E.</p>
<p></p>
<p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Rivera, Michael K.; Ecke, Robert E.</p>
<p>2016-01-14</p>
<p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p>
</li>
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<ol class="result-class" start="201">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1991umas.rept.....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1991umas.rept.....O"><span><span class="hlt">Lagrangian</span> turbulence: Structures and mixing in admissible model flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ottino, Julio M.</p>
<p>1991-12-01</p>
<p>The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory</p>
<p>2012-10-01</p>
<p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a <span class="hlt">Lagrangian</span> Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the <span class="hlt">Lagrangian</span> approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26578642','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26578642"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p>
<p>2016-11-01</p>
<p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis-based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. © The Author(s) 2015.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p>
<p>2016-01-01</p>
<p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis–based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. PMID:26578642</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17151883','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17151883"><span>Structured population dynamics: continuous size and discontinuous stage structures.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Buffoni, Giuseppe; Pasquali, Sara</p>
<p>2007-04-01</p>
<p>A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is <span class="hlt">formulated</span> in the <span class="hlt">Eulerian</span> formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> models are compared.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913844L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913844L"><span>Estimating <span class="hlt">Eulerian</span> spectra from pairs of drifters</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>LaCasce, Joe</p>
<p>2017-04-01</p>
<p>GPS-tracked surface drifters offer the possibility of sampling energetic variations at the ocean surface on scales of only 10s of meters, much less than that resolved by satellite. Here we investigate whether velocity differences between pairs of drifters can be used to estimate kinetic energy spectra. Theoretical relations between the spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived. The structure function is a natural statistic for particle pairs and is easily calculated. However it integrates contributions across wavenumber, and this tends to obscure the spectral dependencies when turbulent inertial ranges are of finite extent. Nevertheless, the transform from spectrum to structure function is robust, as illustrated with <span class="hlt">Eulerian</span> data collected from aircraft. The inverse transform, from structure function to spectrum, is much less robust, yielding poor results in particular at large wavenumbers. This occurs because the transform involves a filter function which magnifies contributions from large pair separations, which tend to be noisy. Fitting the structure function to a polynomial improves the spectral estimate, but not sufficiently to distinguish correct inertial range dependencies. Thus with <span class="hlt">Lagrangian</span> data, it is appears preferable to focus on structure functions, despite their shortcomings.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CQGra..35a5007A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CQGra..35a5007A"><span>Field theory of the <span class="hlt">Eulerian</span> perfect fluid</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ariki, Taketo; Morales, Pablo A.</p>
<p>2018-01-01</p>
<p>The <span class="hlt">Eulerian</span> perfect-fluid theory is reformulated from its action principle in a pure field-theoretic manner. Conservation of the convective current is no longer imposed by Lin’s constraints, but rather adopted as the central idea of the theory. Our <span class="hlt">formulation</span>, for the first time, successfully reduces redundant degrees of freedom promoting one half of the Clebsch variables to true dynamical fields. Interactions on these fields allow for the exchange of the convective current of quantities such as mass and charge, which are uniformly understood as the breaking of the underlying symmetry of the force-free fluid. The Clebsch fields play the essential role of exchanging angular momentum with the force field producing vorticity.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29316401','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29316401"><span>Extended <span class="hlt">Lagrangian</span> Excited State Molecular Dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N</p>
<p>2018-02-13</p>
<p>An extended <span class="hlt">Lagrangian</span> framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The <span class="hlt">formulation</span> is a generalization of the extended <span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750"><span>Investigation of particle inertial migration in high particle concentration suspension flow by multi-electrodes sensing and <span class="hlt">Eulerian-Lagrangian</span> simulation in a square microchannel</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Zhao, Tong; Liu, Kai; Takei, Masahiro</p>
<p>2016-01-01</p>
<p>The inertial migration of neutrally buoyant spherical particles in high particle concentration (αpi > 3%) suspension flow in a square microchannel was investigated by means of the multi-electrodes sensing method which broke through the limitation of conventional optical measurement techniques in the high particle concentration suspensions due to interference from the large particle numbers. Based on the measured particle concentrations near the wall and at the corner of the square microchannel, particle cross-sectional migration ratios are calculated to quantitatively estimate the migration degree. As a result, particle migration to four stable equilibrium positions near the centre of each face of the square microchannel is found only in the cases of low initial particle concentration up to 5.0 v/v%, while the migration phenomenon becomes partial as the initial particle concentration achieves 10.0 v/v% and disappears in the cases of the initial particle concentration αpi ≥ 15%. In order to clarify the influential mechanism of particle-particle interaction on particle migration, an <span class="hlt">Eulerian-Lagrangian</span> numerical model was proposed by employing the Lennard-Jones potential as the inter-particle potential, while the inertial lift coefficient is calculated by a pre-processed semi-analytical simulation. Moreover, based on the experimental and simulation results, a dimensionless number named migration index was proposed to evaluate the influence of the initial particle concentration on the particle migration phenomenon. The migration index less than 0.1 is found to denote obvious particle inertial migration, while a larger migration index denotes the absence of it. This index is helpful for estimation of the maximum initial particle concentration for the design of inertial microfluidic devices. PMID:27158288</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012IJTP...51.2015K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012IJTP...51.2015K"><span>Remarks on the "Non-canonicity Puzzle": <span class="hlt">Lagrangian</span> Symmetries of the Einstein-Hilbert Action</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kiriushcheva, N.; Komorowski, P. G.; Kuzmin, S. V.</p>
<p>2012-07-01</p>
<p>Given the non-canonical relationship between variables used in the Hamiltonian <span class="hlt">formulations</span> of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two <span class="hlt">formulations</span>, the assumption that the <span class="hlt">Lagrangians</span> from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac <span class="hlt">formulations</span>, and the one that arises from the ADM <span class="hlt">formulation</span>. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert <span class="hlt">Lagrangian</span> using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two <span class="hlt">Lagrangians</span> are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170004568','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170004568"><span>A Decadal Inversion of CO2 Using the Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric Model (GELCA): Sensitivity to the Ground-Based Observation Network</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Gomez-Pelaez, A. J.; Langenfelds, R.; <a style="text-decoration: none; " href="javascript:void(0); " onClick="displayelement('author_20170004568'); toggleEditAbsImage('author_20170004568_show'); toggleEditAbsImage('author_20170004568_hide'); "> <img style="display:inline; width:12px; height:12px; " src="images/arrow-up.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_show"> <img style="width:12px; height:12px; display:none; " src="images/arrow-down.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_hide"></p>
<p>2017-01-01</p>
<p>We present an assimilation system for atmospheric carbon dioxide (CO2) using a Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric model (GELCA), and demonstrate its capability to capture the observed atmospheric CO2 mixing ratios and to estimate CO2 fluxes. With the efficient data handling scheme in GELCA, our system assimilates non-smoothed CO2 data from observational data products such as the Observation Package (ObsPack) data products as constraints on surface fluxes. We conducted sensitivity tests to examine the impact of the site selections and the prior uncertainty settings of observation on the inversion results. For these sensitivity tests, we made five different sitedata selections from the ObsPack product. In all cases, the time series of the global net CO2 flux to the atmosphere stayed close to values calculated from the growth rate of the observed global mean atmospheric CO2 mixing ratio. At regional scales, estimated seasonal CO2 fluxes were altered, depending on the CO2 data selected for assimilation. Uncertainty reductions (URs) were determined at the regional scale and compared among cases. As measures of the model-data mismatch, we used the model-data bias, root-mean-square error, and the linear correlation. For most observation sites, the model-data mismatch was reasonably small. Regarding regional flux estimates, tropical Asia was one of the regions that showed a significant impact from the observation network settings. We found that the surface fluxes in tropical Asia were the most sensitive to the use of aircraft measurements over the Pacific, and the seasonal cycle agreed better with the results of bottom-up studies when the aircraft measurements were assimilated. These results confirm the importance of these aircraft observations, especially for constraining surface fluxes in the tropics.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame"><span>Numerical methods for the weakly compressible Generalized Langevin Model in <span class="hlt">Eulerian</span> reference frame</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.</p>
<p>2016-06-01</p>
<p>A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a <span class="hlt">Lagrangian</span> reference frame, typically solvedmore » by particle methods. A representation in a <span class="hlt">Eulerian</span> reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a <span class="hlt">Eulerian</span>-frame numerical flow solver. GLM in a <span class="hlt">Eulerian</span> frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JGRD..11810243H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JGRD..11810243H"><span>Identification and uncertainty estimation of vertical reflectivity profiles using a <span class="hlt">Lagrangian</span> approach to support quantitative precipitation measurements by weather radar</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Hazenberg, P.; Torfs, P. J. J. F.; Leijnse, H.; Delrieu, G.; Uijlenhoet, R.</p>
<p>2013-09-01</p>
<p>This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional <span class="hlt">Eulerian</span> as well as a newly proposed <span class="hlt">Lagrangian</span> implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the <span class="hlt">Lagrangian</span> implementation beyond distances of 100 km. However, by combining this procedure with the global <span class="hlt">Eulerian</span> VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29181888','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29181888"><span>Preconditioned augmented <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for nearly incompressible cardiac mechanics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins</p>
<p>2018-04-01</p>
<p>Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented <span class="hlt">Lagrangian</span> method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented <span class="hlt">Lagrangian</span> method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1184028-generalized-extended-lagrangian-born-oppenheimer-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1184028-generalized-extended-lagrangian-born-oppenheimer-molecular-dynamics"><span>Generalized extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Niklasson, Anders M. N.; Cawkwell, Marc J.</p>
<p>2014-10-29</p>
<p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended <span class="hlt">Lagrangian</span> under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous <span class="hlt">formulations</span>.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29435676','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29435676"><span>Vortex dynamics and <span class="hlt">Lagrangian</span> statistics in a model for active turbulence.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>James, Martin; Wilczek, Michael</p>
<p>2018-02-14</p>
<p>Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016WRR....52.8561Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016WRR....52.8561Z"><span>Bounded fractional diffusion in geological media: Definition and <span class="hlt">Lagrangian</span> approximation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang</p>
<p>2016-11-01</p>
<p>Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a <span class="hlt">Lagrangian</span> solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New <span class="hlt">Lagrangian</span> schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or <span class="hlt">Eulerian</span> solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded <span class="hlt">Lagrangian</span> solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhLB..772..694C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhLB..772..694C"><span>Extended hamiltonian formalism and Lorentz-violating <span class="hlt">lagrangians</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Colladay, Don</p>
<p>2017-09-01</p>
<p>A new perspective on the classical mechanical <span class="hlt">formulation</span> of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant <span class="hlt">lagrangian</span> and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the <span class="hlt">lagrangian</span>. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the <span class="hlt">lagrangians</span> and the field-theoretic solutions to the Dirac equation is also established for a special case.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25903879','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25903879"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N</p>
<p>2015-04-21</p>
<p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer <span class="hlt">formulations</span> exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhLB..779..485L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhLB..779..485L"><span>A unifying framework for ghost-free Lorentz-invariant <span class="hlt">Lagrangian</span> field theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Li, Wenliang</p>
<p>2018-04-01</p>
<p>We propose a framework for Lorentz-invariant <span class="hlt">Lagrangian</span> field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general <span class="hlt">Lagrangians</span> are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established <span class="hlt">Lagrangian</span> theories for spin-0, spin-1, p-form, spin-2 fields have natural <span class="hlt">formulations</span> in this framework. We also propose novel building blocks for <span class="hlt">Lagrangian</span> field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CeMDA.129..137L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CeMDA.129..137L"><span>Note on the ideal frame <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lara, Martin</p>
<p>2017-09-01</p>
<p>An implementation of the ideal frame <span class="hlt">formulation</span> of perturbed Keplerian motion is presented which only requires the integration of a differential system of dimension 7, contrary to the 8 variables traditionally integrated with this approach. The new <span class="hlt">formulation</span> is based on the integration of a scaled version of the <span class="hlt">Eulerian</span> set of redundant parameters and slightly improves runtime performance with respect to the 8-dimensional case while retaining comparable accuracy.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2814836','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2814836"><span>Using hyperbolic <span class="hlt">Lagrangian</span> coherent structures to investigate vortices in bioinspired fluid flows</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Green, Melissa A.; Rowley, Clarence W.; Smits, Alexander J.</p>
<p>2010-01-01</p>
<p>We use direct Lyapunov exponents to identify <span class="hlt">Lagrangian</span> coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used <span class="hlt">Eulerian</span> criteria, the <span class="hlt">Lagrangian</span> method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Kármán vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location. PMID:20370300</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26575565','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26575565"><span>Extended <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of charge-constrained tight-binding molecular dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Cawkwell, M J; Coe, J D; Yadav, S K; Liu, X-Y; Niklasson, A M N</p>
<p>2015-06-09</p>
<p>The extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended <span class="hlt">Lagrangian</span> molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of numerical noise during trajectories was also investigated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.356..174C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.356..174C"><span>A purely <span class="hlt">Lagrangian</span> method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Capecelatro, Jesse</p>
<p>2018-03-01</p>
<p>It has long been suggested that a purely <span class="hlt">Lagrangian</span> solution to global-scale atmospheric/oceanic flows can potentially outperform tradition <span class="hlt">Eulerian</span> schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully <span class="hlt">Lagrangian</span> method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUFMEP42A..04G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUFMEP42A..04G"><span>Modeling Sediment Transport Using a <span class="hlt">Lagrangian</span> Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Garcia, M. H.</p>
<p>2016-12-01</p>
<p>Modeling Sediment Transport Using a <span class="hlt">Lagrangian</span> Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity Som Dutta1, Paul Fischer2, Marcelo H. Garcia11Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 2Department of Computer Science and Department of MechSE, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 Since the seminal work of Niño and Garcia [1994], one-way coupled <span class="hlt">Lagrangian</span> particle tracking has been used extensively for modeling sediment transport. Over time, the <span class="hlt">Lagrangian</span> particle tracking method has been coupled with <span class="hlt">Eulerian</span> flow simulations, ranging from Reynolds Averaged Navier-Stokes (RANS) based models to Detached Eddy Simulations (DES) [Escauriaza and Sotiropoulos, 2011]. Advent of high performance computing (HPC) platforms and faster algorithms have resulted in the work of Dutta et al. [2016], where <span class="hlt">Lagrangian</span> particle tracking was coupled with high-resolution Large Eddy Simulations (LES) to model the complex and highly non-linear phenomenon of Bulle-Effect at diversions. Despite all the advancements in using <span class="hlt">Lagrangian</span> particle tracking, there has not been a study that looks in detail at the limits of the model in the context of sediment transport, and also analyzes the sensitivity of the various force <span class="hlt">formulation</span> in the force balance equation of the particles. Niño and Garcia [1994] did a similar analysis, but the vertical flow velocity distribution was modeled as the log-law. The current study extends the analysis by modeling the flow using high-resolution LES at a Reynolds number comparable to experiments of Niño et al. [1994]. Dutta et al., (2016), Large Eddy Simulation (LES) of flow and bedload transport at an idealized 90-degree diversion: insight into Bulle-Effect, River Flow 2016 - Constantinescu, Garcia & Hanes (Eds), Taylor & Francis Group, London, 101-109. Escauriaza and Sotiropoulos</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics"><span>Extended <span class="hlt">Lagrangian</span> Excited State Molecular Dynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...</p>
<p>2018-01-09</p>
<p>In this work, an extended <span class="hlt">Lagrangian</span> framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The <span class="hlt">formulation</span> is a generalization of the extended <span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics"><span>Extended <span class="hlt">Lagrangian</span> Excited State Molecular Dynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei</p>
<p></p>
<p>In this work, an extended <span class="hlt">Lagrangian</span> framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The <span class="hlt">formulation</span> is a generalization of the extended <span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1919137F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1919137F"><span>Evaluation of the HF-Radar network system around Taiwan using normalized cumulative <span class="hlt">Lagrangian</span> separation.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fredj, Erick; Kohut, Josh; Roarty, Hugh; Lai, Jian-Wu</p>
<p>2017-04-01</p>
<p>The <span class="hlt">Lagrangian</span> separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as over continental shelves and the adjacent deep ocean. A skill score described in detail by (Lui et.al. 2011) was applied to estimate the cumulative <span class="hlt">Lagrangian</span> separation distances normalized by the associated cumulative trajectory lengths. In contrast, the <span class="hlt">Lagrangian</span> separation distance alone gives a misleading result. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional <span class="hlt">Eulerian</span>-based velocity nor a <span class="hlt">Lagrangian</span> based probability density function may be estimated. The skill score assesses The Taiwan Ocean Radar Observing System (TOROS) performance. TOROS consists of 17 SeaSonde type radars around the Taiwan Island. The currents off Taiwan are significantly influenced by the nearby Kuroshio current. The main stream of the Kuroshio flows along the east coast of Taiwan to the north throughout the year. Sometimes its branch current also bypasses the south end of Taiwan and goes north along the west coast of Taiwan. The Kuroshio is also prone to seasonal change in its speed of flow, current capacity, distribution width, and depth. The evaluations of HF-Radar National Taiwanese network performance using <span class="hlt">Lagrangian</span> drifter records demonstrated the high quality and robustness of TOROS HF-Radar data using a purely trajectory-based non-dimensional index. Yonggang Liu and Robert H. Weisberg, "Evaluation of trajectory modeling in different dynamic regions using normalized cumulative <span class="hlt">Lagrangian</span> separation", Journal of Geophysical Research, Vol. 116, C09013, doi:10.1029/2010JC006837, 2011</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2000JFM...402..291B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000JFM...402..291B"><span>On hydrostatic flows in isentropic coordinates</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Bokhove, Onno</p>
<p>2000-01-01</p>
<p>The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic <span class="hlt">Eulerian</span> framework. The use of material isentropic coordinates for the <span class="hlt">Eulerian</span> hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an <span class="hlt">Eulerian</span> isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a <span class="hlt">Lagrangian</span> Hamilton's principle to an <span class="hlt">Eulerian</span> one. This <span class="hlt">Eulerian</span> principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an <span class="hlt">Eulerian</span> ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the <span class="hlt">Eulerian</span> Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the <span class="hlt">Eulerian</span> action principle for hydrostatic flows. Approximations to <span class="hlt">Eulerian</span> variational principles may be more advantageous than approximations to <span class="hlt">Lagrangian</span> ones because non-dimensionalization and scaling tend to be based on <span class="hlt">Eulerian</span> estimates of the characteristic scales involved. These approximations to the stratified hydrostatic <span class="hlt">formulation</span> extend previous</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1422959','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1422959"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.</p>
<p></p>
<p>Here, Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer <span class="hlt">formulations</span> exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1422959-thermostating-extended-lagrangian-born-oppenheimer-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1422959-thermostating-extended-lagrangian-born-oppenheimer-molecular-dynamics"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.; ...</p>
<p>2015-04-21</p>
<p>Here, Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer <span class="hlt">formulations</span> exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.113..185A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.113..185A"><span>Corrigenda of 'explicit wave-averaged primitive equations using a generalized <span class="hlt">Lagrangian</span> Mean'</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ardhuin, F.; Rascle, N.; Belibassakis, K. A.</p>
<p>2017-05-01</p>
<p>Ardhuin et al. (2008) gave a second-order approximation in the wave slope of the exact Generalized <span class="hlt">Lagrangian</span> Mean (GLM) equations derived by Andrews and McIntyre (1978), and also performed a coordinate transformation, going from GLM to a 'GLMz' set of equations. That latter step removed the wandering of the GLM mean sea level away from the <span class="hlt">Eulerian</span>-mean sea level, making the GLMz flow non-divergent. That step contained some inaccuarate statements about the coordinate transformation, while the rest of the paper contained an error on the surface dynamic boundary condition for viscous stresses. I am thankful to Mathias Delpey and Hidenori Aiki for pointing out these errors, which are corrected below.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1328855','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1328855"><span>Action principle for Coulomb collisions in plasmas</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Hirvijoki, Eero</p>
<p></p>
<p>In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural <span class="hlt">Lagrangian</span> exists for the Landau-Fokker-Planck equation, an <span class="hlt">Eulerian</span> variational <span class="hlt">formulation</span> is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order <span class="hlt">Lagrangians</span> and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1328855-action-principle-coulomb-collisions-plasmas','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1328855-action-principle-coulomb-collisions-plasmas"><span>Action principle for Coulomb collisions in plasmas</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Hirvijoki, Eero</p>
<p>2016-09-14</p>
<p>In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural <span class="hlt">Lagrangian</span> exists for the Landau-Fokker-Planck equation, an <span class="hlt">Eulerian</span> variational <span class="hlt">formulation</span> is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order <span class="hlt">Lagrangians</span> and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006JPhy4.133..587K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JPhy4.133..587K"><span>Modeling NIF experimental designs with adaptive mesh refinement and <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.</p>
<p>2006-06-01</p>
<p>Incorporation of adaptive mesh refinement (AMR) into <span class="hlt">Lagrangian</span> hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA590591','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA590591"><span>Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2012-09-30</p>
<p><span class="hlt">Lagrangian</span> methods for free - surface turbulence and wave simulation . In the far field, coupled wind and wave simulations are used to obtain wind...to conserve the mass precisely. When the wave breaks, the flow at the free surface may become very violent, air and water may be highly mixed...fluids free - surface flows that can be used to study the fundamental physics of wave breaking. The research will improve the understanding of air-sea</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CPM.....1...85O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1...85O"><span><span class="hlt">Lagrangian</span> analysis of multiscale particulate flows with the particle finite element method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy</p>
<p>2014-05-01</p>
<p>We present a <span class="hlt">Lagrangian</span> numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure <span class="hlt">formulation</span> and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900036170&hterms=ito&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dito','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900036170&hterms=ito&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dito"><span>The augmented <span class="hlt">Lagrangian</span> method for parameter estimation in elliptic systems</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Ito, Kazufumi; Kunisch, Karl</p>
<p>1990-01-01</p>
<p>In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined <span class="hlt">Lagrangian</span> functional. To obtain this coercivity estimate a seminorm regularization technique is used.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDH23005V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDH23005V"><span>Estimates of <span class="hlt">Lagrangian</span> particle transport by wave groups: forward transport by Stokes drift and backward transport by the return flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>van den Bremer, Ton S.; Taylor, Paul H.</p>
<p>2014-11-01</p>
<p>Although the literature has examined Stokes drift, the net <span class="hlt">Lagrangian</span> transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the <span class="hlt">Eulerian</span> return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the <span class="hlt">Lagrangian</span> transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal <span class="hlt">Lagrangian</span> transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which <span class="hlt">Lagrangian</span> particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22608639-eulerian-frequency-analysis-structural-vibrations-from-high-speed-video','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22608639-eulerian-frequency-analysis-structural-vibrations-from-high-speed-video"><span><span class="hlt">Eulerian</span> frequency analysis of structural vibrations from high-speed video</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Venanzoni, Andrea; Siemens Industry Software NV, Interleuvenlaan 68, B-3001 Leuven; De Ryck, Laurent</p>
<p></p>
<p>An approach for the analysis of the frequency content of structural vibrations from high-speed video recordings is proposed. The techniques and tools proposed rely on an <span class="hlt">Eulerian</span> approach, that is, using the time history of pixels independently to analyse structural motion, as opposed to <span class="hlt">Lagrangian</span> approaches, where the motion of the structure is tracked in time. The starting point is an existing <span class="hlt">Eulerian</span> motion magnification method, which consists in decomposing the video frames into a set of spatial scales through a so-called Laplacian pyramid [1]. Each scale — or level — can be amplified independently to reconstruct a magnified motionmore » of the observed structure. The approach proposed here provides two analysis tools or pre-amplification steps. The first tool provides a representation of the global frequency content of a video per pyramid level. This may be further enhanced by applying an angular filter in the spatial frequency domain to each frame of the video before the Laplacian pyramid decomposition, which allows for the identification of the frequency content of the structural vibrations in a particular direction of space. This proposed tool complements the existing <span class="hlt">Eulerian</span> magnification method by amplifying selectively the levels containing relevant motion information with respect to their frequency content. This magnifies the displacement while limiting the noise contribution. The second tool is a holographic representation of the frequency content of a vibrating structure, yielding a map of the predominant frequency components across the structure. In contrast to the global frequency content representation of the video, this tool provides a local analysis of the periodic gray scale intensity changes of the frame in order to identify the vibrating parts of the structure and their main frequencies. Validation cases are provided and the advantages and limits of the approaches are discussed. The first validation case consists of the frequency</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.350...84S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.350...84S"><span>Parallel implementation of a <span class="hlt">Lagrangian</span>-based model on an adaptive mesh in C++: Application to sea-ice</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar</p>
<p>2017-12-01</p>
<p>We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure <span class="hlt">Lagrangian</span> scheme or an Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004PhR...392..279S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004PhR...392..279S"><span><span class="hlt">Lagrangian</span> fluid description with simple applications in compressible plasma and gas dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Schamel, Hans</p>
<p>2004-03-01</p>
<p>The <span class="hlt">Lagrangian</span> fluid description, in which the dynamics of fluids is <span class="hlt">formulated</span> in terms of trajectories of fluid elements, not only presents an alternative to the more common <span class="hlt">Eulerian</span> description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as <span class="hlt">Lagrangian</span> codes and experimental techniques are developed utilizing the <span class="hlt">Lagrangian</span> point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the <span class="hlt">Lagrangian</span> fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the <span class="hlt">Lagrangian</span> flow velocity is given by its initial value and hence the <span class="hlt">Lagrangian</span> velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1980IJTP...19..405C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1980IJTP...19..405C"><span>Lorentz Invariance of Gravitational <span class="hlt">Lagrangians</span> in the Space of Reference Frames</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cognola, G.</p>
<p>1980-06-01</p>
<p>The recently proposed theories of gravitation in the space of reference frames S are based on a <span class="hlt">Lagrangian</span> invariant with respect to the homogeneous Lorentz group. However, in theories of this kind, the Lorentz invariance is not a necessary consequence of some physical principles, as in the theories <span class="hlt">formulated</span> in space-time, but rather a purely esthetic request. In the present paper, we give a systematic method for the construction of gravitational theories in the space S, without assuming a priori the Lorentz invariance of the <span class="hlt">Lagrangian</span>. The Einstein-Cartan equations of gravitation are obtained requiring only that the <span class="hlt">Lagrangian</span> is invariant under proper rotations and has particular transformation properties under space reflections and space-time dilatations</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950004350','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950004350"><span>A combined <span class="hlt">Eulerian</span>-volume of fraction-<span class="hlt">Lagrangian</span> method for atomization simulation</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Seung, S. P.; Chen, C. P.; Ziebarth, John P.</p>
<p>1994-01-01</p>
<p>The tracking of free surfaces between liquid and gas phases and analysis of the interfacial phenomena between the two during the atomization and breakup process of a liquid fuel jet is modeled. Numerical modeling of liquid-jet atomization requires the resolution of different conservation equations. Detailed <span class="hlt">formulation</span> and validation are presented for the confined dam broken problem, the water surface problem, the single droplet problem, a jet breakup problem, and the liquid column instability problem.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1084178-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1084178-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system"><span>Multi-Phase CFD Modeling of Solid Sorbent Carbon Capture System</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ryan, Emily M.; DeCroix, David; Breault, Ronald W.</p>
<p>2013-07-30</p>
<p>Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD codes for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® <span class="hlt">Eulerian-Lagrangian</span> simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA <span class="hlt">Eulerian-Lagrangian</span> model is able to simulate the system given appropriate simplifying assumptions. FLUENT® <span class="hlt">Eulerian-Eulerian</span> simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040086560','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040086560"><span><span class="hlt">Lagrangian</span> Assimilation of Satellite Data for Climate Studies in the Arctic</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Lindsay, Ronald W.; Zhang, Jin-Lun; Stern, Harry</p>
<p>2004-01-01</p>
<p>Under this grant we have developed and tested a new <span class="hlt">Lagrangian</span> model of sea ice. A <span class="hlt">Lagrangian</span> model keeps track of material parcels as they drift in the model domain. Besides providing a natural framework for the assimilation of <span class="hlt">Lagrangian</span> data, it has other advantages: 1) a model that follows material elements is well suited for a medium such as sea ice in which an element retains its identity for a long period of time; 2) model cells can be added or dropped as needed, allowing the spatial resolution to be increased in areas of high variability or dense observations; 3) ice from particular regions, such as the marginal seas, can be marked and traced for a long time; and 4) slip lines in the ice motion are accommodated more naturally because there is no internal grid. Our work makes use of these strengths of the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MeSol..47..137K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MeSol..47..137K"><span>Forms of null <span class="hlt">Lagrangians</span> in field theories of continuum mechanics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kovalev, V. A.; Radaev, Yu. N.</p>
<p>2012-02-01</p>
<p>The divergence representation of a null <span class="hlt">Lagrangian</span> that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null <span class="hlt">Lagrangian</span> can contain up to 15 independent elements in total. The general form of a null <span class="hlt">Lagrangian</span> in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null <span class="hlt">Lagrangian</span> for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null <span class="hlt">Lagrangians</span> are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to <span class="hlt">formulate</span> a divergence conservation law on solutions to the system.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950014634','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950014634"><span>A <span class="hlt">Lagrangian</span> dynamic subgrid-scale model turbulence</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Meneveau, C.; Lund, T. S.; Cabot, W.</p>
<p>1994-01-01</p>
<p>A new <span class="hlt">formulation</span> of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic <span class="hlt">Lagrangian</span> time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The <span class="hlt">formulation</span> is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the <span class="hlt">Lagrangian</span> tracking through first-order Euler time integration and linear interpolation in space.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MPAG...15...85R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MPAG...15...85R"><span>k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk <span class="hlt">Formulations</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia</p>
<p>2012-06-01</p>
<p>The k-cosymplectic <span class="hlt">Lagrangian</span> and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative <span class="hlt">formulations</span> for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the <span class="hlt">Lagrangian</span> and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk <span class="hlt">formulation</span> on classical mechanics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhFl...25g3302D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhFl...25g3302D"><span>Stochastic-field cavitation model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Dumond, J.; Magagnato, F.; Class, A.</p>
<p>2013-07-01</p>
<p>Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on <span class="hlt">Lagrangian</span> "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel <span class="hlt">formulation</span> called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.L2010Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.L2010Z"><span>Dual domain material point method for multiphase flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zhang, Duan</p>
<p>2017-11-01</p>
<p>Although the particle-in-cell method was first invented in the 60's for fluid computations, one of its later versions, the material point method, is mostly used for solid calculations. Recent development of the multi-velocity <span class="hlt">formulations</span> for multiphase flows and fluid-structure interactions requires the <span class="hlt">Lagrangian</span> capability of the method be combined with <span class="hlt">Eulerian</span> calculations for fluids. Because of different numerical representations of the materials, additional numerical schemes are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed numerical difficulties in various versions of the method. To resolve these difficulties, the dual domain material point method is introduced and improved. Unlike other particle based methods, the material point method uses both <span class="hlt">Lagrangian</span> particles and <span class="hlt">Eulerian</span> mesh, therefore it avoids direct communication between particles. With this unique property and the <span class="hlt">Lagrangian</span> capability of the method, it is shown that a multiscale numerical scheme can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. Numerical examples will be shown. Work sponsored by the next generation code project of LANL.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009EGUGA..1110202W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009EGUGA..1110202W"><span>ATLAS - A new <span class="hlt">Lagrangian</span> transport and mixing model with detailed stratospheric chemistry</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Wohltmann, I.; Rex, M.; Lehmann, R.</p>
<p>2009-04-01</p>
<p>We present a new global Chemical Transport Model (CTM) with full stratospheric chemistry and <span class="hlt">Lagrangian</span> transport and mixing called ATLAS. <span class="hlt">Lagrangian</span> models have some crucial advantages over <span class="hlt">Eulerian</span> grid-box based models, like no numerical diffusion, no limitation of the time step of the model by the CFL criterion, conservation of mixing ratios by design and easy parallelization of code. The transport module is based on a trajectory code developed at the Alfred Wegener Institute. The horizontal and vertical resolution, the vertical coordinate system (pressure, potential temperature, hybrid coordinate) and the time step of the model are flexible, so that the model can be used both for process studies and long-time runs over several decades. Mixing of the <span class="hlt">Lagrangian</span> air parcels is parameterized based on the local shear and strain of the flow with a method similar to that used in the CLaMS model, but with some modifications like a triangulation that introduces no vertical layers. The stratospheric chemistry module was developed at the Institute and includes 49 species and 170 reactions and a detailed treatment of heterogenous chemistry on polar stratospheric clouds. We present an overview over the model architecture, the transport and mixing concept and some validation results. Comparison of model results with tracer data from flights of the ER2 aircraft in the stratospheric polar vortex in 1999/2000 which are able to resolve fine tracer filaments show that excellent agreement with observed tracer structures can be achieved with a suitable mixing parameterization.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017GeoRL..44.4880D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017GeoRL..44.4880D"><span>Time-variant <span class="hlt">Lagrangian</span> transport <span class="hlt">formulation</span> reduces aggregation bias of water and solute mean travel time in heterogeneous catchments</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Danesh-Yazdi, Mohammad; Botter, Gianluca; Foufoula-Georgiou, Efi</p>
<p>2017-05-01</p>
<p>Lack of hydro-bio-chemical data at subcatchment scales necessitates adopting an aggregated system approach for estimating water and solute transport properties, such as residence and travel time distributions, at the catchment scale. In this work, we show that within-catchment spatial heterogeneity, as expressed in spatially variable discharge-storage relationships, can be appropriately encapsulated within a lumped time-varying stochastic <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of transport. This time (variability) for space (heterogeneity) substitution yields mean travel times (MTTs) that are not significantly biased to the aggregation of spatial heterogeneity. Despite the significant variability of MTT at small spatial scales, there exists a characteristic scale above which the MTT is not impacted by the aggregation of spatial heterogeneity. Extensive simulations of randomly generated river networks reveal that the ratio between the characteristic scale and the mean incremental area is on average independent of river network topology and the spatial arrangement of incremental areas.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19890059396&hterms=nozzle+failure&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dnozzle%2Bfailure','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890059396&hterms=nozzle+failure&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dnozzle%2Bfailure"><span>A combined <span class="hlt">Eulerian-Lagrangian</span> two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Mcconnaughey, P. K.; Garcia, R.; Dejong, F. J.; Sabnis, J. S.; Pribik, D. A.</p>
<p>1989-01-01</p>
<p>An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a <span class="hlt">Lagrangian</span> method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22482601','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22482601"><span><span class="hlt">Lagrangian</span> displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Ma, Chi; Varghese, Tomy</p>
<p>2012-04-01</p>
<p>Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires <span class="hlt">Lagrangian</span> description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. <span class="hlt">Lagrangian</span> based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure <span class="hlt">Lagrangian</span> description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our <span class="hlt">Lagrangian</span> approach to strain estimation. Traditional <span class="hlt">Eulerian</span> based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. <span class="hlt">Lagrangian</span> displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920016571&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920016571&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing"><span>A new <span class="hlt">Lagrangian</span> method for real gases at supersonic speed</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Loh, C. Y.; Liou, Meng-Sing</p>
<p>1992-01-01</p>
<p>With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is <span class="hlt">formulated</span> using the <span class="hlt">Lagrangian</span> description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new <span class="hlt">formulation</span> avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the <span class="hlt">Lagrangian</span> level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5367296','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5367296"><span>A non-conventional discontinuous <span class="hlt">Lagrangian</span> for viscous flow</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Marner, F.</p>
<p>2017-01-01</p>
<p>Drawing an analogy with quantum mechanics, a new <span class="hlt">Lagrangian</span> is proposed for a variational <span class="hlt">formulation</span> of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting <span class="hlt">Lagrangian</span> is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28386415','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28386415"><span>A non-conventional discontinuous <span class="hlt">Lagrangian</span> for viscous flow.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Scholle, M; Marner, F</p>
<p>2017-02-01</p>
<p>Drawing an analogy with quantum mechanics, a new <span class="hlt">Lagrangian</span> is proposed for a variational <span class="hlt">formulation</span> of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting <span class="hlt">Lagrangian</span> is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1424084-toroidal-regularization-guiding-center-lagrangian','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1424084-toroidal-regularization-guiding-center-lagrangian"><span>Toroidal regularization of the guiding center <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Burby, J. W.; Ellison, C. L.</p>
<p>2017-11-22</p>
<p>In the <span class="hlt">Lagrangian</span> theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the <span class="hlt">Lagrangian</span> guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the <span class="hlt">formulation</span> of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center <span class="hlt">Lagrangian</span> by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1424084-toroidal-regularization-guiding-center-lagrangian','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1424084-toroidal-regularization-guiding-center-lagrangian"><span>Toroidal regularization of the guiding center <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Burby, J. W.; Ellison, C. L.</p>
<p></p>
<p>In the <span class="hlt">Lagrangian</span> theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the <span class="hlt">Lagrangian</span> guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the <span class="hlt">formulation</span> of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center <span class="hlt">Lagrangian</span> by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less</p>
</li>
</ol>
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<ol class="result-class" start="261">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19990097981','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19990097981"><span><span class="hlt">Eulerian</span> Time-Domain Filtering for Spatial LES</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Pruett, C. David</p>
<p>1997-01-01</p>
<p><span class="hlt">Eulerian</span> time-domain filtering seems to be appropriate for LES (large eddy simulation) of flows whose large coherent structures convect approximately at a common characteristic velocity; e.g., mixing layers, jets, and wakes. For these flows, we develop an approach to LES based on an explicit second-order digital Butterworth filter, which is applied in,the time domain in an <span class="hlt">Eulerian</span> context. The approach is validated through a priori and a posteriori analyses of the simulated flow of a heated, subsonic, axisymmetric jet.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AIPC.1376...29S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AIPC.1376...29S"><span>Multiphase Fluid Dynamics for Spacecraft Applications</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Shyy, W.; Sim, J.</p>
<p>2011-09-01</p>
<p>Multiphase flows involving moving interfaces between different fluids/phases are observed in nature as well as in a wide range of engineering applications. With the recent development of high fidelity computational techniques, a number of challenging multiphase flow problems can now be computed. We introduce the basic notion of the main categories of multiphase flow computation; <span class="hlt">Lagrangian</span>, <span class="hlt">Eulerian</span>, and <span class="hlt">Eulerian-Lagrangian</span> techniques to represent and follow interface, and sharp and continuous interface methods to model interfacial dynamics. The marker-based adaptive <span class="hlt">Eulerian-Lagrangian</span> method, which is one of the most popular methods, is highlighted with microgravity and space applications including droplet collision and spacecraft liquid fuel tank surface stability.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvF...3d4303M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvF...3d4303M"><span>Topology of two-dimensional turbulent flows of dust and gas</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mitra, Dhrubaditya; Perlekar, Prasad</p>
<p>2018-04-01</p>
<p>We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, St<1 . We solve for the particles using both a <span class="hlt">Lagrangian</span> and an <span class="hlt">Eulerian</span> approach (with a shock-capturing scheme). In the latter, the particles are described by a dust-density field and a dust-velocity field. We find the following: the dust-density field in our <span class="hlt">Eulerian</span> simulations has the same correlation dimension d2 as obtained from the clustering of particles in the <span class="hlt">Lagrangian</span> simulations for St<1 ; the cumulative probability distribution function of the dust density coarse grained over a scale r , in the inertial range, has a left tail with a power-law falloff indicating the presence of voids; the energy spectrum of the dust velocity has a power-law range with an exponent that is the same as the gas-velocity spectrum except at very high Fourier modes; the compressibility of the dust-velocity field is proportional to St2. We quantify the topological properties of the dust velocity and the gas velocity through their gradient matrices, called A and B , respectively. Our DNS confirms that the statistics of topological properties of B are the same in <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frames only if the <span class="hlt">Eulerian</span> data are weighed by the dust density. We use this correspondence to study the statistics of topological properties of A in the <span class="hlt">Lagrangian</span> frame from our <span class="hlt">Eulerian</span> simulations by calculating density-weighted probability distribution functions. We further find that in the <span class="hlt">Lagrangian</span> frame, the mean value of the trace of A is negative and its magnitude increases with St approximately as exp(-C /St) with a constant C ≈0.1 . The statistical distribution of different topological structures that appear in the dust flow is different in <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> (density-weighted <span class="hlt">Eulerian</span>) cases, particularly for St close to unity. In both of these cases, for small St the topological structures</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992JCoPh.100..143B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992JCoPh.100..143B"><span>Momentum Advection on a Staggered Mesh</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Benson, David J.</p>
<p>1992-05-01</p>
<p><span class="hlt">Eulerian</span> and ALE (arbitrary <span class="hlt">Lagrangian-Eulerian</span>) hydrodynamics programs usually split a timestep into two parts. The first part is a <span class="hlt">Lagrangian</span> step, which calculates the incremental motion of the material. The second part is referred to as the <span class="hlt">Eulerian</span> step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element <span class="hlt">formulations</span>, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a code.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28425587','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28425587"><span>Hybrid finite difference/finite element immersed boundary method.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>E Griffith, Boyce; Luo, Xiaoyu</p>
<p>2017-12-01</p>
<p>The immersed boundary method is an approach to fluid-structure interaction that uses a <span class="hlt">Lagrangian</span> description of the structural deformations, stresses, and forces along with an <span class="hlt">Eulerian</span> description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require <span class="hlt">Lagrangian</span> meshes that are finer than the <span class="hlt">Eulerian</span> grid. This work introduces a coupling scheme for the immersed boundary method to link the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the <span class="hlt">Eulerian</span> variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed <span class="hlt">Eulerian</span> grid spacing, coarser <span class="hlt">Lagrangian</span> structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The <span class="hlt">Lagrangian-Eulerian</span> coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..1713527P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..1713527P"><span>Inverse constraints for emission fluxes of atmospheric tracers estimated from concentration measurements and <span class="hlt">Lagrangian</span> transport</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pisso, Ignacio; Patra, Prabir; Breivik, Knut</p>
<p>2015-04-01</p>
<p><span class="hlt">Lagrangian</span> transport models based on times series of <span class="hlt">Eulerian</span> fields provide a computationally affordable way of achieving very high resolution for limited areas and time periods. This makes them especially suitable for the analysis of point-wise measurements of atmospheric tracers. We present an application illustrated with examples of greenhouse gases from anthropogenic emissions in urban areas and biogenic emissions in Japan and of pollutants in the Arctic. We asses the algorithmic complexity of the numerical implementation as well as the use of non-procedural techniques such as Object-Oriented programming. We discuss aspects related to the quantification of uncertainty from prior information in the presence of model error and limited number of observations. The case of non-linear constraints is explored using direct numerical optimisation methods.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011icov.conf..765K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011icov.conf..765K"><span>Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.</p>
<p></p>
<p>Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary <span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">formulation</span>. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930065904&hterms=lean&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dlean','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930065904&hterms=lean&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dlean"><span>Computations of spray, fuel-air mixing, and combustion in a lean-premixed-prevaporized combustor</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Dasgupta, A.; Li, Z.; Shih, T. I.-P.; Kundu, K.; Deur, J. M.</p>
<p>1993-01-01</p>
<p>A code was developed for computing the multidimensional flow, spray, combustion, and pollutant formation inside gas turbine combustors. The code developed is based on a <span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">formulation</span> and utilizes an implicit finite-volume method. The focus of this paper is on the spray part of the code (both <span class="hlt">formulation</span> and algorithm), and a number of issues related to the computation of sprays and fuel-air mixing in a lean-premixed-prevaporized combustor. The issues addressed include: (1) how grid spacings affect the diffusion of evaporated fuel, and (2) how spurious modes can arise through modelling of the spray in the <span class="hlt">Lagrangian</span> computations. An upwind interpolation scheme is proposed to account for some effects of grid spacing on the artificial diffusion of the evaporated fuel. Also, some guidelines are presented to minimize errors associated with the spurious modes.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960011642','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960011642"><span>Floating shock fitting via <span class="hlt">Lagrangian</span> adaptive meshes</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Vanrosendale, John</p>
<p>1995-01-01</p>
<p>In recent work we have <span class="hlt">formulated</span> a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting <span class="hlt">Lagrangian</span> Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28726683','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28726683"><span>Canonical-ensemble extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi</p>
<p>2017-10-11</p>
<p>We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended <span class="hlt">Lagrangian</span> BOMD is developed and discussed in the context of the Liouville operator <span class="hlt">formulation</span>. Linear scaling DFT canonical-ensemble extended <span class="hlt">Lagrangian</span> BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. I - General theory</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Van Dommelen, Leon L.; Cowley, Stephen J.</p>
<p>1990-01-01</p>
<p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22666212-santa-barbara-cluster-comparison-test-disph','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22666212-santa-barbara-cluster-comparison-test-disph"><span>SANTA BARBARA CLUSTER COMPARISON TEST WITH DISPH</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Saitoh, Takayuki R.; Makino, Junichiro, E-mail: saitoh@elsi.jp</p>
<p>2016-06-01</p>
<p>The Santa Barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by <span class="hlt">Eulerian</span> mesh and <span class="hlt">Lagrangian</span> smoothed particle hydrodynamics (SPH) codes: mesh codes gave a core with a constant entropy, whereas SPH codes did not. One possible reason for this difference is that mesh codes are not Galilean invariant. Another possible reason is the problem of the SPH method, which might give too much “protection” to cold clumps because of the unphysical surface tension induced at contact discontinuities. In this paper, we apply the density-independent <span class="hlt">formulation</span> of SPH (DISPH), whichmore » can handle contact discontinuities accurately, to simulations of a cluster of galaxies and compare the results with those with the standard SPH. We obtained the entropy core when we adopt DISPH. The size of the core is, however, significantly smaller than those obtained with mesh simulations and is comparable to those obtained with quasi-<span class="hlt">Lagrangian</span> schemes such as “moving mesh” and “mesh free” schemes. We conclude that both the standard SPH without artificial conductivity and <span class="hlt">Eulerian</span> mesh codes have serious problems even with such an idealized simulation, while DISPH, SPH with artificial conductivity, and quasi-<span class="hlt">Lagrangian</span> schemes have sufficient capability to deal with it.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ36002K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ36002K"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for fluid-particle flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kong, Bo; Patel, Ravi G.; Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.</p>
<p>2017-11-01</p>
<p>In this work, we study the performance of three simulation techniques for fluid-particle flows: (1) a volume-filtered Euler-Lagrange approach (EL), (2) a quadrature-based moment method using the anisotropic Gaussian closure (AG), and (3) a traditional two-fluid model. By simulating two problems: particles in frozen homogeneous isotropic turbulence (HIT), and cluster-induced turbulence (CIT), the convergence of the methods under grid refinement is found to depend on the simulation method and the specific problem, with CIT simulations facing fewer difficulties than HIT. Although EL converges under refinement for both HIT and CIT, its statistical results exhibit dependence on the techniques used to extract statistics for the particle phase. For HIT, converging both EE methods (TFM and AG) poses challenges, while for CIT, AG and EL produce similar results. Overall, all three methods face challenges when trying to extract converged, parameter-independent statistics due to the presence of shocks in the particle phase. National Science Foundation and National Energy Technology Laboratory.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhyS...83c5007N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhyS...83c5007N"><span>Some <span class="hlt">Lagrangians</span> for systems without a <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nucci, M. C.; Leach, P. G. L.</p>
<p>2011-03-01</p>
<p>We demonstrate how to construct many different <span class="hlt">Lagrangians</span> for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a <span class="hlt">Lagrangian</span>. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22311051-stochastic-field-cavitation-model','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22311051-stochastic-field-cavitation-model"><span>Stochastic-field cavitation model</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.</p>
<p>2013-07-15</p>
<p>Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on <span class="hlt">Lagrangian</span> “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel <span class="hlt">formulation</span> called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21806100','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21806100"><span>GVVPT2 energy gradient using a <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Theis, Daniel; Khait, Yuriy G; Hoffmann, Mark R</p>
<p>2011-07-28</p>
<p>A <span class="hlt">Lagrangian</span> based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the near-C(2v) minimum on the conical intersection seam between the 1 (1)A(1) and 2 (1)A(1) surfaces of O(3) with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory. © 2011 American Institute of Physics</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24229270','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24229270"><span><span class="hlt">Lagrangian</span> statistics across the turbulent-nonturbulent interface in a turbulent plane jet.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Taveira, Rodrigo R; Diogo, José S; Lopes, Diogo C; da Silva, Carlos B</p>
<p>2013-10-01</p>
<p><span class="hlt">Lagrangian</span> statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of <span class="hlt">Lagrangian</span> statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The <span class="hlt">Lagrangian</span> statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using <span class="hlt">Eulerian</span> statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002IJMPA..17..405H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002IJMPA..17..405H"><span>Hamiltonian vs <span class="hlt">Lagrangian</span> Embedding of a Massive Spin-One Theory Involving Two-Form Field</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Harikumar, E.; Sivakumar, M.</p>
<p></p>
<p>We consider the Hamiltonian and <span class="hlt">Lagrangian</span> embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg <span class="hlt">formulation</span> of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the <span class="hlt">Lagrangian</span> embedded model. We show that to obtain manifestly covariant Stückelberg <span class="hlt">Lagrangian</span> from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900013702','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900013702"><span>The coupling effects of kinematics and flexibility on the <span class="hlt">Lagrangian</span> dynamic <span class="hlt">formulation</span> of open chain deformable links</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Changizi, Koorosh</p>
<p>1989-01-01</p>
<p>A nonlinear <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for the spatial kinematic and dynamic analysis of open chain deformable links consisting of cylindrical joints that connect pairs of flexible links is developed. The special cases of revolute or prismatic joint can also be obtained from the kinematic equations. The kinematic equations are described using a 4x4 matrix method. The configuration of each deformable link in the open loop kinematic chain is identified using a coupled set of relative joint variables, constant geometric parameters, and elastic coordinates. The elastic coordinates define the link deformation with respect to a selected joint coordinate system that is consistent with the kinematic constraints on the boundary of the deformable link. These coordinates can be introduced using approximation techniques such as Rayleigh-Ritz method, finite element technique or any other desired approach. The large relative motion between two neighboring links are defined by a set of joint coordinates which describes the large relative translational and rotational motion between two neighboring joint coordinate systems. The origin of these coordinate systems are rigidly attached to the neighboring links at the joint definition points along the axis of motion.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD19001F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD19001F"><span><span class="hlt">Lagrangian</span> particle drift and surface deformation in a rotating wave on a free liquid surface</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fontana, Paul W.; Francois, Nicolas; Xia, Hua; Punzmann, Horst; Shats, Michael</p>
<p>2017-11-01</p>
<p>A nonlinear model of a rotating wave on the free surface of a liquid is presented. The flow is assumed to be inviscid and irrotational. The wave is constructed as a superposition of two perpendicular, monochromatic standing Stokes waves and is standing-wave-like, but with ``antinodes'' or cells consisting of rotating surface gradients of alternating polarity. <span class="hlt">Lagrangian</span> fluid particle trajectories show a rotational drift about each cell in the direction of wave rotation, corresponding to a rotating Stokes drift. Each cell therefore has a circulating flow and localized angular momentum even though the <span class="hlt">Eulerian</span> flow is irrotational. Meanwhile, the wave sets up a static displacement of the free surface, making a trough in each cell. This static surface gradient provides a centripetal force that may account for additional rotation seen in experiments.</p>
</li>
</ol>
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<ol class="result-class" start="281">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007CoPhC.176..170D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007CoPhC.176..170D"><span>A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>de Niem, D.; Kührt, E.; Motschmann, U.</p>
<p>2007-02-01</p>
<p>A two-dimensional <span class="hlt">Eulerian</span> hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit <span class="hlt">Lagrangian</span> step with an explicit <span class="hlt">Eulerian</span> advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic <span class="hlt">formulation</span>. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890014450','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890014450"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary layer separation. Part 1: General theory</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Vandommelen, Leon L.; Cowley, Stephen J.</p>
<p>1989-01-01</p>
<p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009SIGMA...5..100R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009SIGMA...5..100R"><span>Multisymplectic <span class="hlt">Lagrangian</span> and Hamiltonian Formalisms of Classical Field Theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Román-Roy, Narciso</p>
<p>2009-11-01</p>
<p>This review paper is devoted to presenting the standard multisymplectic <span class="hlt">formulation</span> for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the <span class="hlt">Lagrangian</span> formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new <span class="hlt">formulation</span> (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26575769','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26575769"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas</p>
<p>2015-07-14</p>
<p>A computationally fast quantum mechanical molecular dynamics scheme using an extended <span class="hlt">Lagrangian</span> density functional tight-binding <span class="hlt">formulation</span> has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.358..150M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.358..150M"><span>A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias</p>
<p>2018-04-01</p>
<p>A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is <span class="hlt">formulated</span> in terms of an operator splitting technique in which <span class="hlt">Lagrangian</span> particles are used to discretize an advection operator, and an <span class="hlt">Eulerian</span> mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to <span class="hlt">formulate</span> the projections between the <span class="hlt">Lagrangian</span> particle space and the <span class="hlt">Eulerian</span> finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCHyd.172...48T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCHyd.172...48T"><span>Modeling coupled nanoparticle aggregation and transport in porous media: A <span class="hlt">Lagrangian</span> approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Taghavy, Amir; Pennell, Kurt D.; Abriola, Linda M.</p>
<p>2015-01-01</p>
<p>Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an <span class="hlt">Eulerian</span> modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general <span class="hlt">Lagrangian</span> modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and <span class="hlt">Eulerian</span> modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25437227','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25437227"><span>Modeling coupled nanoparticle aggregation and transport in porous media: a <span class="hlt">Lagrangian</span> approach.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Taghavy, Amir; Pennell, Kurt D; Abriola, Linda M</p>
<p>2015-01-01</p>
<p>Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an <span class="hlt">Eulerian</span> modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general <span class="hlt">Lagrangian</span> modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and <span class="hlt">Eulerian</span> modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media. Copyright © 2014 Elsevier B.V. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....53.3513E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....53.3513E"><span><span class="hlt">Lagrangian</span> simulation of mixing and reactions in complex geochemical systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Engdahl, Nicholas B.; Benson, David A.; Bolster, Diogo</p>
<p>2017-04-01</p>
<p>Simulations of detailed geochemical systems have traditionally been restricted to <span class="hlt">Eulerian</span> reactive transport algorithms. This note introduces a <span class="hlt">Lagrangian</span> method for modeling multicomponent reaction systems. The approach uses standard random walk-based methods for the particle motion steps but allows the particles to interact with each other by exchanging mass of their various chemical species. The colocation density of each particle pair is used to calculate the mass transfer rate, which creates a local disequilibrium that is then relaxed back toward equilibrium using the reaction engine PhreeqcRM. The mass exchange is the only step where the particles interact and the remaining transport and reaction steps are entirely independent for each particle. Several validation examples are presented, which reproduce well-known analytical solutions. These are followed by two demonstration examples of a competitive decay chain and an acid-mine drainage system. The source code, entitled Complex Reaction on Particles (CRP), and files needed to run these examples are hosted openly on GitHub (https://github.com/nbengdahl/CRP), so as to enable interested readers to readily apply this approach with minimal modifications.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1798b0042C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1798b0042C"><span>Modelling emission turbulence-radiation interaction by using a hybrid flamelet/stochastic <span class="hlt">Eulerian</span> field method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Consalvi, Jean-Louis</p>
<p>2017-01-01</p>
<p>The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as `absorption Turbulence Radiation Interaction (TRI)' and `emission TRI'. Emission TRI is related to the non-linear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic <span class="hlt">Eulerian</span> Field Model is used to solve the transport equation of the one-point one-time PDF. In this <span class="hlt">formulation</span>, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic <span class="hlt">Eulerian</span> Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/274296-lagrangian-formulation-component-model-its-connection-skew-symmetric-tensor-description','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/274296-lagrangian-formulation-component-model-its-connection-skew-symmetric-tensor-description"><span><span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the 2(2S+1)-component model and its connection with the skew symmetric/tensor description</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dvoeglazov, V.V.</p>
<p>1993-12-01</p>
<p>In the framework of the 2(2S + 1)-component theory for massless particles, the dynamical invariants have been derived from the <span class="hlt">Lagrangian</span> density which is considered to be a 4-vector. A la Majorana interpretation of the 6-component spinors, the field operators of S=1 particles, as the left- and right-circularly polarized radiation, leads the author to the conserved quantities which are analogous to ones obtained by Lipkin and Sudbery. The scalar <span class="hlt">Lagrangian</span> of this model is shown to be equivalent to the <span class="hlt">Lagrangian</span> of a free massless field, introduced by Hayashi. As a consequence of a new {open_quotes}gauge{close_quotes} invariance this skew-symmetric fieldmore » describes physical particles with the longitudinal components only.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009AGUSM.A34A..01S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009AGUSM.A34A..01S"><span>Implications of <span class="hlt">Lagrangian</span> Tracer Transport for Coupled Chemistry-Climate Simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Stenke, A.</p>
<p>2009-05-01</p>
<p>Today's coupled chemistry-climate models (CCM) consider a large number of trace species and feedback processes. Due to the radiative effect of some species, errors in simulated tracer distributions can feed back to model dynamics. Thus, shortcomings of the applied transport schemes can have severe implications for the overall model performance. Traditional <span class="hlt">Eulerian</span> approaches show a satisfactory performance in case of homogeneously distributed trace species, but they can lead to severe problems when applied to highly inhomogeneous tracer distributions. In case of sharp gradients many schemes show a considerable numerical diffusion. <span class="hlt">Lagrangian</span> approaches, on the other hand, combine a number of favourable numerical properties: They are strictly mass-conserving and do not suffer from numerical diffusion. Therefore they are able to maintain steeper gradients. A further advantage is that they allow the transport of a large number of tracers without being prohibitively expensive. A variety of benefits for stratospheric dynamics and chemistry resulting from a <span class="hlt">Lagrangian</span> transport algorithm are demonstrated by the example of the CCM E39C. In an updated version of E39C, called E39C-A, the operational semi-<span class="hlt">Lagrangian</span> advection scheme has been replaced with the purely <span class="hlt">Lagrangian</span> scheme ATTILA. It will be shown that several model deficiencies can be cured by the choice of an appropriate transport algorithm. The most important advancement concerns the reduction of a pronounced wet bias in the extra- tropical lowermost stratosphere. In turn, the associated temperature error ("cold bias") is significantly reduced. Stratospheric wind variations are now in better agreement with observations, e.g. E39C-A is able to reproduce the stratospheric wind reversal in the Southern Hemisphere in summer which was not captured by the previous model version. Resulting changes in wave propagation and dissipation lead to a weakening of the simulated mean meridional circulation and therefore a more</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26672054','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26672054"><span>Learn the <span class="hlt">Lagrangian</span>: A Vector-Valued RKHS Approach to Identifying <span class="hlt">Lagrangian</span> Systems.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Cheng, Ching-An; Huang, Han-Pang</p>
<p>2016-12-01</p>
<p>We study the modeling of <span class="hlt">Lagrangian</span> systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of <span class="hlt">Lagrangian</span> systems and vector-valued reproducing kernel Hilbert space. We reformulate <span class="hlt">Lagrangian</span> systems with kernels that embed the governing Euler-Lagrange equation-the <span class="hlt">Lagrangian</span> kernels-and show that these kernels span a subspace capturing the <span class="hlt">Lagrangian</span>'s projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's <span class="hlt">Lagrangian</span>, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying <span class="hlt">Lagrangian</span> systems, despite using only inputs and outputs.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JHyDy..30..122C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JHyDy..30..122C"><span>3-D <span class="hlt">Lagrangian</span>-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cheng, Huai-yu; Long, Xin-ping; Ji, Bin; Liu, Qi; Bai, Xiao-rui</p>
<p>2018-02-01</p>
<p>In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D <span class="hlt">Lagrangian</span> technology is developed, which can provide the particle tracks and the 3-D <span class="hlt">Lagrangian</span> coherent structures (LCSs). Combined with the traditional methods based on the <span class="hlt">Eulerian</span> viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D <span class="hlt">Lagrangian</span> technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D <span class="hlt">Lagrangian</span> technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D <span class="hlt">Lagrangian</span> technologies indicates the advantages of the latter. It is demonstrated that the 3-D <span class="hlt">Lagrangian</span> technology is a promising tool in the investigation of complex cavitating flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940017007','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940017007"><span>A semi-<span class="hlt">Lagrangian</span> approach to the shallow water equation</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad</p>
<p>1993-01-01</p>
<p>We present a <span class="hlt">formulation</span> of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-<span class="hlt">Lagrangian</span> time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..SHK.H5003N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..SHK.H5003N"><span>Next Generation Extended <span class="hlt">Lagrangian</span> Quantum-based Molecular Dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Negre, Christian</p>
<p>2017-06-01</p>
<p>A new framework for extended <span class="hlt">Lagrangian</span> first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009JPhA...42U5207C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009JPhA...42U5207C"><span>Unambiguous formalism for higher order <span class="hlt">Lagrangian</span> field theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris</p>
<p>2009-11-01</p>
<p>The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the <span class="hlt">Lagrangian</span> and the Hamiltonian description, since the field equations are <span class="hlt">formulated</span> using the <span class="hlt">Lagrangian</span> on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001AGUFMNG42A0407P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001AGUFMNG42A0407P"><span>Predictability of the <span class="hlt">Lagrangian</span> Motion in the Upper Ocean</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Piterbarg, L. I.; Griffa, A.; Griffa, A.; Mariano, A. J.; Ozgokmen, T. M.; Ryan, E. H.</p>
<p>2001-12-01</p>
<p>The complex non-linear dynamics of the upper ocean leads to chaotic behavior of drifter trajectories in the ocean. Our study is focused on estimating the predictability limit for the position of an individual <span class="hlt">Lagrangian</span> particle or a particle cluster based on the knowledge of mean currents and observations of nearby particles (predictors). The <span class="hlt">Lagrangian</span> prediction problem, besides being a fundamental scientific problem, is also of great importance for practical applications such as search and rescue operations and for modeling the spread of fish larvae. A stochastic multi-particle model for the <span class="hlt">Lagrangian</span> motion has been rigorously <span class="hlt">formulated</span> and is a generalization of the well known "random flight" model for a single particle. Our model is mathematically consistent and includes a few easily interpreted parameters, such as the <span class="hlt">Lagrangian</span> velocity decorrelation time scale, the turbulent velocity variance, and the velocity decorrelation radius, that can be estimated from data. The top Lyapunov exponent for an isotropic version of the model is explicitly expressed as a function of these parameters enabling us to approximate the predictability limit to first order. <span class="hlt">Lagrangian</span> prediction errors for two new prediction algorithms are evaluated against simple algorithms and each other and are used to test the predictability limits of the stochastic model for isotropic turbulence. The first algorithm is based on a Kalman filter and uses the developed stochastic model. Its implementation for drifter clusters in both the Tropical Pacific and Adriatic Sea, showed good prediction skill over a period of 1-2 weeks. The prediction error is primarily a function of the data density, defined as the number of predictors within a velocity decorrelation spatial scale from the particle to be predicted. The second algorithm is model independent and is based on spatial regression considerations. Preliminary results, based on simulated, as well as, real data, indicate that it performs</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20140011468','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20140011468"><span>Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Ko, William L.; Fleischer, Van Tran</p>
<p>2013-01-01</p>
<p>Large deformation displacement transfer functions were <span class="hlt">formulated</span> for deformed shape predictions of highly flexible slender structures like aircraft wings. In the <span class="hlt">formulation</span>, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (<span class="hlt">Eulerian</span>), physical (<span class="hlt">Lagrangian</span>), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1227099','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1227099"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas</p>
<p></p>
<p>A computationally fast quantum mechanical molecular dynamics scheme using an extended <span class="hlt">Lagrangian</span> density functional tight-binding <span class="hlt">formulation</span> has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1227099-extended-lagrangian-density-functional-tight-binding-molecular-dynamics-molecules-solids','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1227099-extended-lagrangian-density-functional-tight-binding-molecular-dynamics-molecules-solids"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas</p>
<p>2015-06-26</p>
<p>A computationally fast quantum mechanical molecular dynamics scheme using an extended <span class="hlt">Lagrangian</span> density functional tight-binding <span class="hlt">formulation</span> has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less</p>
</li>
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<ol class="result-class" start="301">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980197321','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980197321"><span>EUPDF: An <span class="hlt">Eulerian</span>-Based Monte Carlo Probability Density Function (PDF) Solver. User's Manual</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.</p>
<p>1998-01-01</p>
<p>EUPDF is an <span class="hlt">Eulerian</span>-based Monte Carlo PDF solver developed for application with sprays, combustion, parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with the coding required to couple the PDF code to any given flow code and a basic understanding of the EUPDF code structure as well as the models involved in the PDF <span class="hlt">formulation</span>. The source code of EUPDF will be available with the release of the National Combustion Code (NCC) as a complete package.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013NuPhB.869..523R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013NuPhB.869..523R"><span>General <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> for higher spin fields with arbitrary index symmetry. 2. Fermionic fields</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Reshetnyak, A.</p>
<p>2013-04-01</p>
<p>We continue the construction of a <span class="hlt">Lagrangian</span> description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, arXiv:1110.5044 [hep-th</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.326...91S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.326...91S"><span>A hybridizable discontinuous Galerkin method for modeling fluid-structure interaction</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.</p>
<p>2016-12-01</p>
<p>This work presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid-structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG <span class="hlt">formulations</span> for linear elastostatics, a nonlinear elastodynamic model, and arbitrary <span class="hlt">Lagrangian-Eulerian</span> Navier-Stokes are derived. The elasticity <span class="hlt">formulations</span> are written in a <span class="hlt">Lagrangian</span> reference frame, with the nonlinear <span class="hlt">formulation</span> restricted to hyperelastic materials. With these individual solid and fluid <span class="hlt">formulations</span>, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid-solid interface. This coupling is presented, along with the resultant HDG FSI <span class="hlt">formulation</span>. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG <span class="hlt">formulation</span> presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGRC..123.1994T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGRC..123.1994T"><span>Transformation of Deep Water Masses Along <span class="hlt">Lagrangian</span> Upwelling Pathways in the Southern Ocean</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tamsitt, V.; Abernathey, R. P.; Mazloff, M. R.; Wang, J.; Talley, L. D.</p>
<p>2018-03-01</p>
<p>Upwelling of northern deep waters in the Southern Ocean is fundamentally important for the closure of the global meridional overturning circulation and delivers carbon and nutrient-rich deep waters to the sea surface. We quantify water mass transformation along upwelling pathways originating in the Atlantic, Indian, and Pacific and ending at the surface of the Southern Ocean using <span class="hlt">Lagrangian</span> trajectories in an eddy-permitting ocean state estimate. Recent related work shows that upwelling in the interior below about 400 m depth is localized at hot spots associated with major topographic features in the path of the Antarctic Circumpolar Current, while upwelling through the surface layer is more broadly distributed. In the ocean interior upwelling is largely isopycnal; Atlantic and to a lesser extent Indian Deep Waters cool and freshen while Pacific deep waters are more stable, leading to a homogenization of water mass properties. As upwelling water approaches the mixed layer, there is net strong transformation toward lighter densities due to mixing of freshwater, but there is a divergence in the density distribution as Upper Circumpolar Deep Water tends become lighter and dense Lower Circumpolar Deep Water tends to become denser. The spatial distribution of transformation shows more rapid transformation at eddy hot spots associated with major topography where density gradients are enhanced; however, the majority of cumulative density change along trajectories is achieved by background mixing. We compare the <span class="hlt">Lagrangian</span> analysis to diagnosed <span class="hlt">Eulerian</span> water mass transformation to attribute the mechanisms leading to the observed transformation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/510351','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/510351"><span>An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.</p>
<p>1997-06-01</p>
<p>A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a <span class="hlt">Lagrangian</span> model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a <span class="hlt">Eulerian</span> grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of <span class="hlt">Eulerian/Eulerian</span> continuum models and <span class="hlt">Eulerian/Lagrangian</span> discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the <span class="hlt">Lagrangian</span> particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950049298&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950049298&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DLagrangian"><span><span class="hlt">Lagrangian</span> mixed layer modeling of the western equatorial Pacific</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Shinoda, Toshiaki; Lukas, Roger</p>
<p>1995-01-01</p>
<p>Processes that control the upper ocean thermohaline structure in the western equatorial Pacific are examined using a <span class="hlt">Lagrangian</span> mixed layer model. The one-dimensional bulk mixed layer model of Garwood (1977) is integrated along the trajectories derived from a nonlinear 1 1/2 layer reduced gravity model forced with actual wind fields. The Global Precipitation Climatology Project (GPCP) data are used to estimate surface freshwater fluxes for the mixed layer model. The wind stress data which forced the 1 1/2 layer model are used for the mixed layer model. The model was run for the period 1987-1988. This simple model is able to simulate the isothermal layer below the mixed layer in the western Pacific warm pool and its variation. The subduction mechanism hypothesized by Lukas and Lindstrom (1991) is evident in the model results. During periods of strong South Equatorial Current, the warm and salty mixed layer waters in the central Pacific are subducted below the fresh shallow mixed layer in the western Pacific. However, this subduction mechanism is not evident when upwelling Rossby waves reach the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific due to episodes of strong wind and light precipitation associated with the El Nino-Southern Oscillation. Comparison of the results between the <span class="hlt">Lagrangian</span> mixed layer model and a locally forced <span class="hlt">Eulerian</span> mixed layer model indicated that horizontal advection of salty waters from the central Pacific strongly affects the upper ocean salinity variation in the western Pacific, and that this advection is necessary to maintain the upper ocean thermohaline structure in this region.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840024358','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840024358"><span>Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Przekwas, A. J.; Singhal, A. K.; Tam, L. T.</p>
<p>1984-01-01</p>
<p>The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical <span class="hlt">formulation</span> of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1414290','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1414290"><span>An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Patel, Saumil S.; Fischer, Paul F.; Min, Misun</p>
<p></p>
<p>In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary <span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">formulation</span>, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20180002538','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20180002538"><span>Acoustic Radiation Pressure</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Cantrell, John H.</p>
<p>2018-01-01</p>
<p>The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in <span class="hlt">Lagrangian</span> coordinates (not <span class="hlt">Eulerian</span> coordinates) and that the terms in the BST are not the momentum flux density and mean excess <span class="hlt">Eulerian</span> stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in <span class="hlt">Eulerian</span> coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean <span class="hlt">Eulerian</span> pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the <span class="hlt">Eulerian</span> pressure. It is shown that the transformation between <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the <span class="hlt">Lagrangian</span> radiation pressure in the propagation direction is equal to (2K) and the BST result that the <span class="hlt">Eulerian</span> radiation pressure in that direction</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.C32B..06D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.C32B..06D"><span>Discrete-element simulation of sea-ice mechanics: Contact mechanics and granular jamming</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.</p>
<p>2017-12-01</p>
<p><span class="hlt">Lagrangian</span> models of sea-ice dynamics offer several advantages to <span class="hlt">Eulerian</span> continuum methods. Spatial discretization on the ice-floe scale is natural for <span class="hlt">Lagrangian</span> models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in <span class="hlt">Eulerian</span> models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum <span class="hlt">formulations</span>, jamming occurs naturally in dense granular systems simulated in a <span class="hlt">Lagrangian</span> framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-element framework for simulating <span class="hlt">Lagrangian</span> sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22069184-about-non-standard-lagrangians-cosmology','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22069184-about-non-standard-lagrangians-cosmology"><span>About non standard <span class="hlt">Lagrangians</span> in cosmology</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dimitrijevic, Dragoljub D.; Milosevic, Milan</p>
<p></p>
<p>A review of non standard <span class="hlt">Lagrangians</span> present in modern cosmological models will be considered. Well known example of non standard <span class="hlt">Lagrangian</span> is Dirac-Born-Infeld (DBI) type <span class="hlt">Lagrangian</span> for tachyon field. Another type of non standard <span class="hlt">Lagrangian</span> under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory <span class="hlt">Lagrangian</span>. We will investigate homogenous cases of both DBI and p-adic fields and obtain <span class="hlt">Lagrangians</span> of the standard type which have the same equations of motions as aforementioned non standard one.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CPM.....1..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1..103G"><span>Evaluating the performance of the particle finite element method in parallel architectures</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.</p>
<p>2014-05-01</p>
<p>This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based <span class="hlt">formulation</span> of the equations with a hybrid spatial discretization which uses an <span class="hlt">Eulerian</span> mesh and <span class="hlt">Lagrangian</span> particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical <span class="hlt">Eulerian</span> alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve <span class="hlt">Eulerian</span> stages of PFEM-2. However, <span class="hlt">Lagrangian</span> stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical <span class="hlt">Eulerian</span> strategies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960001867','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960001867"><span>Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet <span class="hlt">Formulation</span> in Heated Falling Films</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.</p>
<p>1995-01-01</p>
<p>A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19750023590','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19750023590"><span>An investigation of turbulent transport in the extreme lower atmosphere</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Koper, C. A., Jr.; Sadeh, W. Z.</p>
<p>1975-01-01</p>
<p>A model in which the <span class="hlt">Lagrangian</span> autocorrelation is expressed by a domain integral over a set of usual <span class="hlt">Eulerian</span> autocorrelations acquired concurrently at all points within a turbulence box is proposed along with a method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble to investigate the flow in the extreme lower atmosphere. Simultaneous measurements of turbulent velocity on a turbulence line along the wake axis were carried out utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity is approximated as a realization of a weakly self-stationary random process. Based on the <span class="hlt">Lagrangian</span> autocorrelation it is found that: (1) large diffusion time predominated; (2) ratios of <span class="hlt">Lagrangian</span> to <span class="hlt">Eulerian</span> time and spatial scales were smaller than unity; and, (3) short and long diffusion time scales and diffusion spatial scales were constrained within their <span class="hlt">Eulerian</span> counterparts.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70174360','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70174360"><span>On inter-tidal transport equation</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi</p>
<p>1989-01-01</p>
<p>The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the <span class="hlt">formulation</span> of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the <span class="hlt">Eulerian</span> residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the <span class="hlt">Lagrangian</span> residual current suggest that the long-term transport problem is more closely related to the <span class="hlt">Lagrangian</span> residual current than to the <span class="hlt">Eulerian</span> residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order <span class="hlt">Lagrangian</span> residual current (the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CPM.....5..345F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CPM.....5..345F"><span>A hybrid <span class="hlt">Lagrangian</span> Voronoi-SPH scheme</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.</p>
<p>2018-07-01</p>
<p>A hybrid <span class="hlt">Lagrangian</span> Voronoi-SPH scheme, with an explicit weakly compressible <span class="hlt">formulation</span> for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CPM...tmp...26F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CPM...tmp...26F"><span>A hybrid <span class="hlt">Lagrangian</span> Voronoi-SPH scheme</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.</p>
<p>2017-11-01</p>
<p>A hybrid <span class="hlt">Lagrangian</span> Voronoi-SPH scheme, with an explicit weakly compressible <span class="hlt">formulation</span> for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018BoLMe.166..153S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018BoLMe.166..153S"><span>Comment on: "Corrections to the Mathematical <span class="hlt">Formulation</span> of a Backwards <span class="hlt">Lagrangian</span> Particle Dispersion Model" by Gibson and Sailor (2012: Boundary-Layer Meteorology 145, 399-406)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Stöckl, Stefan; Rotach, Mathias W.; Kljun, Natascha</p>
<p>2018-01-01</p>
<p>We discuss the results of Gibson and Sailor (Boundary-Layer Meteorol 145:399-406, 2012) who suggest several corrections to the mathematical <span class="hlt">formulation</span> of the <span class="hlt">Lagrangian</span> particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367-389, 1996). While most of the suggested corrections had already been implemented in the 1990s, one suggested correction raises a valid point, but results in a violation of the well-mixed criterion. Here we improve their idea and test the impact on model results using a well-mixed test and a comparison with wind-tunnel experimental data. The new approach results in similar dispersion patterns as the original approach, while the approach suggested by Gibson and Sailor leads to erroneously reduced concentrations near the ground in convective and especially forced convective conditions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..MARV13002A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..MARV13002A"><span>Advances in Quantum Trajectory Approaches to Dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Askar, Attila</p>
<p>2001-03-01</p>
<p>The quantum fluid dynamics (QFD) <span class="hlt">formulation</span> is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The <span class="hlt">Lagrangian</span> [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The <span class="hlt">Eulerian</span> [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The <span class="hlt">Lagrangian</span> description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The <span class="hlt">Eulerian</span> representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the <span class="hlt">Lagrangian</span> representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical <span class="hlt">formulation</span> of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016E%26ES...49f2008M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016E%26ES...49f2008M"><span>Verification of transport equations in a general purpose commercial CFD code.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Melot, Matthieu; Nennemann, Bernd; Deschênes, Claire</p>
<p>2016-11-01</p>
<p>In this paper, the Verification and Validation methodology is presented. This method aims to increase the reliability and the trust that can be placed into complex CFD simulations. The first step of this methodology, the code verification is presented in greater details. The CFD transport equations in steady state, transient and Arbitrary <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> (ALE, used for transient moving mesh) <span class="hlt">formulations</span> in Ansys CFX are verified. It is shown that the expected spatial and temporal order of convergence are achieved for the steady state and the transient <span class="hlt">formulations</span>. Unfortunately this is not completely the case for the ALE <span class="hlt">formulation</span>. As for a lot of other commercial and in-house CFD codes, the temporal convergence of the velocity is limited to a first order where a second order would have been expected.</p>
</li>
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<ol class="result-class" start="321">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013IJCFD..27...32C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013IJCFD..27...32C"><span>Hyperviscosity for unstructured ALE meshes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cook, Andrew W.; Ulitsky, Mark S.; Miller, Douglas S.</p>
<p>2013-01-01</p>
<p>An artificial viscosity, originally designed for <span class="hlt">Eulerian</span> schemes, is adapted for use in arbitrary <span class="hlt">Lagrangian-Eulerian</span> simulations. Changes to the <span class="hlt">Eulerian</span> model (dubbed 'hyperviscosity') are discussed, which enable it to work within a <span class="hlt">Lagrangian</span> framework. New features include a velocity-weighted grid scale and a generalised filtering procedure, applicable to either structured or unstructured grids. The model employs an artificial shear viscosity for treating small-scale vorticity and an artificial bulk viscosity for shock capturing. The model is based on the Navier-Stokes form of the viscous stress tensor, including the diagonal rate-of-expansion tensor. A second-order version of the model is presented, in which Laplacian operators act on the velocity divergence and the grid-weighted strain-rate magnitude to ensure that the velocity field remains smooth at the grid scale. Unlike sound-speed-based artificial viscosities, the hyperviscosity model is compatible with the low Mach number limit. The new model outperforms a commonly used <span class="hlt">Lagrangian</span> artificial viscosity on a variety of test problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA588350','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA588350"><span>Nonlinear <span class="hlt">Eulerian</span> Thermoelasticity for Anisotropic Crystals</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2013-08-01</p>
<p>the applied pressure. However, some crystalline materials such as ceramics and hard minerals may retain significant shear strength at finite strain...which elastic properties have been measured. Benefits of using <span class="hlt">Eulerian</span> strain measures for nonlinear elasticity of isotropic materials were extolled by...highly symmetric anharmonic properties . Deviations may be expected for highly anisotropic materials , as shown in Section 4. This work is focused</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EPJH...42..537F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EPJH...42..537F"><span>A contemporary look at Hermann Hankel's 1861 pioneering work on <span class="hlt">Lagrangian</span> fluid dynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Frisch, Uriel; Grimberg, Gérard; Villone, Barbara</p>
<p>2017-12-01</p>
<p>The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with connected documents [Eur. Phys. J. H 42, 557-609 (2017)]. Here we give a critical assessment of Hankel's work, which covers many important aspects of fluid dynamics considered from a <span class="hlt">Lagrangian</span>-coordinates point of view: variational <span class="hlt">formulation</span> in the spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say Lie transport) of vorticity, the <span class="hlt">Lagrangian</span> significance of Clebsch variables, etc. Hankel's work is also put in the perspective of previous and future work. Hence, the action spans about two centuries: from Lagrange's 1760-1761 Turin paper on variational approaches to mechanics and fluid mechanics problems to Arnold's 1966 founding paper on the geometrical/variational <span class="hlt">formulation</span> of incompressible flow. The 22-year-old Hankel - who was to die 12 years later — emerges as a highly innovative master of mathematical fluid dynamics, fully deserving Riemann's assessment that his Preisschrift contains "all manner of good things."</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005JHEP...03..011L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005JHEP...03..011L"><span>BRST theory without Hamiltonian and <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lyakhovich, S. L.; Sharapov, A. A.</p>
<p>2005-03-01</p>
<p>We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST <span class="hlt">formulation</span>, which includes the conventional BV <span class="hlt">Lagrangian</span> and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20150023469','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20150023469"><span>LSPRAY-V: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.</p>
<p>2015-01-01</p>
<p>LSPRAY-V is a <span class="hlt">Lagrangian</span> spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray <span class="hlt">formulation</span>, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1341976-multi-material-closure-model-high-order-finite-element-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1341976-multi-material-closure-model-high-order-finite-element-lagrangian-hydrodynamics"><span>Multi-Material Closure Model for High-Order Finite Element <span class="hlt">Lagrangian</span> Hydrodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...</p>
<p>2016-04-27</p>
<p>We present a new closure model for single fluid, multi-material <span class="hlt">Lagrangian</span> hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–<span class="hlt">Eulerian</span> calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1341976','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1341976"><span>Multi-Material Closure Model for High-Order Finite Element <span class="hlt">Lagrangian</span> Hydrodynamics</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.</p>
<p></p>
<p>We present a new closure model for single fluid, multi-material <span class="hlt">Lagrangian</span> hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–<span class="hlt">Eulerian</span> calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985AmJPh..53..982J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985AmJPh..53..982J"><span>Form of the manifestly covariant <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Johns, Oliver Davis</p>
<p>1985-10-01</p>
<p>The preferred form for the manifestly covariant <span class="hlt">Lagrangian</span> function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' <span class="hlt">Lagrangian</span> and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant <span class="hlt">Lagrangian</span> theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' <span class="hlt">Lagrangian</span>, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives <span class="hlt">Lagrangian</span> theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' <span class="hlt">Lagrangian</span> is a completely adequate basis for covariant <span class="hlt">Lagrangian</span> theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the <span class="hlt">Lagrangian</span> and other four-vector equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013IJMPA..2850142M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013IJMPA..2850142M"><span><span class="hlt">Lagrangian</span> <span class="hlt">Formulation</span> of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Moayedi, S. K.; Setare, M. R.; Khosropour, B.</p>
<p>2013-11-01</p>
<p>In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β‧)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)\\min = \\hbar √ {Dβ +β '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β‧ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.5284P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.5284P"><span>A <span class="hlt">Lagrangian</span> stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Parsakhoo, Zahra; Shao, Yaping</p>
<p>2017-04-01</p>
<p>Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in <span class="hlt">Eulerian</span> models directly. We have developed a <span class="hlt">Lagrangian</span> stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different <span class="hlt">Lagrangian</span> time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDG32004C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDG32004C"><span>Fluid-particle characteristics in fully-developed cluster-induced turbulence</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney</p>
<p>2014-11-01</p>
<p>In this study, we present a theoretical framework for collisional fluid-particle turbulence. To identify the key mechanisms responsible for energy exchange between the two phases, an <span class="hlt">Eulerian-Lagrangian</span> strategy is used to simulate fully-developed cluster-inudced turbulence (CIT) under a range of Reynolds numbers, where fluctuations in particle concentration generate and sustain the carrier-phase turbulence. Using a novel filtering approach, a length-scale separation between the correlated particle velocity and uncorrelated granular temperature (GT) is achieved. This separation allows us to extract the instantaneous <span class="hlt">Eulerian</span> volume fraction, velocity and GT fields from the <span class="hlt">Lagrangian</span> data. Direct comparisons can thus be made with the relevant terms that appear in the multiphase turbulence model. It is shown that the granular pressure is highly anisotropic, and thus additional transport equations (as opposed to a single equation for GT) are necessary in <span class="hlt">formulating</span> a predictive multiphase turbulence model. In addition to reporting the relevant contributions to the Reynolds stresses of each phase, two-point statistics, integral length/timescales, averages conditioned on the local volume fraction, and PDFs of the key multiphase statistics are presented and discussed. The research reported in this paper is partially supported by the HPC equipment purchased through U.S. National Science Foundation MRI Grant Number CNS 1229081 and CRI Grant Number 1205413.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A51A2030N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A51A2030N"><span>Understanding spatial and temporal behavior of sea spray droplets in the marine atmospheric boundary layer using an <span class="hlt">Eulerian-Lagrangian</span> model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nissanka, I. D.; Richter, D. H.</p>
<p>2017-12-01</p>
<p>Previous studies have shown that sea spray droplets can play a significant role in air-sea heat and moisture exchange. The larger spray droplets have potential to transfer considerable amount of mass, momentum and heat, however they remain closer to surface and their residence times are shorter due to the faster settling. On the other hand, smaller droplets have high vertical mobility which allows sufficient time for droplets to adjust to ambient conditions. Hence, to study the heat and moisture characteristics of sea spray droplets it is important to understand how different droplet sizes behave in the Marine Atmospheric Boundary Layer (MABL), especially their temporal evolutions. In this study sea spray droplet transport in the MABL is simulated using Large Eddy Simulation combined with a <span class="hlt">Lagrangian</span> Particle model which represents spray droplets of varying size. The individual droplets are tracked while their radius and temperature evolve based on local ambient conditions. The particles are advected based on the local resolved velocities and the particle dispersion due to sub-filtered scale motions are modeled using a <span class="hlt">Lagrangian</span> stochastic model. In this study a series of simulations are conducted with the focus of understanding fundamental droplet microphysics, which will help characterize and quantify the lifetime and airborne concentrations of spray droplets in the MABL, thus elucidating ongoing knowledge gaps which are impossible to fill using observations alone. We measure the size resolved spray droplet vertical concentrations, particle residence times, and temporal evolution of droplet radius and temperature to explain the behavior of sea spry droplets in MABL. The PDF of residence time of different initial droplet sizes and joint PDFs of droplet life time and radius and temperature for different droplet sizes are calculated to further quantify the temporal and spatial behavior of sea spray droplets in the MABL, which can be used as inputs into bulk models</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AIPC.1770c0069K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AIPC.1770c0069K"><span>Analytical solution of the problem of a shock wave in the collapsing gas in <span class="hlt">Lagrangian</span> coordinates</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kuropatenko, V. F.; Shestakovskaya, E. S.</p>
<p>2016-10-01</p>
<p>It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in <span class="hlt">Lagrangian</span> coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in <span class="hlt">Lagrangian</span> coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and <span class="hlt">Lagrangian</span> coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For <span class="hlt">Lagrangian</span> coordinates the problem is first solved. It is fundamentally different from previously known <span class="hlt">formulations</span> of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18518379','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18518379"><span>Extreme <span class="hlt">Lagrangian</span> acceleration in confined turbulent flow.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kadoch, Benjamin; Bos, Wouter J T; Schneider, Kai</p>
<p>2008-05-09</p>
<p>A <span class="hlt">Lagrangian</span> study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the <span class="hlt">Lagrangian</span> dynamics. It is found that the <span class="hlt">Lagrangian</span> acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the <span class="hlt">Lagrangian</span> acceleration as a function of the radius shows that the influence of the wall on the <span class="hlt">Lagrangian</span> dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the <span class="hlt">Lagrangian</span> statistics between this region, not directly influenced by the walls, and a critical radius which defines a <span class="hlt">Lagrangian</span> boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27176403','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27176403"><span>Turbulent transport with intermittency: Expectation of a scalar concentration.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D</p>
<p>2016-04-01</p>
<p>Scalar transport by turbulent flows is best described in terms of <span class="hlt">Lagrangian</span> parcel motions. Here we measure the <span class="hlt">Eulerian</span> distance travel along <span class="hlt">Lagrangian</span> trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared <span class="hlt">Eulerian</span> displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the <span class="hlt">Eulerian</span> integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the <span class="hlt">Lagrangian</span> integral time and times longer than the <span class="hlt">Eulerian</span> integral time. The very short-time enhancement reflects the underlying <span class="hlt">Lagrangian</span> velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of <span class="hlt">Lagrangian</span> tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CNSNS..39..300K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CNSNS..39..300K"><span>Turbulence and fire-spotting effects into wild-land fire simulators</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kaur, Inderpreet; Mentrelli, Andrea; Bosseur, Frédéric; Filippi, Jean-Baptiste; Pagnini, Gianni</p>
<p>2016-10-01</p>
<p>This paper presents a mathematical approach to model the effects and the role of phenomena with random nature such as turbulence and fire-spotting into the existing wildfire simulators. The <span class="hlt">formulation</span> proposes that the propagation of the fire-front is the sum of a drifting component (obtained from an existing wildfire simulator without turbulence and fire-spotting) and a random fluctuating component. The modelling of the random effects is embodied in a probability density function accounting for the fluctuations around the fire perimeter which is given by the drifting component. In past, this <span class="hlt">formulation</span> has been applied to include these random effects into a wildfire simulator based on an <span class="hlt">Eulerian</span> moving interface method, namely the Level Set Method (LSM), but in this paper the same <span class="hlt">formulation</span> is adapted for a wildfire simulator based on a <span class="hlt">Lagrangian</span> front tracking technique, namely the Discrete Event System Specification (DEVS). The main highlight of the present study is the comparison of the performance of a <span class="hlt">Lagrangian</span> and an <span class="hlt">Eulerian</span> moving interface method when applied to wild-land fire propagation. Simple idealised numerical experiments are used to investigate the potential applicability of the proposed <span class="hlt">formulation</span> to DEVS and to compare its behaviour with respect to the LSM. The results show that DEVS based wildfire propagation model qualitatively improves its performance (e.g., reproducing flank and back fire, increase in fire spread due to pre-heating of the fuel by hot air and firebrands, fire propagation across no fuel zones, secondary fire generation, ...) when random effects are included according to the present <span class="hlt">formulation</span>. The performance of DEVS and LSM based wildfire models is comparable and the only differences which arise among the two are due to the differences in the geometrical construction of the direction of propagation. Though the results presented here are devoid of any validation exercise and provide only a proof of concept, they show a</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/87306','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/87306"><span>Velocity boundary conditions for vorticity <span class="hlt">formulations</span> of the incompressible Navier-Stokes equations</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Kempka, S.N.; Strickland, J.H.; Glass, M.W.</p>
<p>1995-04-01</p>
<p><span class="hlt">formulation</span> to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical <span class="hlt">formulation</span> which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these <span class="hlt">formulations</span> resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. Anmore » analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a <span class="hlt">Lagrangian</span> transport algorithm in the hydrocode ALEGRA. ALEGRA`s <span class="hlt">Lagrangian</span> transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition <span class="hlt">formulation</span> allow vorticity-based <span class="hlt">formulations</span> to be used in a wider range of engineering problems.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26551100','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26551100"><span>"<span class="hlt">Lagrangian</span>" for a Non-<span class="hlt">Lagrangian</span> Field Theory with N=2 Supersymmetry.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian</p>
<p>2015-10-23</p>
<p>We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 <span class="hlt">Lagrangian</span> description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a <span class="hlt">Lagrangian</span> description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.119...45G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.119...45G"><span>Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> ocean model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Gibson, Angus H.; Hogg, Andrew McC.; Kiss, Andrew E.; Shakespeare, Callum J.; Adcroft, Alistair</p>
<p>2017-11-01</p>
<p>We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ALE ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which changes only due to mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITGCM and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel. The split RPE diagnostic demonstrates that the spurious mixing in a lock exchange test case is dominated by horizontal tracer advection, due to the spatial variability in the velocity field. In contrast, the vertical component of spurious mixing dominates in an internal waves test case. MOM6 performs well in this test case owing to its quasi-<span class="hlt">Lagrangian</span> implementation of ALE. Finally, the effects of model resolution are examined in a baroclinic eddies test case. In particular, the vertical component of spurious mixing dominates as horizontal resolution increases, an important consideration as global models evolve towards higher horizontal resolutions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1984JMP....25.2007N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1984JMP....25.2007N"><span>Hamiltonian <span class="hlt">formulation</span> of the KdV equation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nutku, Y.</p>
<p>1984-06-01</p>
<p>We consider the canonical <span class="hlt">formulation</span> of Whitham's variational principle for the KdV equation. This <span class="hlt">Lagrangian</span> is degenerate and we have found it necessary to use Dirac's theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=158803&keyword=nitrate+AND+multiscale&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=158803&keyword=nitrate+AND+multiscale&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>LINKING THE CMAQ AND HYSPLIT MODELING SYSTEM INTERFACE PROGRAM AND EXAMPLE APPLICATION</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>A new software tool has been developed to link the <span class="hlt">Eulerian</span>-based Community Multiscale Air Quality (CMAQ) modeling system with the <span class="hlt">Lagrangian</span>-based HYSPLIT (HYbrid Single-Particle <span class="hlt">Lagrangian</span> Integrated Trajectory) model. Both models require many of the same hourly meteorological...</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29684700','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29684700"><span>How physiological and physical processes contribute to the phenology of cyanobacterial blooms in large shallow lakes: A new Euler-<span class="hlt">Lagrangian</span> coupled model.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Feng, Tao; Wang, Chao; Wang, Peifang; Qian, Jin; Wang, Xun</p>
<p>2018-09-01</p>
<p>Cyanobacterial blooms have emerged as one of the most severe ecological problems affecting large and shallow freshwater lakes. To improve our understanding of the factors that influence, and could be used to predict, surface blooms, this study developed a novel Euler-<span class="hlt">Lagrangian</span> coupled approach combining the <span class="hlt">Eulerian</span> model with agent-based modelling (ABM). The approach was subsequently verified based on monitoring datasets and MODIS data in a large shallow lake (Lake Taihu, China). The <span class="hlt">Eulerian</span> model solves the <span class="hlt">Eulerian</span> variables and physiological parameters, whereas ABM generates the complete life cycle and transport processes of cyanobacterial colonies. This model ensemble performed well in fitting historical data and predicting the dynamics of cyanobacterial biomass, bloom distribution, and area. Based on the calculated physical and physiological characteristics of surface blooms, principal component analysis (PCA) captured the major processes influencing surface bloom formation at different stages (two bloom clusters). Early bloom outbreaks were influenced by physical processes (horizontal transport and vertical turbulence-induced mixing), whereas buoyancy-controlling strategies were essential for mature bloom outbreaks. Canonical correlation analysis (CCA) revealed the combined actions of multiple environment variables on different bloom clusters. The effects of buoyancy-controlling strategies (ISP), vertical turbulence-induced mixing velocity of colony (VMT) and horizontal drift velocity of colony (HDT) were quantitatively compared using scenario simulations in the coupled model. VMT accounted for 52.9% of bloom formations and maintained blooms over long periods, thus demonstrating the importance of wind-induced turbulence in shallow lakes. In comparison, HDT and buoyancy controlling strategies influenced blooms at different stages. In conclusion, the approach developed here presents a promising tool for understanding the processes of onshore/offshore algal</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21418120-backward-phase-flow-fbi-transform-based-eulerian-gaussian-beams-schroedinger-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21418120-backward-phase-flow-fbi-transform-based-eulerian-gaussian-beams-schroedinger-equation"><span>The backward phase flow and FBI-transform-based <span class="hlt">Eulerian</span> Gaussian beams for the Schroedinger equation</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Leung Shingyu, E-mail: masyleung@ust.h; Qian Jianliang, E-mail: qian@math.msu.ed</p>
<p>2010-11-20</p>
<p>We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based <span class="hlt">Eulerian</span> Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of <span class="hlt">Eulerian</span> Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the <span class="hlt">Eulerian</span> Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the <span class="hlt">Eulerian</span> Gaussian beam framework. Essentially we reinitialize beam propagation by applying themore » FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017RSPSA.47370558O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017RSPSA.47370558O"><span><span class="hlt">Lagrangian</span> averaging with geodesic mean</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Oliver, Marcel</p>
<p>2017-11-01</p>
<p>This paper revisits the derivation of the <span class="hlt">Lagrangian</span> averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy <span class="hlt">Lagrangian</span> of an ideal fluid yields the LAE <span class="hlt">Lagrangian</span>. The derivation presented here assumes a Euclidean spatial domain without boundaries.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29225505','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29225505"><span><span class="hlt">Lagrangian</span> averaging with geodesic mean.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Oliver, Marcel</p>
<p>2017-11-01</p>
<p>This paper revisits the derivation of the <span class="hlt">Lagrangian</span> averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy <span class="hlt">Lagrangian</span> of an ideal fluid yields the LAE <span class="hlt">Lagrangian</span>. The derivation presented here assumes a Euclidean spatial domain without boundaries.</p>
</li>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753b2042L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753b2042L"><span>Forced pitch motion of wind turbines</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Leble, V.; Barakos, G.</p>
<p>2016-09-01</p>
<p>The possibility of a wind turbine entering vortex ring state during pitching oscillations is explored in this paper. The aerodynamic performance of the rotor was computed using the Helicopter Multi-Block flow solver. This code solves the Navier-Stokes equations in integral form using the arbitrary <span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">formulation</span> for time-dependent domains with moving boundaries. A 10-MW wind turbine was put to perform yawing and pitching oscillations suggesting the partial vortex ring state during pitching motion. The results also show the strong effect of the frequency and amplitude of oscillations on the wind turbine performance.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018EPJWC.18002117V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018EPJWC.18002117V"><span>Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vimmr, Jan; Bublík, Ondřej; Prausová, Helena; Hála, Jindřich; Pešek, Luděk</p>
<p>2018-06-01</p>
<p>This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) <span class="hlt">formulation</span> completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20364958','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20364958"><span>Asymptotic shape of the region visited by an <span class="hlt">Eulerian</span> walker.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kapri, Rajeev; Dhar, Deepak</p>
<p>2009-11-01</p>
<p>We study an <span class="hlt">Eulerian</span> walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, <RN2> approximately <RN2> approximately N2nu, shows a crossover from the <span class="hlt">Eulerian</span> (nu=1/3) to a simple random-walk (nu=1/2) behavior.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985PhRvD..31.3104A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985PhRvD..31.3104A"><span>Spinor matter fields in SL(2,C) gauge theories of gravity: <span class="hlt">Lagrangian</span> and Hamiltonian approaches</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Antonowicz, Marek; Szczyrba, Wiktor</p>
<p>1985-06-01</p>
<p>We consider the SL(2,C)-covariant <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian <span class="hlt">formulation</span>. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant <span class="hlt">formulation</span> enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian <span class="hlt">formulation</span> the primary constraints, which are generic for first-order matter <span class="hlt">Lagrangians</span> (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPlPh..82c9004B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPlPh..82c9004B"><span>The initial value problem in <span class="hlt">Lagrangian</span> drift kinetic theory</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Burby, J. W.</p>
<p>2016-06-01</p>
<p>> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space <span class="hlt">Lagrangian</span> instead of the usual `field particle' <span class="hlt">Lagrangian</span>. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional <span class="hlt">formulations</span>, does not support the troublesome rapidly varying modes.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1088058','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1088058"><span>Penetration of rod projectiles in semi-infinite targets : a validation test for <span class="hlt">Eulerian</span> X-FEM in ALEGRA.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Park, Byoung Yoon; Leavy, Richard Brian; Niederhaus, John Henry J.</p>
<p>2013-03-01</p>
<p>The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the <span class="hlt">Eulerian</span> frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA <span class="hlt">formulation</span>. The X-FEM results for depth of penetration differ from previously measured experimental data by lessmore » than 2%, and from the standard <span class="hlt">formulation</span> results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.347..183B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.347..183B"><span>An Immersed Boundary method with divergence-free velocity interpolation and force spreading</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Bao, Yuanxun; Donev, Aleksandar; Griffith, Boyce E.; McQueen, David M.; Peskin, Charles S.</p>
<p>2017-10-01</p>
<p>The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB <span class="hlt">formulation</span> uses an <span class="hlt">Eulerian</span> representation of the fluid and a <span class="hlt">Lagrangian</span> representation of the structure. The <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated <span class="hlt">Lagrangian</span> velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother <span class="hlt">Lagrangian</span> forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010028951','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010028951"><span><span class="hlt">Lagrangian</span> Approach to Jet Mixing and Optimization of the Reactor for Production of Carbon Nanotubes</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Povitsky, Alex; Salas, Manuel D.</p>
<p>2001-01-01</p>
<p>This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process for the production of carbon nanotubes from gaseous carbon oxide, The goal is to achieve rapid and uniform heating of catalyst particles by an optimal arrangement of jets. A mixed <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approach is implemented to track the temperature of catalyst particles along their trajectories as a function of time. The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor configuration is explained in terms of features of particle trajectories. The trajectories most exposed to the hot jets appear to be the most problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor configuration with three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhFl...21f5101K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhFl...21f5101K"><span><span class="hlt">Lagrangian</span> particles with mixing. I. Simulating scalar transport</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Klimenko, A. Y.</p>
<p>2009-06-01</p>
<p>The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking <span class="hlt">Lagrangian</span> particles with scalar properties and assess errors associated with this scheme. Particles with scalar properties and localized mixing represent an alternative <span class="hlt">formulation</span> for the process, which is selected to represent the continuous diffusion. Simulating diffusion by <span class="hlt">Lagrangian</span> particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by <span class="hlt">Lagrangian</span> particles with localized mixing is specifically considered.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21044884-assessment-eulerian-particle-flamelet-model-nonpremixed-turbulent-jet-flames','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21044884-assessment-eulerian-particle-flamelet-model-nonpremixed-turbulent-jet-flames"><span>Assessment of the <span class="hlt">Eulerian</span> particle flamelet model for nonpremixed turbulent jet flames</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Kim, Seong-Ku; Kim, Yongmo</p>
<p>2008-07-15</p>
<p>Although the <span class="hlt">Eulerian</span> particle flamelet model (EPFM) recently proposed by Barths et al. [Proc. Combust. Inst. 27 (1998) 1841-1847] has shown the potential capabilities to realistically predict detailed pollutant (NO{sub x}, soot) formation in a turbulent reacting flow occurring within practical combustion devices, there still exists room to improve the predicative capability in terms of local flame structure and turbulence-chemistry interaction. In this study, the EPFM approach was applied to simulate two turbulent nonpremixed jet flames of CO/H{sub 2}/N{sub 2} fuel having the same jet Reynolds number but different nozzle diameters, and the capability of predicting the NO{sub x} formationmore » as well as both similarity of major species and sensitivity of minor species to fluid-dynamic scaling for the two flames has been assessed deeply in terms of both conditional and unconditional mean structures. The present results indicate that the original EPFM substantially overpredicts the conditional scalar dissipation rate at the downstream region and consequently underpredicts the streamwise decay of superequilibrium radical concentrations to the equilibrium state. In this study, in order to correctly estimate the averaged conditional scalar dissipation rate, a new modeling of the conditional scalar dissipation rate based on a least-squares fit through a mass weighted spatial distribution has been devised. In terms of both conditional and unconditional means, the EPFM utilizing this new procedure yields nearly the same results as the <span class="hlt">Lagrangian</span> flamelet model, and provides closer agreement with experimental data than the original EPFM approach. (author)« less</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=85010&Lab=NERL&keyword=Network+AND+security&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=85010&Lab=NERL&keyword=Network+AND+security&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>QUANTIFYING SUBGRID POLLUTANT VARIABILITY IN <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>In order to properly assess human risk due to exposure to hazardous air pollutants or air toxics, detailed information is needed on the location and magnitude of ambient air toxic concentrations. Regional scale <span class="hlt">Eulerian</span> air quality models are typically limited to relatively coar...</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25059889','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25059889"><span><span class="hlt">Lagrangian</span> postprocessing of computational hemodynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Shadden, Shawn C; Arzani, Amirhossein</p>
<p>2015-01-01</p>
<p>Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform <span class="hlt">Lagrangian</span> particle tracking, and other <span class="hlt">Lagrangian</span>-based postprocessing. As described herein, <span class="hlt">Lagrangian</span> methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review <span class="hlt">Lagrangian</span> methods that have been used in post-processing velocity data of cardiovascular flows.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4289096','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4289096"><span><span class="hlt">Lagrangian</span> postprocessing of computational hemodynamics</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Shadden, Shawn C.; Arzani, Amirhossein</p>
<p>2014-01-01</p>
<p>Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform <span class="hlt">Lagrangian</span> particle tracking, and other <span class="hlt">Lagrangian</span>-based postprocessing. As described herein, <span class="hlt">Lagrangian</span> methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review <span class="hlt">Lagrangian</span> methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..15.8041M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..15.8041M"><span>Testing of a new dense gas approach in the <span class="hlt">Lagrangian</span> Dispersion Model SPRAY.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mortarini, Luca; Alessandrini, Stefano; Ferrero, Enrico; Anfossi, Domenico; Manfrin, Massimiliano</p>
<p>2013-04-01</p>
<p>A new original method for the dispersion of a positively and negatively buoyant plume is proposed. The buoyant pollutant movement is treated introducing a fictitious scalar inside the <span class="hlt">Lagrangian</span> Stochastic Particle Model SPRAY. The method is based on the same idea of Alessandrini and Ferrero (Phys. A 388:1375-1387, 2009) for the treatment of a background substance entrainment into the plume. In this application, the fictitious scalar is the density and momentum difference between the plume portions and the environment air that naturally takes into account the interaction between the plume and the environment. As a consequence, no more particles than those inside the plume have to be released to simulate the entrainment of the background air temperature. In this way the entrainment is properly simulated and the plume sink is calculated from the local property of the flow. This new approach is wholly <span class="hlt">Lagrangian</span> in the sense that the <span class="hlt">Eulerian</span> grid is only used to compute the propriety of a portion of the plume from the particles contained in every cell. No equation of the bulk plume is solved on a fixed grid. To thoroughly test the turbulent velocity field calculated by the model, the latter is compared with a water tank experiment carried out in the TURLAB laboratory in Turin (Italy). A vertical density driven current was created releasing a saline solution (salt and water) in a water tank with no mean flow. The experiment reproduces in physical similarity, based on the density Froud number, the release of a dense gas in the planetary boundary layer and the Particle Image Velocimetry technique has been used to analyze the buoyancy generated velocity field. The high temporal and spatial resolution of the measurements gives a deep insight to the problems of the bouncing of the dense gas and of the creation of the outflow velocity at the ground.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013753','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013753"><span>Forecasting Future Sea Ice Conditions: A <span class="hlt">Lagrangian</span> Approach</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2015-09-30</p>
<p>1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Forecasting Future Sea Ice Conditions: A <span class="hlt">Lagrangian</span> ...GCMs participating in IPCC AR5 agree with observed source region patterns from the satellite- derived dataset. 4- Compare <span class="hlt">Lagrangian</span> ice... <span class="hlt">Lagrangian</span> sea-ice back trajectories to estimate thermodynamic and dynamic (advection) ice loss. APPROACH We use a <span class="hlt">Lagrangian</span> trajectory model to</p>
</li>
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<ol class="result-class" start="361">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JMP....59c2904M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JMP....59c2904M"><span>On the <span class="hlt">Lagrangian</span> description of dissipative systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Martínez-Pérez, N. E.; Ramírez, C.</p>
<p>2018-03-01</p>
<p>We consider the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and conserved quantities, like the Hamiltonian, that generate symmetry transformations and do not correspond to observables. We show that there are simple relations among the equations satisfied by these two types of quantities. In the case of the damped harmonic oscillator, from the quantities obtained by the Noether theorem follows the algebra of Feshbach and Tikochinsky. Furthermore, if we consider the whole dynamics, the degrees of freedom separate into a physical and an unphysical sector. We analyze several cases, with linear and nonlinear dissipative forces; the physical consistency of the solutions is ensured, observing that the unphysical sector has always the trivial solution.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..APR.S1054C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..APR.S1054C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chacon, Luis; Del-Castillo-Negrete, Diego</p>
<p>2012-03-01</p>
<p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel <span class="hlt">Lagrangian</span> Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the <span class="hlt">Lagrangian</span> Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical <span class="hlt">formulation</span>, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhyA..393..337B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhyA..393..337B"><span>Option volatility and the acceleration <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Baaquie, Belal E.; Cao, Yang</p>
<p>2014-01-01</p>
<p>This paper develops a volatility formula for option on an asset from an acceleration <span class="hlt">Lagrangian</span> model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent <span class="hlt">Lagrangian</span>. The acceleration <span class="hlt">Lagrangian</span> is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the <span class="hlt">Lagrangian</span> is fixed. The call option price is obtained using the conditional probability and the path integral method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002APS..DFD.AK010R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002APS..DFD.AK010R"><span>Stochastic modeling of <span class="hlt">Lagrangian</span> accelerations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Reynolds, Andy</p>
<p>2002-11-01</p>
<p>It is shown how Sawford's second-order <span class="hlt">Lagrangian</span> stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a <span class="hlt">Lagrangian</span> stochastic model that is consistent with both the measured distribution of <span class="hlt">Lagrangian</span> accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CMaPh.351..689B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CMaPh.351..689B"><span>A Constructive Approach to Regularity of <span class="hlt">Lagrangian</span> Trajectories for Incompressible Euler Flow in a Bounded Domain</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Besse, Nicolas; Frisch, Uriel</p>
<p>2017-04-01</p>
<p>The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the Euler equations and second, by taking advantage of analyticity results of the <span class="hlt">Lagrangian</span> trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the <span class="hlt">Lagrangian</span> map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the <span class="hlt">Lagrangian</span> flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the <span class="hlt">Lagrangian</span> trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-<span class="hlt">Lagrangian</span> method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29507245','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29507245"><span>Coherent <span class="hlt">Lagrangian</span> swirls among submesoscale motions.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G</p>
<p>2018-03-05</p>
<p>The emergence of coherent <span class="hlt">Lagrangian</span> swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for <span class="hlt">Lagrangian</span> coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent <span class="hlt">Lagrangian</span> eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20080034887','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20080034887"><span>LSPRAY-III: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.</p>
<p>2008-01-01</p>
<p>LSPRAY-III is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray <span class="hlt">formulation</span>, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-III, we have advanced the state-of-the-art in spray computations in several important ways.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040050627','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040050627"><span>LSPRAY-II: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.</p>
<p>2004-01-01</p>
<p>LSPRAY-II is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray <span class="hlt">formulation</span>, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-II, we have advanced the state-of-the-art in spray computations in several important ways.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JPhA...43R5204S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JPhA...43R5204S"><span>Alternative kinetic energy metrics for <span class="hlt">Lagrangian</span> systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sarlet, W.; Prince, G.</p>
<p>2010-11-01</p>
<p>We examine <span class="hlt">Lagrangian</span> systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative <span class="hlt">Lagrangians</span> with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such <span class="hlt">Lagrangians</span>. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous <span class="hlt">Lagrangians</span> for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002JMP....43.1441N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002JMP....43.1441N"><span>Multi-<span class="hlt">Lagrangians</span> for integrable systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nutku, Y.; Pavlov, M. V.</p>
<p>2002-03-01</p>
<p>We propose a general scheme to construct multiple <span class="hlt">Lagrangians</span> for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new <span class="hlt">Lagrangian</span> and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 <span class="hlt">Lagrangians</span> which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new <span class="hlt">Lagrangian</span> for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JCoPh.229.8888L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JCoPh.229.8888L"><span>The backward phase flow and FBI-transform-based <span class="hlt">Eulerian</span> Gaussian beams for the Schrödinger equation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Leung, Shingyu; Qian, Jianliang</p>
<p>2010-11-01</p>
<p>We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based <span class="hlt">Eulerian</span> Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of <span class="hlt">Eulerian</span> Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the <span class="hlt">Eulerian</span> Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the <span class="hlt">Eulerian</span> Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010CompM..46..147S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010CompM..46..147S"><span>Full <span class="hlt">Eulerian</span> simulations of biconcave neo-Hookean particles in a Poiseuille flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro</p>
<p>2010-03-01</p>
<p>For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full <span class="hlt">Eulerian</span> finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the <span class="hlt">Eulerian</span> frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present <span class="hlt">Eulerian</span> approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MNRAS.471.1215S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MNRAS.471.1215S"><span>Dynamical instability of a charged gaseous cylinder</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sharif, M.; Mumtaz, Saadia</p>
<p>2017-10-01</p>
<p>In this paper, we discuss dynamical instability of a charged dissipative cylinder under radial oscillations. For this purpose, we follow the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approaches to evaluate linearized perturbed equation of motion. We <span class="hlt">formulate</span> perturbed pressure in terms of adiabatic index by applying the conservation of baryon numbers. A variational principle is established to determine characteristic frequencies of oscillation which define stability criteria for a gaseous cylinder. We compute the ranges of radii as well as adiabatic index for both charged and uncharged cases in Newtonian and post-Newtonian limits. We conclude that dynamical instability occurs in the presence of charge if the gaseous cylinder contracts to the radius R*.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27739805','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27739805"><span>Target <span class="hlt">Lagrangian</span> kinematic simulation for particle-laden flows.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Murray, S; Lightstone, M F; Tullis, S</p>
<p>2016-09-01</p>
<p>The target <span class="hlt">Lagrangian</span> kinematic simulation method was motivated as a stochastic <span class="hlt">Lagrangian</span> particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target <span class="hlt">Lagrangian</span> integral timescale. In addition to recovering the expected <span class="hlt">Lagrangian</span> properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26827193','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26827193"><span>Communication: A simplified coupled-cluster <span class="hlt">Lagrangian</span> for polarizable embedding.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Krause, Katharina; Klopper, Wim</p>
<p>2016-01-28</p>
<p>A simplified coupled-cluster <span class="hlt">Lagrangian</span>, which is linear in the <span class="hlt">Lagrangian</span> multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the <span class="hlt">Lagrangian</span> multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the <span class="hlt">Lagrangian</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22493676-communication-simplified-coupled-cluster-lagrangian-polarizable-embedding','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22493676-communication-simplified-coupled-cluster-lagrangian-polarizable-embedding"><span>Communication: A simplified coupled-cluster <span class="hlt">Lagrangian</span> for polarizable embedding</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu</p>
<p></p>
<p>A simplified coupled-cluster <span class="hlt">Lagrangian</span>, which is linear in the <span class="hlt">Lagrangian</span> multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the <span class="hlt">Lagrangian</span> multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the <span class="hlt">Lagrangian</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018LMaPh.108..699C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018LMaPh.108..699C"><span>A Chiang-type <span class="hlt">lagrangian</span> in CP^2</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cannas da Silva, Ana</p>
<p>2018-03-01</p>
<p>We analyse a monotone <span class="hlt">lagrangian</span> in CP^2 that is hamiltonian isotopic to the standard <span class="hlt">lagrangian</span> RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This <span class="hlt">lagrangian</span> thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020052438','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020052438"><span><span class="hlt">Eulerian</span> Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>He, Guowei; Bushnell, Dennis M. (Technical Monitor)</p>
<p>2002-01-01</p>
<p>The <span class="hlt">Eulerian</span> mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An <span class="hlt">Eulerian</span> mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IzMat..80.1257T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IzMat..80.1257T"><span>Special Bohr-Sommerfeld <span class="hlt">Lagrangian</span> submanifolds</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tyurin, N. A.</p>
<p>2016-12-01</p>
<p>We introduce a new notion in symplectic geometry, that of speciality for <span class="hlt">Lagrangian</span> submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld <span class="hlt">Lagrangian</span> submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012PhFl...24h5101V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012PhFl...24h5101V"><span>A <span class="hlt">Lagrangian</span> subgrid-scale model with dynamic estimation of <span class="hlt">Lagrangian</span> time scale for large eddy simulation of complex flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Verma, Aman; Mahesh, Krishnan</p>
<p>2012-08-01</p>
<p>The dynamic <span class="hlt">Lagrangian</span> averaging approach for the dynamic Smagorinsky model for large eddy simulation is extended to an unstructured grid framework and applied to complex flows. The <span class="hlt">Lagrangian</span> time scale is dynamically computed from the solution and does not need any adjustable parameter. The time scale used in the standard <span class="hlt">Lagrangian</span> model contains an adjustable parameter θ. The dynamic time scale is computed based on a "surrogate-correlation" of the Germano-identity error (GIE). Also, a simple material derivative relation is used to approximate GIE at different events along a pathline instead of <span class="hlt">Lagrangian</span> tracking or multi-linear interpolation. Previously, the time scale for homogeneous flows was computed by averaging along directions of homogeneity. The present work proposes modifications for inhomogeneous flows. This development allows the <span class="hlt">Lagrangian</span> averaged dynamic model to be applied to inhomogeneous flows without any adjustable parameter. The proposed model is applied to LES of turbulent channel flow on unstructured zonal grids at various Reynolds numbers. Improvement is observed when compared to other averaging procedures for the dynamic Smagorinsky model, especially at coarse resolutions. The model is also applied to flow over a cylinder at two Reynolds numbers and good agreement with previous computations and experiments is obtained. Noticeable improvement is obtained using the proposed model over the standard <span class="hlt">Lagrangian</span> model. The improvement is attributed to a physically consistent <span class="hlt">Lagrangian</span> time scale. The model also shows good performance when applied to flow past a marine propeller in an off-design condition; it regularizes the eddy viscosity and adjusts locally to the dominant flow features.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1364765','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1364765"><span>Drekar v.2.0</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Seefeldt, Ben; Sondak, David; Hensinger, David M.</p>
<p></p>
<p>Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element <span class="hlt">formulations</span>, stabilized finite element <span class="hlt">formulations</span>, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.327...67W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.327...67W"><span>Coupling fluid-structure interaction with phase-field fracture</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Wick, Thomas</p>
<p>2016-12-01</p>
<p>In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary <span class="hlt">Lagrangian-Eulerian</span> technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-<span class="hlt">formulated</span> in <span class="hlt">Lagrangian</span> coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented <span class="hlt">Lagrangian</span> iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26613354','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26613354"><span>Dredging for dilution: A simulation based case study in a Tidal River.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Bilgili, Ata; Proehl, Jeffrey A; Swift, M Robinson</p>
<p>2016-02-01</p>
<p>A 2-D hydrodynamic finite element model with a <span class="hlt">Lagrangian</span> particle module is used to investigate the effects of dredging on the hydrodynamics and the horizontal dilution of pollutant particles originating from a wastewater treatment facility (WWTF) in tidal Oyster River in New Hampshire, USA. The model is driven by the semi-diurnal (M2) tidal component and includes the effect of flooding and drying of riverine mud flats. The particle tracking method consists of tidal advection plus a horizontal random walk model of sub-grid scale turbulent processes. Our approach is to perform continuous pollutant particle releases from the outfall, simulating three different scenarios: a base-case representing the present conditions and two different dredged channel/outfall location configurations. Hydrodynamics are investigated in an <span class="hlt">Eulerian</span> framework and <span class="hlt">Lagrangian</span> particle dilution improvement ratios are calculated for all cases. Results show that the simulated hydrodynamics are consistent with observed conditions. <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residuals predict an outward path suggesting flushing of pollutants on longer (>M2) time scales. Simulated dilution maps show that, in addition to dredging, the relocation of the WWTF outfall into the dredged main channel is required for increased dilution performance. The methodology presented here can be applied to similar managerial problems in all similar systems worldwide with relatively little effort, with the combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods working together towards a better solution. The statistical significance brought into methodology, by using a large number of particles (16000 in this case), is to be emphasized, especially with the growing number of networked parallel computer clusters worldwide. This paper improves on the study presented in Bilgili et al., 2006b, by adding an <span class="hlt">Eulerian</span> analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFD.D7004C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFD.D7004C"><span><span class="hlt">Eulerian</span> Simulation of Acoustic Waves Over Long Range in Realistic Environments</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chitta, Subhashini; Steinhoff, John</p>
<p>2015-11-01</p>
<p>In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its <span class="hlt">Eulerian</span> treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an <span class="hlt">Eulerian</span> solution of the wave equation. However, conventional <span class="hlt">Eulerian</span> methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70012388','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70012388"><span>Littoral transport in the surf zone elucidated by an <span class="hlt">Eulerian</span> sediment tracer.</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Duane, D.B.; James, W.R.</p>
<p>1980-01-01</p>
<p>An <span class="hlt">Eulerian</span>, or time integration, sand tracer experiment was designed and carried out in the surf zone near Pt. Mugu, California on April 19, 1972. Data indicate that conditions of stationarity and finite boundaries required for proper application of <span class="hlt">Eulerian</span> tracer theory exist for short time periods in the surf zone. Grain counts suggest time required for tracer sand to attain equilibrium concentration is on the order of 30-60 minutes. Grain counts also indicate transport (discharge) was strongly dependent upon grain size, with the maximum rate occurring in the size 2.5-2.75 phi, decreasing to both finer and coarser sizes. The measured instantaneous transport was at the annual rate of 2.4 x 106 m3/yr.- Authors</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.; Willis, E. A.</p>
<p>1990-01-01</p>
<p>A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900004433','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900004433"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.; Willis, E. A.</p>
<p>1989-01-01</p>
<p>A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890010209','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890010209"><span>Mixed <span class="hlt">formulation</span> for frictionless contact problems</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Noor, Ahmed K.; Kim, Kyun O.</p>
<p>1989-01-01</p>
<p>Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical <span class="hlt">formulation</span> is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the <span class="hlt">formulation</span> by using a perturbed <span class="hlt">Lagrangian</span> approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JGRC..120.3624L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JGRC..120.3624L"><span>Seagrass metabolism across a productivity gradient using the eddy covariance, <span class="hlt">Eulerian</span> control volume, and biomass addition techniques</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Long, Matthew H.; Berg, Peter; Falter, James L.</p>
<p>2015-05-01</p>
<p>The net ecosystem metabolism of the seagrass Thalassia testudinum was studied across a nutrient and productivity gradient in Florida Bay, Florida, using the <span class="hlt">Eulerian</span> control volume, eddy covariance, and biomass addition techniques. In situ oxygen fluxes were determined by a triangular <span class="hlt">Eulerian</span> control volume with sides 250 m long and by eddy covariance instrumentation at its center. The biomass addition technique evaluated the aboveground seagrass productivity through the net biomass added. The spatial and temporal resolutions, accuracies, and applicability of each method were compared. The eddy covariance technique better resolved the short-term flux rates and the productivity gradient across the bay, which was consistent with the long-term measurements from the biomass addition technique. The net primary production rates from the biomass addition technique, which were expected to show greater autotrophy due to the exclusion of sediment metabolism and belowground production, were 71, 53, and 30 mmol carbon m-2 d-1 at 3 sites across the bay. The net ecosystem metabolism was 35, 25, and 11 mmol oxygen m-2 d-1 from the eddy covariance technique and 10, -103, and 14 mmol oxygen m-2 d-1 from the <span class="hlt">Eulerian</span> control volume across the same sites, respectively. The low-flow conditions in the shallow bays allowed for periodic stratification and long residence times within the <span class="hlt">Eulerian</span> control volume that likely reduced its precision. Overall, the eddy covariance technique had the highest temporal resolution while producing accurate long-term flux rates that surpassed the capabilities of the biomass addition and <span class="hlt">Eulerian</span> control volume techniques in these shallow coastal bays.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1611016B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1611016B"><span>Development of CO2 inversion system based on the adjoint of the global coupled transport model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon</p>
<p>2014-05-01</p>
<p>We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) <span class="hlt">Eulerian</span> transport model (TM) and the <span class="hlt">Lagrangian</span> plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the <span class="hlt">Lagrangian</span> model FLEXPART. The <span class="hlt">Lagrangian</span> component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the <span class="hlt">Lagrangian</span> part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to <span class="hlt">Eulerian</span> part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of <span class="hlt">Lagrangian</span> model is required, making it applicable to combination of global NIES TM and any <span class="hlt">Lagrangian</span> model; 2. Once run, the <span class="hlt">Lagrangian</span> output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1986PhFl...29.3573A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1986PhFl...29.3573A"><span>Vaporization of irradiated droplets</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Armstrong, R. L.; O'Rourke, P. J.; Zardecki, A.</p>
<p>1986-11-01</p>
<p>The vaporization of a spherically symmetric liquid droplet subject to a high-intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid-gas interface are <span class="hlt">formulated</span> by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer code (``CON1D: A computer program for calculating spherically symmetric droplet combustion,'' Los Alamos National Laboratory Report No. LA-10269-MS, December, 1984), based on the implict continuous-fluid <span class="hlt">Eulerian</span> (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22809180','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22809180"><span><span class="hlt">Lagrangian</span> motion, coherent structures, and lines of persistent material strain.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Samelson, R M</p>
<p>2013-01-01</p>
<p><span class="hlt">Lagrangian</span> motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating <span class="hlt">Lagrangian</span> regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, <span class="hlt">Lagrangian</span> regime boundaries may often be indicated as material curves on which the <span class="hlt">Lagrangian</span>-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate <span class="hlt">Lagrangian</span> regime boundaries and lines of principal <span class="hlt">Lagrangian</span> strain (also called <span class="hlt">Lagrangian</span> coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/<span class="hlt">Lagrangian</span> strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PhTea..48..512H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PhTea..48..512H"><span>Gravity, Time, and <span class="hlt">Lagrangians</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Huggins, Elisha</p>
<p>2010-11-01</p>
<p>Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the <span class="hlt">Lagrangian</span>. (Why would one subtract potential energy from kinetic energy?) In this paper we discuss a thought experiment that relates gravity and time. Then we use a Feynman thought experiment to explain the minus sign in the <span class="hlt">Lagrangian</span>. Our surprise was that these two topics are related.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950011695','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950011695"><span>Floating shock fitting via <span class="hlt">Lagrangian</span> adaptive meshes</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Vanrosendale, John</p>
<p>1994-01-01</p>
<p>In recent works we have <span class="hlt">formulated</span> a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting <span class="hlt">Lagrangian</span> Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22596686-hamiltonian-analysis-linearly-acceleration-dependent-lagrangians','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22596686-hamiltonian-analysis-linearly-acceleration-dependent-lagrangians"><span>Hamiltonian analysis for linearly acceleration-dependent <span class="hlt">Lagrangians</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx</p>
<p>2016-06-15</p>
<p>We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies togethermore » with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order <span class="hlt">Lagrangians</span>. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian <span class="hlt">formulation</span> of covariant field theories.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22524964-reach-perturbative-methods-dark-matter-density-fields','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22524964-reach-perturbative-methods-dark-matter-density-fields"><span>On the reach of perturbative methods for dark matter density fields</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Baldauf, Tobias; Zaldarriaga, Matias; Schaan, Emmanuel, E-mail: baldauf@ias.edu, E-mail: eschaan@astro.princeton.edu, E-mail: matiasz@ias.edu</p>
<p></p>
<p>We study the mapping from <span class="hlt">Lagrangian</span> to <span class="hlt">Eulerian</span> space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute <span class="hlt">Lagrangian</span> displacements with <span class="hlt">Lagrangian</span> Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard <span class="hlt">Eulerian</span> Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regimemore » of validity of this approach is expected to extend that of the <span class="hlt">Eulerian</span> EFT, and match that of the IR-resummed <span class="hlt">Eulerian</span> EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z = 0 the power spectrum of the density field is reproduced with an accuracy of 1% (10%) up to k = 0.25 hMpc{sup −1} (k = 0.46 hMpc{sup −1}). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as k{sup 4} as it does in the very low k regime. Thus, modeling this contribution might be challenging.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; ...</p>
<p>2017-11-24</p>
<p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018OcMod.121...49V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018OcMod.121...49V"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H. A. M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.</p>
<p>2018-01-01</p>
<p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan</p>
<p></p>
<p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DPPGP9002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DPPGP9002C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chacon, Luis; Del-Castillo-Negrete, Diego</p>
<p>2011-10-01</p>
<p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy introduced by the presence of the magnetic field (χ∥ /χ⊥ ~1010 in fusion plasmas). Recently, a novel <span class="hlt">Lagrangian</span> method has been proposed to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution (in fact, it respects transport barriers -flux surfaces- exactly by construction), is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the <span class="hlt">Lagrangian</span> approach to include perpendicular transport and sources. We present an asymptotic-preserving numerical <span class="hlt">formulation</span> that ensures a consistent numerical discretization temporally and spatially for arbitrary χ∥ /χ⊥ ratios. This is of importance because parallel and perpendicular transport terms in the transport equation may become comparable in regions of the plasma (e.g., at incipient islands), while remaining disparate elsewhere. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry. D. del-Castillo-Negrete, L. Chacón, PRL, 106, 195004 (2011); DPP11 invited talk by del-Castillo-Negrete.</p>
</li>
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<ol class="result-class" start="401">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120003371','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120003371"><span>LSPRAY-IV: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, M. S.</p>
<p>2012-01-01</p>
<p>LSPRAY-IV is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray <span class="hlt">formulation</span>, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22047333-tess-relativistic-hydrodynamics-code-moving-voronoi-mesh','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22047333-tess-relativistic-hydrodynamics-code-moving-voronoi-mesh"><span>TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu</p>
<p>2011-12-01</p>
<p>We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an <span class="hlt">Eulerian</span> <span class="hlt">formulation</span>. Moving the points at the local fluid velocity makes the <span class="hlt">formulation</span> effectively <span class="hlt">Lagrangian</span>. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in <span class="hlt">Lagrangian</span> mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70013803','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70013803"><span>Two-dimensional <span class="hlt">Lagrangian</span> simulation of suspended sediment</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Schoellhamer, David H.</p>
<p>1988-01-01</p>
<p>A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the <span class="hlt">Lagrangian</span> reference frame is presented. The layered <span class="hlt">Lagrangian</span> transport model (LLTM) for suspended sediment performs laterally averaged concentration. The elevations of nearly horizontal streamlines and the simulation time step are selected to optimize model stability and efficiency. The computational elements are parcels of water that are moved along the streamlines in the <span class="hlt">Lagrangian</span> sense and are mixed with neighboring parcels. Three applications show that the LLTM can accurately simulate theoretical and empirical nonequilibrium suspended sediment distributions and slug injections of suspended sediment in a laboratory flume.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1997PhFl....9..433P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1997PhFl....9..433P"><span><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> view of the bursting period</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Podvin, Bérengère; Gibson, John; Berkooz, Gal; Lumley, John</p>
<p>1997-02-01</p>
<p>Low-dimensional models for the turbulent wall layer display an intermittent phenomenon with an ejection phase and a sweep phase that strongly resembles the bursting phenomenon observed in experimental flows. The probability distribution of inter-burst times has the observed shape [E. Stone and P. J. Holmes, Physica D 37, 20 (1989); SIAM J. Appl. Math. 50, 726 (1990); Phys. Lett. A 5, 29 (1991); P. J. Holmes and E. Stone, in Studies in Turbulence, edited by T. B. Gatski, S. Sarkar, and C. G. Speziale (Springer, Heidelberg, 1992)]. However, the time scales both for bursts and interburst durations are unrealistically long, a fact that was not appreciated until recently. We believe that the long time scales are due to the model's inclusion of only a single coherent structure, when in fact a succession of quasi-independent structures are being swept past the sensor in an experiment. A simple statistical model of this situation restores the magnitude of the observed bursting period, although there is a great deal of flexibility in the various parameters involved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000060808','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000060808"><span>Magnetic Photon Splitting: The S-Matrix <span class="hlt">Formulation</span> in the Landau Representation</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Baring, Matthew G.</p>
<p>1999-01-01</p>
<p>Calculations of reaction rates for the third-order QED process of photon splitting gamma yields gamma.gamma in strong magnetic fields traditionally have employed either the effective <span class="hlt">Lagrangian</span> method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner [1] presented an alternative derivation via an S-matrix <span class="hlt">formulation</span> in the Landau representation. Advantages of such a <span class="hlt">formulation</span> include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant, advances beyond the work of [1] by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective <span class="hlt">Lagrangian</span>/proper- time <span class="hlt">formulations</span> is demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PPN....41..976R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PPN....41..976R"><span>Towards <span class="hlt">Lagrangian</span> <span class="hlt">formulations</span> of mixed-symmetry higher spin fields on AdS-space within BFV-BRST formalism</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Reshetnyak, A. A.</p>
<p>2010-11-01</p>
<p>The spectrum of superstring theory on the AdS 5 × S 5 Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux Y( s 1, s 2). We review the details of a gauge-invariant <span class="hlt">Lagrangian</span> description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDG28009L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDG28009L"><span>Scale-by-scale contributions to <span class="hlt">Lagrangian</span> particle acceleration</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lalescu, Cristian C.; Wilczek, Michael</p>
<p>2017-11-01</p>
<p>Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. <span class="hlt">Lagrangian</span> particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on <span class="hlt">Lagrangian</span> statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the <span class="hlt">Lagrangian</span> tracer acceleration as the short time limit of the <span class="hlt">Lagrangian</span> velocity increment, we also quantify the influence of filtering on <span class="hlt">Lagrangian</span> intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28505811','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28505811"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Lacorata, Guglielmo; Vulpiani, Angelo</p>
<p>2017-04-01</p>
<p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lacorata, Guglielmo; Vulpiani, Angelo</p>
<p>2017-04-01</p>
<p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ascl.soft02021T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ascl.soft02021T"><span>COLAcode: COmoving <span class="hlt">Lagrangian</span> Acceleration code</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tassev, Svetlin V.</p>
<p>2016-02-01</p>
<p>COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving <span class="hlt">Lagrangian</span> Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in <span class="hlt">Lagrangian</span> Perturbation Theory (LPT). It differs from standard N-body code by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29543033','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29543033"><span>Nonunitary <span class="hlt">Lagrangians</span> and Unitary Non-<span class="hlt">Lagrangian</span> Conformal Field Theories.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Buican, Matthew; Laczko, Zoltan</p>
<p>2018-02-23</p>
<p>In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us <span class="hlt">Lagrangians</span> for particular observables in certain subsectors of many "non-<span class="hlt">Lagrangian</span>" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvL.120h1601B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvL.120h1601B"><span>Nonunitary <span class="hlt">Lagrangians</span> and Unitary Non-<span class="hlt">Lagrangian</span> Conformal Field Theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Buican, Matthew; Laczko, Zoltan</p>
<p>2018-02-01</p>
<p>In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us <span class="hlt">Lagrangians</span> for particular observables in certain subsectors of many "non-<span class="hlt">Lagrangian</span>" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017GMD....10.1961T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017GMD....10.1961T"><span>Vorticity-divergence semi-<span class="hlt">Lagrangian</span> global atmospheric model SL-AV20: dynamical core</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tolstykh, Mikhail; Shashkin, Vladimir; Fadeev, Rostislav; Goyman, Gordey</p>
<p>2017-05-01</p>
<p>SL-AV (semi-<span class="hlt">Lagrangian</span>, based on the absolute vorticity equation) is a global hydrostatic atmospheric model. Its latest version, SL-AV20, provides global operational medium-range weather forecast with 20 km resolution over Russia. The lower-resolution configurations of SL-AV20 are being tested for seasonal prediction and climate modeling. The article presents the model dynamical core. Its main features are a vorticity-divergence <span class="hlt">formulation</span> at the unstaggered grid, high-order finite-difference approximations, semi-<span class="hlt">Lagrangian</span> semi-implicit discretization and the reduced latitude-longitude grid with variable resolution in latitude. The accuracy of SL-AV20 numerical solutions using a reduced lat-lon grid and the variable resolution in latitude is tested with two idealized test cases. Accuracy and stability of SL-AV20 in the presence of the orography forcing are tested using the mountain-induced Rossby wave test case. The results of all three tests are in good agreement with other published model solutions. It is shown that the use of the reduced grid does not significantly affect the accuracy up to the 25 % reduction in the number of grid points with respect to the regular grid. Variable resolution in latitude allows us to improve the accuracy of a solution in the region of interest.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18165256','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18165256"><span>An overview of a <span class="hlt">Lagrangian</span> method for analysis of animal wake dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Peng, Jifeng; Dabiri, John O</p>
<p>2008-01-01</p>
<p>The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a <span class="hlt">Lagrangian</span> approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the <span class="hlt">Eulerian</span> perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=124866&keyword=Lagrangian&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=124866&keyword=Lagrangian&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>3DFATMIC: THREE DIMENSIONAL SUBSURFACE FLOW, FATE AND TRANSPORT OF MICROBES AND CHEMICALS MODEL - USER'S MANUAL VERSION 1.0</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>This document is the user's manual of 3DFATMIC, a 3-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals Model using a <span class="hlt">Lagrangian-Eulerian</span> adapted zooming and peak capturing (LEZOOMPC) algorithm.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1163152','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1163152"><span>Geometric multigrid for an implicit-time immersed boundary method</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.</p>
<p>2014-10-12</p>
<p>The immersed boundary (IB) method is an approach to fluid-structure interaction that uses <span class="hlt">Lagrangian</span> variables to describe the deformations and resulting forces of the structure and <span class="hlt">Eulerian</span> variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for <span class="hlt">Eulerian</span> equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> variables simultaneously. Moreover, several different approaches to solving the coupled <span class="hlt">Lagrangian-Eulerian</span> equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A41L..02A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A41L..02A"><span>Using <span class="hlt">Lagrangian</span> Chemical Transport Modeling to Assess the Impact of Biomass Burning on Ozone and PM2.5</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Alvarado, M. J.; Lonsdale, C. R.; Brodowski, C. M.</p>
<p>2017-12-01</p>
<p>One of the challenges of using in situ measurements to study the air quality and climate impacts of biomass burning is correctly determining the contribution of biomass burning sources to the measured ambient concentrations. This is especially important for policy purposes, as the ozone (O3) and fine particulate matter (PM2.5) from natural wildfires should not be confused with that from controllable anthropogenic sources. We have developed a <span class="hlt">Lagrangian</span> chemical transport model called STILT-ASP that is able to quantify the impact of wildfire events on O3 and PM2.5 measurements made at surface monitoring sites, by mobile laboratories, or by aircraft. STILT-ASP is built by coupling the Stochastic Time Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model with AER's Aerosol Simulation Program (ASP), which has been used in many studies of the gas and aerosol chemistry of biomass burning smoke. Here we present recent revisions made in STILT-ASP v2.0, including the use of more detailed chemical speciation of fire emissions and biogenic emissions calculated using the MEGAN model with meteorological inputs consistent with those used to drive STILT. We will present the results of an evaluation of the performance of STILT-ASP v2.0 using surface, mobile lab, and aircraft data from the 2013 Houston DISCOVER-AQ campaign. STILT-ASP v2.0 showed good average performance for O3 during the peak of the high O3 episodes on Sept. 25-26, 2013, with a mean bias of -4 ppbv. We will also demonstrate the use of STILT-ASP to evaluate the impact of biomass burning on O3 and PM2.5 in urban areas and to assess the impact of remote fires on the boundary conditions used in <span class="hlt">Eulerian</span> chemical transport models like CAMx.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017IJGMM..1450171E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017IJGMM..1450171E"><span>Scalar curvature of <span class="hlt">Lagrangian</span> Riemannian submersions and their harmonicity</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n</p>
<p></p>
<p>In this paper, we consider a <span class="hlt">Lagrangian</span> Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a <span class="hlt">Lagrangian</span> Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of <span class="hlt">Lagrangian</span> Riemannian submersions and obtain a characterization for such submersions to be harmonic.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MNRAS.458.1517F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MNRAS.458.1517F"><span><span class="hlt">Lagrangian</span> methods of cosmic web classification</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.</p>
<p>2016-05-01</p>
<p>The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a <span class="hlt">Lagrangian</span> approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The <span class="hlt">Lagrangian</span> approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the <span class="hlt">Lagrangian</span> nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010CompM..46..883R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010CompM..46..883R"><span>A monolithic <span class="hlt">Lagrangian</span> approach for fluid-structure interaction problems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ryzhakov, P. B.; Rossi, R.; Idelsohn, S. R.; Oñate, E.</p>
<p>2010-11-01</p>
<p>Current work presents a monolithic method for the solution of fluid-structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a <span class="hlt">Lagrangian</span> description for both the fluid and the structure. A linear displacement-pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based <span class="hlt">formulation</span>. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.</p>
</li>
</ol>
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<ol class="result-class" start="421">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ZaMP...68...55S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ZaMP...68...55S"><span>Classical Dynamics of Fullerenes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sławianowski, Jan J.; Kotowski, Romuald K.</p>
<p>2017-06-01</p>
<p>The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed <span class="hlt">Lagrangian</span> (material) and <span class="hlt">Eulerian</span> (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to <span class="hlt">formulate</span> the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to <span class="hlt">formulate</span> their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018ZaMP...69...55R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018ZaMP...69...55R"><span>A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Roubíček, Tomáš; Tomassetti, Giuseppe</p>
<p>2018-06-01</p>
<p>A theory of elastic magnets is <span class="hlt">formulated</span> under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (<span class="hlt">Eulerian</span>) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The <span class="hlt">formulation</span> of the problem uses <span class="hlt">Lagrangian</span> (reference) configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-self-penetration is considered. The analysis as far as existence of weak solutions of the (thermo) dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetallics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1128909-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1128909-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system"><span>Multi-phase CFD modeling of solid sorbent carbon capture system</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ryan, E. M.; DeCroix, D.; Breault, R.</p>
<p>2013-07-01</p>
<p>Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both Eulerian–<span class="hlt">Eulerian</span> and Eulerian–<span class="hlt">Lagrangian</span> multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD codes for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® Eulerian–<span class="hlt">Lagrangian</span> simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA Eulerian–<span class="hlt">Lagrangian</span> model is able to simulate the system given appropriate simplifying assumptions. FLUENT® Eulerian–<span class="hlt">Eulerian</span> simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622245-one-dimensional-lagrangian-implicit-hydrodynamic-algorithm-inertial-confinement-fusion-applications','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622245-one-dimensional-lagrangian-implicit-hydrodynamic-algorithm-inertial-confinement-fusion-applications"><span>One-dimensional <span class="hlt">Lagrangian</span> implicit hydrodynamic algorithm for Inertial Confinement Fusion applications</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ramis, Rafael, E-mail: rafael.ramis@upm.es</p>
<p></p>
<p>A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity <span class="hlt">formulation</span>. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted tomore » optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1326055-hybridizable-discontinuous-galerkin-method-modeling-fluidstructure-interaction','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1326055-hybridizable-discontinuous-galerkin-method-modeling-fluidstructure-interaction"><span>A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.</p>
<p>2016-08-31</p>
<p>This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG <span class="hlt">formulations</span> for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–<span class="hlt">Eulerian</span> Navier–Stokes are derived. The elasticity <span class="hlt">formulations</span> are written in a <span class="hlt">Lagrangian</span> reference frame, with the nonlinear <span class="hlt">formulation</span> restricted to hyperelastic materials. With these individual solid and fluid <span class="hlt">formulations</span>, the remaining challenge in FSI modelingmore » is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI <span class="hlt">formulation</span>. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG <span class="hlt">formulation</span> presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.272....1V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.272....1V"><span>An improved bounded semi-<span class="hlt">Lagrangian</span> scheme for the turbulent transport of passive scalars</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Verma, Siddhartha; Xuan, Y.; Blanquart, G.</p>
<p>2014-09-01</p>
<p>An improved bounded semi-<span class="hlt">Lagrangian</span> scalar transport scheme based on cubic Hermite polynomial reconstruction is proposed in this paper. Boundedness of the scalar being transported is ensured by applying derivative limiting techniques. Single sub-cell extrema are allowed to exist as they are often physical, and help minimize numerical dissipation. This treatment is distinct from enforcing strict monotonicity as done by D.L. Williamson and P.J. Rasch [5], and allows better preservation of small scale structures in turbulent simulations. The proposed bounding algorithm, although a seemingly subtle difference from strict monotonicity enforcement, is shown to result in significant performance gain in laminar cases, and in three-dimensional turbulent mixing layers. The scheme satisfies several important properties, including boundedness, low numerical diffusion, and high accuracy. Performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes. The results indicate that the proposed scheme is capable of furnishing extremely accurate results, with less severe resolution requirements than all the other bounded schemes tested. Additional simulations in homogeneous isotropic turbulence, with scalar timestep size unconstrained by the CFL number, show good agreement with spectral scheme results available in the literature. Detailed analytical examination of gain and phase error characteristics of the original cubic Hermite polynomial is also included, and points to dissipation and dispersion characteristics comparable to, or better than, those of a fifth order upwind <span class="hlt">Eulerian</span> scheme.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1366294','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1366294"><span>Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented <span class="hlt">Lagrangian</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Picheny, Victor; Gramacy, Robert B.; Wild, Stefan M.</p>
<p></p>
<p>An augmented <span class="hlt">Lagrangian</span> (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this <span class="hlt">formulation</span> the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof.more » We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDG20009S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDG20009S"><span>A Numerical Investigation of Two-Different Drosophila Forward Flight Modes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sahin, Mehmet; Dilek, Ezgi; Erzincanli, Belkis</p>
<p>2016-11-01</p>
<p>The parallel large-scale unstructured finite volume method based on an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) <span class="hlt">formulation</span> has been applied in order to investigate the near wake structure of Drosophila in forward flight. DISTENE MeshGems-Hexa algorithm based on the octree method is used to generate the all hexahedral mesh for the wing-body combination. The mesh deformation algorithm is based on the indirect radial basis function (RBF) method at each time level while avoiding remeshing in order to enhance numerical robustness. The large-scale numerical simulations are carried out for a flapping Drosophila in forward flight. In the first case, the wing tip-path plane is tilted forward to generate forward force. In the second case, paddling wing motion is used to generate the forward fore. The λ2-criterion proposed by Jeong and Hussain (1995) is used for investigating the time variation of the <span class="hlt">Eulerian</span> coherent structures in the near wake. The present simulations reveal highly detailed near wake topology for a hovering Drosophila. This is very useful in terms of understanding physics in biological flights which can provide a very useful tool for designing bio-inspired MAVs.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhDT........55L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhDT........55L"><span>Simulation of Richtmyer-Meshkov flows for elastic-plastic solids in planar and converging geometries using an <span class="hlt">Eulerian</span> framework</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lopez Ortega, Alejandro</p>
<p></p>
<p>This thesis presents a numerical and analytical study of two problems of interest involving shock waves propagating through elastic-plastic media: the motion of converging (imploding) shocks and the Richtmyer-Meshkov (RM) instability. Since the stress conditions encountered in these cases normally produce large deformations in the materials, an <span class="hlt">Eulerian</span> description, in which the spatial coordinates are fixed, is employed. This <span class="hlt">formulation</span> enables a direct comparison of similarities and differences between the present study of phenomena driven by shock-loading in elastic-plastic solids, and in fluids, where they have been studied extensively. In the first application, Whitham's shock dynamics (WSD) theory is employed for obtaining an approximate description of the motion of an elastic-plastic material processed by a cylindrically/spherically converging shock. Comparison with numerical simulations of the full set of equations of motion reveal that WSD is an accurate tool for characterizing the evolution of converging shocks at all stages. The study of the Richtmyer-Meshkov flow (i.e., interaction between the interface separating two materials of different density and a shock wave incoming at an angle) in solids is performed by means of analytical models for purely elastic solids and numerical simulations when plasticity is included in the material model. To this effect, an updated version of a previously developed multi-material, level-set-based, <span class="hlt">Eulerian</span> framework for solid mechanics is employed. The revised code includes the use of a multi-material HLLD Riemann problem for imposing material boundary conditions, and a new <span class="hlt">formulation</span> of the equations of motion that makes use of the stretch tensor while avoiding the degeneracy of the stress tensor under rotation. Results reveal that the interface separating two elastic solids always behaves in a stable oscillatory or decaying oscillatory manner due to the existence of shear waves, which are able to transport the</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhDT.........8B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhDT.........8B"><span>On the <span class="hlt">formulation</span> and assessment of flamelet-generated manifolds applied to two-phase turbulent combustion</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Bojko, Brian T.</p>
<p></p>
<p> solving the 1D flame equations at varying drop sizes, where the source terms for energy, mixture fraction, and progress variable are cataloged as a function of normalized diameter. A unique coupling of the DFGM and planar UFGM is developed and is used to account for individual and gas phase combustion processes in turbulent combustion situations, such as spray flames, particle laden blasts, etc. The DFGM for the methanol and aluminum droplets are used in mixed <span class="hlt">Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> <span class="hlt">formulations</span> of compressible multiphase flows. System level simulations are conducted and compared experimental data for a methanol spray flame and an aluminized blast studied at the Explosives Components Facility (ECF) at Sandia National Laboratories.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1001413','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1001413"><span>Quantifying Discretization Effects on Brain Trauma Simulations</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2016-01-01</p>
<p>arbitrarily formed meshes can propagate error when resolving interactions among the skull , cerebrospinal fluid, and brain. We compared <span class="hlt">Lagrangian</span>, pure...embedded methods from top to bottom. ......3 Fig. 2 Loading node-set for <span class="hlt">Eulerian</span> rotational problem. The dark shaded area around the skull is the area to...and top inner edges of the skull . The example shown is a <span class="hlt">Lagrangian</span> rotational model. The red and green materials represent the brain and skull</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930035782&hterms=passive+transport&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dpassive%2Btransport','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930035782&hterms=passive+transport&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dpassive%2Btransport"><span>Enhancement of diffusive transport in oscillatory flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Knobloch, E.; Merryfield, W. J.</p>
<p>1992-01-01</p>
<p>The theory of transport of passive scalars in oscillatory flows is reexamined. The differences between transport in standing and traveling waves are emphasized. Both <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> diffusivities are calculated, and the conditions for their applicability are discussed. Numerical simulations are conducted to understand the expulsion of gradients from time-dependent eddies and the resulting transport. The results indicate that it is the <span class="hlt">Eulerian</span> diffusivity that is of primary relevance for describing enhanced transport on spatial scales larger than that of the eddies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......102P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......102P"><span>Implementing a Loosely Coupled Fluid Structure Interaction Finite Element Model in PHASTA</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pope, David</p>
<p></p>
<p>Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015GMDD....8.8895C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015GMDD....8.8895C"><span>ASHEE: a compressible, Equilibrium-<span class="hlt">Eulerian</span> model for volcanic ash plumes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.</p>
<p>2015-10-01</p>
<p>A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase <span class="hlt">Eulerian</span> transport equations (Neri et al., 2003) for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model (Ferry and Balachandar, 2001), valid for low concentration regimes (particle volume fraction less than 10-3) and particles Stokes number (St, i.e., the ratio between their relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium <span class="hlt">Eulerian</span>), is significantly faster than the N-phase <span class="hlt">Eulerian</span> model while retaining the capability to describe gas-particle non-equilibrium effects. Direct numerical simulation accurately reproduce the dynamics of isotropic, compressible turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980007176','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980007176"><span>Implementation of Free-<span class="hlt">Formulation</span>-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Barut, A.; Madenci, Erdogan; Tessler, A.</p>
<p>1997-01-01</p>
<p>This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics <span class="hlt">formulation</span> for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the <span class="hlt">formulation</span> in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span>. The shallow shell element <span class="hlt">formulation</span> is based on the Reissner-Mindlin and Marguerre theory.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008ACPD....818727S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008ACPD....818727S"><span>Implications of <span class="hlt">Lagrangian</span> transport for coupled chemistry-climate simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.</p>
<p>2008-10-01</p>
<p>For the first time a purely <span class="hlt">Lagrangian</span> transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the <span class="hlt">Lagrangian</span> scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the <span class="hlt">Lagrangian</span> approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-<span class="hlt">Lagrangian</span> transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the <span class="hlt">Lagrangian</span> transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-<span class="hlt">Lagrangian</span> advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the <span class="hlt">Lagrangian</span> transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGP...128..140K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGP...128..140K"><span>Hamiltonian stability for weighted measure and generalized <span class="hlt">Lagrangian</span> mean curvature flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kajigaya, Toru; Kunikawa, Keita</p>
<p>2018-06-01</p>
<p>In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of <span class="hlt">Lagrangian</span> submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a <span class="hlt">Lagrangian</span> submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized <span class="hlt">Lagrangian</span> mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial <span class="hlt">Lagrangian</span> submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable <span class="hlt">Lagrangian</span> submanifold, then the generalized MCF converges exponentially fast to an f-minimal <span class="hlt">Lagrangian</span> submanifold.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27327139','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27327139"><span><span class="hlt">Lagrangian</span> descriptors in dissipative systems.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Junginger, Andrej; Hernandez, Rigoberto</p>
<p>2016-11-09</p>
<p>The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of <span class="hlt">Lagrangian</span> descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the <span class="hlt">Lagrangian</span> descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the <span class="hlt">Lagrangian</span> descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740019118','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740019118"><span>A macroscopic plasma <span class="hlt">Lagrangian</span> and its application to wave interactions and resonances</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Peng, Y. K. M.</p>
<p>1974-01-01</p>
<p>The derivation of a macroscopic plasma <span class="hlt">Lagrangian</span> is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the <span class="hlt">Lagrangian</span> is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a <span class="hlt">Lagrangian</span> are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The <span class="hlt">Lagrangians</span> for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma <span class="hlt">Lagrangian</span> is shown to differ from the velocity-integrated low <span class="hlt">Lagrangian</span> by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006AGUFMOS41C0633K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006AGUFMOS41C0633K"><span><span class="hlt">Lagrangian</span> particle statistics of numerically simulated shear waves</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kirby, J.; Briganti, R.; Brocchini, M.; Chen, Q. J.</p>
<p>2006-12-01</p>
<p>The properties of numerical solutions of various circulation models (Boussinesq-type and wave-averaged NLSWE) have been investigated on the basis of the induced horizontal flow mixing, for the case of shear waves. The mixing properties of the flow have been investigated using particle statistics, following the approach of LaCasce (2001) and Piattella et al. (2006). Both an idealized barred beach bathymetry and a test case taken from SANDYDUCK '97 have been considered. Random seeding patterns of passive tracer particles are used. The flow exhibits features similar to those discussed in literature. Differences are also evident due both to the physics (intense longshore shear shoreward of the bar) and the procedure used to obtain the statistics (lateral conditions limit the time/space window for the longshore flow). Within the Boussinesq framework, different <span class="hlt">formulations</span> of Boussinesq type equations have been used and the results compared (Wei et al. 1995, Chen et al. (2003), Chen et al. (2006)). Analysis based on the <span class="hlt">Eulerian</span> velocity fields suggests a close similarity between Wei et al. (1995) and Chen et. al (2006), while examination of particle displacements and implied mixing suggests a closer behaviour between Chen et al. (2003) and Chen et al. (2006). Two distinct stages of mixing are evident in all simulations: i) the first stage ends at t</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=30913&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=30913&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>AN OPTIMAL ADAPTIVE LOCAL GRID REFINEMENT APPROACH TO MODELING CONTAMINANT TRANSPORT</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>A <span class="hlt">Lagrangian-Eulerian</span> method with an optimal adaptive local grid refinement is used to model contaminant transport equations. pplication of this approach to two bench-mark problems indicates that it completely resolves difficulties of peak clipping, numerical diffusion, and spuri...</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19830044831&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19830044831&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian"><span>Microscopic <span class="hlt">Lagrangian</span> description of warm plasmas. IV - Macroscopic approximation</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kim, H.; Crawford, F. W.</p>
<p>1983-01-01</p>
<p>The averaged-<span class="hlt">Lagrangian</span> method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic <span class="hlt">Lagrangian</span> treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic <span class="hlt">Lagrangian</span> density.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvF...2e4602S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvF...2e4602S"><span><span class="hlt">Lagrangian</span> acceleration statistics in a turbulent channel flow</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Stelzenmuller, Nickolas; Polanco, Juan Ignacio; Vignal, Laure; Vinkovic, Ivana; Mordant, Nicolas</p>
<p>2017-05-01</p>
<p><span class="hlt">Lagrangian</span> acceleration statistics in a fully developed turbulent channel flow at Reτ=1440 are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the <span class="hlt">Lagrangian</span> velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced <span class="hlt">Lagrangian</span> stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95b5017K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95b5017K"><span>Effective <span class="hlt">Lagrangian</span> in de Sitter spacetime</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kitamoto, Hiroyuki; Kitazawa, Yoshihisa</p>
<p>2017-01-01</p>
<p>Scale invariant fluctuations of metric are a universal feature of quantum gravity in de Sitter spacetime. We construct an effective <span class="hlt">Lagrangian</span> which summarizes their implications on local physics by integrating superhorizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective <span class="hlt">Lagrangian</span> as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009IJMPA..24.5319K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009IJMPA..24.5319K"><span>Quantization of Non-<span class="hlt">Lagrangian</span> Systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kochan, Denis</p>
<p></p>
<p>A novel method for quantization of non-<span class="hlt">Lagrangian</span> (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (<span class="hlt">Lagrangian</span>) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1200671','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1200671"><span>Edge remap for solids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Kamm, James R.; Love, Edward; Robinson, Allen C.</p>
<p></p>
<p>We review the edge element <span class="hlt">formulation</span> for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approachmore » is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.« less</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhyA..471..540S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhyA..471..540S"><span>The S-<span class="hlt">Lagrangian</span> and a theory of homeostasis in living systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sandler, U.; Tsitolovsky, L.</p>
<p>2017-04-01</p>
<p>A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized <span class="hlt">Lagrangian</span> approach (S-<span class="hlt">Lagrangian</span>), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-<span class="hlt">Lagrangian</span>, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-<span class="hlt">Lagrangian</span>. Additionally, we reveal that plausible assumptions about S-<span class="hlt">Lagrangian</span> features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930041272&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930041272&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>A global multilevel atmospheric model using a vector semi-<span class="hlt">Lagrangian</span> finite-difference scheme. I - Adiabatic <span class="hlt">formulation</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bates, J. R.; Moorthi, S.; Higgins, R. W.</p>
<p>1993-01-01</p>
<p>An adiabatic global multilevel primitive equation model using a two time-level, semi-<span class="hlt">Lagrangian</span> semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26861803','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26861803"><span>Computing the stresses and deformations of the human eye components due to a high explosive detonation using fluid-structure interaction model.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Karimi, Alireza; Razaghi, Reza; Navidbakhsh, Mahdi; Sera, Toshihiro; Kudo, Susumu</p>
<p>2016-05-01</p>
<p>In spite the fact that a very small human body surface area is comprised by the eye, its wounds due to detonation have recently been dramatically amplified. Although many efforts have been devoted to measure injury of the globe, there is still a lack of knowledge on the injury mechanism due to Primary Blast Wave (PBW). The goal of this study was to determine the stresses and deformations of the human eye components, including the cornea, aqueous, iris, ciliary body, lens, vitreous, retina, sclera, optic nerve, and muscles, attributed to PBW induced by trinitrotoluene (TNT) explosion via a <span class="hlt">Lagrangian-Eulerian</span> computational coupling model. Magnetic Resonance Imaging (MRI) was employed to establish a Finite Element (FE) model of the human eye according to a normal human eye. The solid components of the eye were modelled as <span class="hlt">Lagrangian</span> mesh, while an explosive TNT, air domain, and aqueous were modelled using Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) mesh. Nonlinear dynamic FE simulations were accomplished using the explicit FE code, namely LS-DYNA. In order to simulate the blast wave generation, propagation, and interaction with the eye, the ALE <span class="hlt">formulation</span> with Jones-Wilkins-Lee (JWL) equation defining the explosive material were employed. The results revealed a peak stress of 135.70kPa brought about by detonation upsurge on the cornea at the distance of 25cm. The highest von Mises stresses were observed on the sclera (267.3kPa), whereas the lowest one was seen on the vitreous body (0.002kPa). The results also showed a relatively high resultant displacement for the macula as well as a high variation for the radius of curvature for the cornea and lens, which can result in both macular holes, optic nerve damage and, consequently, vision loss. These results may have implications not only for understanding the value of stresses and strains in the human eye components but also giving an outlook about the process of PBW triggers damage to the eye. Copyright © 2016 Elsevier Ltd</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvD..97f5019R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvD..97f5019R"><span>Leading-order classical <span class="hlt">Lagrangians</span> for the nonminimal standard-model extension</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Reis, J. A. A. S.; Schreck, M.</p>
<p>2018-03-01</p>
<p>In this paper, we derive the general leading-order classical <span class="hlt">Lagrangian</span> covering all fermion operators of the nonminimal standard-model extension (SME). Such a <span class="hlt">Lagrangian</span> is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the <span class="hlt">Lagrangian</span> obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1134155-asymptotic-preserving-lagrangian-algorithm-time-dependent-anisotropic-heat-transport-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1134155-asymptotic-preserving-lagrangian-algorithm-time-dependent-anisotropic-heat-transport-equation"><span>An asymptotic-preserving <span class="hlt">Lagrangian</span> algorithm for the time-dependent anisotropic heat transport equation</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.</p>
<p>2014-09-01</p>
<p>We propose a <span class="hlt">Lagrangian</span> numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split <span class="hlt">formulation</span>, with two straightforward steps: a perpendicular transport step (including sources), and a <span class="hlt">Lagrangian</span> (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C"><span>A new approach to enforce element-wise mass/species balance using the augmented <span class="hlt">Lagrangian</span> method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Chang, J.; Nakshatrala, K.</p>
<p>2015-12-01</p>
<p>The least-squares finite element method (LSFEM) is one of many ways in which one can discretize and express a set of first ordered partial differential equations as a mixed <span class="hlt">formulation</span>. However, the standard LSFEM is not locally conservative by design. The absence of this physical property can have serious implications in the numerical simulation of subsurface flow and transport. Two commonly employed ways to circumvent this issue is through the Lagrange multiplier method, which explicitly satisfies the element-wise divergence by introducing new unknowns, or through appending a penalty factor to the continuity constraint, which reduces the violation in the mass balance. However, these methodologies have some well-known drawbacks. Herein, we propose a new approach to improve the local balance of species/mass balance. The approach augments constraints to a least-square function by a novel mathematical construction of the local species/mass balance, which is different from the conventional ways. The resulting constrained optimization problem is solved using the augmented <span class="hlt">Lagrangian</span>, which corrects the balance errors in an iterative fashion. The advantages of this methodology are that the problem size is not increased (thus preserving the symmetry and positive definite-ness) and that one need not provide an accurate guess for the initial penalty to reach a prescribed mass balance tolerance. We derive the least-squares weighting needed to ensure accurate solutions. We also demonstrate the robustness of the weighted LSFEM coupled with the augmented <span class="hlt">Lagrangian</span> by solving large-scale heterogenous and variably saturated flow through porous media problems. The performance of the iterative solvers with respect to various user-defined augmented <span class="hlt">Lagrangian</span> parameters will be documented.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1009440','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1009440"><span>DOE SBIR Phase-1 Report on Hybrid CPU-GPU Parallel Development of the <span class="hlt">Eulerian-Lagrangian</span> Barracuda Multiphase Program</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dr. Dale M. Snider</p>
<p>2011-02-28</p>
<p>This report gives the result from the Phase-1 work on demonstrating greater than 10x speedup of the Barracuda computer program using parallel methods and GPU processors (General-Purpose Graphics Processing Unit or Graphics Processing Unit). Phase-1 demonstrated a 12x speedup on a typical Barracuda function using the GPU processor. The problem test case used about 5 million particles and 250,000 <span class="hlt">Eulerian</span> grid cells. The relative speedup, compared to a single CPU, increases with increased number of particles giving greater than 12x speedup. Phase-1 work provided a path for reformatting data structure modifications to give good parallel performance while keeping a friendlymore » environment for new physics development and code maintenance. The implementation of data structure changes will be in Phase-2. Phase-1 laid the ground work for the complete parallelization of Barracuda in Phase-2, with the caveat that implemented computer practices for parallel programming done in Phase-1 gives immediate speedup in the current Barracuda serial running code. The Phase-1 tasks were completed successfully laying the frame work for Phase-2. The detailed results of Phase-1 are within this document. In general, the speedup of one function would be expected to be higher than the speedup of the entire code because of I/O functions and communication between the algorithms. However, because one of the most difficult Barracuda algorithms was parallelized in Phase-1 and because advanced parallelization methods and proposed parallelization optimization techniques identified in Phase-1 will be used in Phase-2, an overall Barracuda code speedup (relative to a single CPU) is expected to be greater than 10x. This means that a job which takes 30 days to complete will be done in 3 days. Tasks completed in Phase-1 are: Task 1: Profile the entire Barracuda code and select which subroutines are to be parallelized (See Section Choosing a Function to Accelerate) Task 2: Select a GPU consultant</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19810057814&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19810057814&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian"><span><span class="hlt">Lagrangian</span> methods in nonlinear plasma wave interaction</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Crawford, F. W.</p>
<p>1980-01-01</p>
<p>Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-<span class="hlt">Lagrangian</span> methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable <span class="hlt">Lagrangian</span> densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CSR....47..145F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CSR....47..145F"><span>Using <span class="hlt">Lagrangian</span> Coherent Structures to understand coastal water quality</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.</p>
<p>2012-09-01</p>
<p>The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore <span class="hlt">Lagrangian</span> circulation. Specifically, we reveal <span class="hlt">Lagrangian</span> Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the <span class="hlt">Lagrangian</span> circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a <span class="hlt">Lagrangian</span> circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017RvMPP...1....9S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017RvMPP...1....9S"><span>Modern gyrokinetic <span class="hlt">formulation</span> of collisional and turbulent transport in toroidally rotating plasmas</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sugama, H.</p>
<p>2017-12-01</p>
<p>Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are <span class="hlt">formulated</span> based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the <span class="hlt">Lagrangian</span> variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive <span class="hlt">formulations</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JMPSo.105...25D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JMPSo.105...25D"><span>Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Danas, K.</p>
<p>2017-08-01</p>
<p>This work provides a rigorous analysis of the effective response, i.e., average magnetization and magnetostriction, of magnetoelastic composites that are subjected to overall magnetic and mechanical loads. It clarifies the differences between a coupled magnetomechanical analysis in which one applies a <span class="hlt">Eulerian</span> (current) magnetic field and an electroactive one where the <span class="hlt">Lagrangian</span> (reference) electric field is usually applied. For this, we propose an augmented vector potential variational <span class="hlt">formulation</span> to carry out numerical periodic homogenization studies of magnetoelastic solids at finite strains and magnetic fields. We show that the developed variational principle can be used for bottom-up design of microstructures with desired magnetomechanical coupling by properly canceling out the macro-geometry and specimen shape effects. To achieve that, we properly treat the average Maxwell stresses arising from the medium surrounding the magnetoelastic representative volume element (RVE), while at the same time we impose a uniform average <span class="hlt">Eulerian</span> and not <span class="hlt">Lagrangian</span> magnetic field. The developed variational principle is then used to study a large number of ideal as well as more realistic two-dimensional microstructures. We study the effect of particle volume fraction, particle distribution and particle shape and orientation upon the effective magnetoelastic response at finite strains. We consider also unstructured isotropic microstructures based on random adsorption algorithms and we carry out a convergence study of the representativity of the proposed unit cells. Finally, three-phase two-dimensional auxetic microstructures are analyzed. The first consists of a periodic distribution of voids and particle chains in a polymer matrix, while the second takes advantage of particle shape and chirality to produce negative and positive swelling by proper change of the chirality and the applied magnetic field.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.H32D..06A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.H32D..06A"><span>Chemical Continuous Time Random Walks</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Aquino, T.; Dentz, M.</p>
<p>2017-12-01</p>
<p>Traditional methods for modeling solute transport through heterogeneous media employ <span class="hlt">Eulerian</span> schemes to solve for solute concentration. More recently, <span class="hlt">Lagrangian</span> methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to <span class="hlt">Lagrangian</span> methods, these remain less developed than their <span class="hlt">Eulerian</span> counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and <span class="hlt">formulate</span> a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018NuPhB.928..107M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018NuPhB.928..107M"><span>Integration over families of <span class="hlt">Lagrangian</span> submanifolds in BV formalism</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mikhailov, Andrei</p>
<p>2018-03-01</p>
<p>Gauge fixing is interpreted in BV formalism as a choice of <span class="hlt">Lagrangian</span> submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of <span class="hlt">Lagrangian</span> submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of <span class="hlt">Lagrangian</span> submanifolds.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=magnetic+AND+particles&id=EJ832524','ERIC'); return false;" href="https://eric.ed.gov/?q=magnetic+AND+particles&id=EJ832524"><span>Symmetries in <span class="hlt">Lagrangian</span> Dynamics</span></a></p>
<p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p>
<p>Ferrario, Carlo; Passerini, Arianna</p>
<p>2007-01-01</p>
<p>In the framework of Noether's theorem, a distinction between <span class="hlt">Lagrangian</span> and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1910943P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1910943P"><span>Transport upscaling from pore- to Darcy-scale: Incorporating pore-scale Berea sandstone <span class="hlt">Lagrangian</span> velocity statistics into a Darcy-scale transport CTRW model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Puyguiraud, Alexandre; Dentz, Marco; Gouze, Philippe</p>
<p>2017-04-01</p>
<p>For the past several years a lot of attention has been given to pore-scale flow in order to understand and model transport, mixing and reaction in porous media. Nevertheless we believe that an accurate study of spatial and temporal evolution of velocities could bring important additional information for the upscaling from pore to higher scales. To gather these pieces of information, we perform Stokes flow simulations on pore-scale digitized images of a Berea sandstone core. First, micro-tomography (XRMT) imaging and segmentation processes allow us to obtain 3D black and white images of the sample [1]. Then we used an OpenFoam solver to perform the Stokes flow simulations mentioned above, which gives us the velocities at the interfaces of a cubic mesh. Subsequently, we use a particle streamline reconstruction technique which uses the <span class="hlt">Eulerian</span> velocity field previously obtained. This technique, based on a modified Pollock algorithm [2], enables us to make particle tracking simulations on the digitized sample. In order to build a stochastic pore-scale transport model, we analyze the <span class="hlt">Lagrangian</span> velocity series in two different ways. First we investigate the velocity evolution by sampling isochronically (t-<span class="hlt">Lagrangian</span>), and by studying its statistical properties in terms of one- and two-points statistics. Intermittent patterns can be observed. These are due to the persistance of low velocities over a characteristic space length. Other results are investigated, such as correlation functions and velocity PDFs, which permit us to study more deeply this persistence in the velocities and to compute the correlation times. However, with the second approach, doing these same analysis in space by computing the velocities equidistantly, enables us to remove the intermittency shown in the temporal evolution and to model these velocity series as a Markov process. This renders the stochastic particle dynamics into a CTRW [3]. [1] Gjetvaj, F., A. Russian, P. Gouze, and M. Dentz (2015</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913672M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913672M"><span>Three dimensional <span class="hlt">Lagrangian</span> structures in the Antarctic Polar Vortex.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen</p>
<p>2017-04-01</p>
<p>Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as <span class="hlt">Lagrangian</span> Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use <span class="hlt">Lagrangian</span> Descriptors [1,2,3,4] (function M) for visualizing 3D <span class="hlt">Lagrangian</span> structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. <span class="hlt">Lagrangian</span> Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. <span class="hlt">Lagrangian</span> descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDA30006S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDA30006S"><span>A volume-filtered <span class="hlt">formulation</span> to capture particle-shock interactions in multiphase compressible flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Shallcross, Gregory; Capecelatro, Jesse</p>
<p>2017-11-01</p>
<p>Compressible particle-laden flows are common in engineering systems. Applications include but are not limited to water injection in high-speed jet flows for noise suppression, rocket-plume surface interactions during planetary landing, and explosions during coal mining operations. Numerically, it is challenging to capture these interactions due to the wide range of length and time scales. Additionally, there are many forms of the multiphase compressible flow equations with volume fraction effects, some of which are conflicting in nature. The purpose of this presentation is to develop the capability to accurately capture particle-shock interactions in systems with a large number of particles from dense to dilute regimes. A thorough derivation of the volume filtered equations is presented. The volume filtered equations are then implemented in a high-order, energy-stable <span class="hlt">Eulerian-Lagrangian</span> framework. We show this framework is capable of decoupling the fluid mesh from the particle size, enabling arbitrary particle size distributions in the presence of shocks. The proposed method is then assessed against particle-laden shock tube data. Quantities of interest include fluid-phase pressure profiles and particle spreading rates. The effect of collisions in 2D and 3D are also evaluated.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003APS..DPPQP1015B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003APS..DPPQP1015B"><span>Comparisons of 'Identical' Simulations by the <span class="hlt">Eulerian</span> Gyrokinetic Codes GS2 and GYRO</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Bravenec, R. V.; Ross, D. W.; Candy, J.; Dorland, W.; McKee, G. R.</p>
<p>2003-10-01</p>
<p>A major goal of the fusion program is to be able to predict tokamak transport from first-principles theory. To this end, the <span class="hlt">Eulerian</span> gyrokinetic code GS2 was developed years ago and continues to be improved [1]. Recently, the <span class="hlt">Eulerian</span> code GYRO was developed [2]. These codes are not subject to the statistical noise inherent to particle-in-cell (PIC) codes, and have been very successful in treating electromagnetic fluctuations. GS2 is fully spectral in the radial coordinate while GYRO uses finite-differences and ``banded" spectral schemes. To gain confidence in nonlinear simulations of experiment with these codes, ``apples-to-apples" comparisons (identical profile inputs, flux-tube geometry, two species, etc.) are first performed. We report on a series of linear and nonlinear comparisons (with overall agreement) including kinetic electrons, collisions, and shaped flux surfaces. We also compare nonlinear simulations of a DIII-D discharge to measurements of not only the fluxes but also the turbulence parameters. [1] F. Jenko, et al., Phys. Plasmas 7, 1904 (2000) and refs. therein. [2] J. Candy, J. Comput. Phys. 186, 545 (2003).</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhyD..372...31B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhyD..372...31B"><span>Generalized <span class="hlt">Lagrangian</span> coherent structures</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Balasuriya, Sanjeeva; Ouellette, Nicholas T.; Rypina, Irina I.</p>
<p>2018-06-01</p>
<p>The notion of a <span class="hlt">Lagrangian</span> Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized <span class="hlt">Lagrangian</span> Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1422338-movement-collision-lagrangian-particles-hydro-turbine-intakes-acasestudy','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1422338-movement-collision-lagrangian-particles-hydro-turbine-intakes-acasestudy"><span>Movement and collision of <span class="hlt">Lagrangian</span> particles in hydro-turbine intakes: a case study</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Romero-Gomez, Pedro; Richmond, Marshall C.</p>
<p></p>
<p>Studies of the stress/survival of migratory fish during downstream passage through operating hydro-turbines are normally conducted to determine the fish-friendliness of units. One field approach consisting of recording extreme hydraulics with autonomous sensors is largely sensitive to the conditions of sensor release and the initial trajectories at the turbine intake. This study applies a modelling strategy based on flow simulations using computational fluid dynamics and <span class="hlt">Lagrangian</span> particle tracking to represent the travel of live fish and autonomous sensor devices through hydro-turbine intakes. For the flow field calculation, the simulations were conducted with both a time-averaging turbulence model and an eddy-resolvingmore » technique. For the particle tracking calculation, different modelling assumptions for turbulence forcing, mass <span class="hlt">formulation</span>, buoyancy, and release condition were tested. The modelling assumptions are evaluated with respect to data sets collected using a laboratory physical model and an autonomous sensor device deployed at Ice Harbor Dam (Snake River, State of Washington, U.S.A.) at the same discharge and release point as in the present computer simulations. We found an acceptable agreement between the simulated results and observed data and discuss relevant features of <span class="hlt">Lagrangian</span> particle movement that are critical in turbine design and in the experimental design of field studies.« less</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ExFl...58...33V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ExFl...58...33V"><span>Comparative assessment of pressure field reconstructions from particle image velocimetry measurements and <span class="hlt">Lagrangian</span> particle tracking</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>van Gent, P. L.; Michaelis, D.; van Oudheusden, B. W.; Weiss, P.-É.; de Kat, R.; Laskari, A.; Jeon, Y. J.; David, L.; Schanz, D.; Huhn, F.; Gesemann, S.; Novara, M.; McPhaden, C.; Neeteson, N. J.; Rival, D. E.; Schneiders, J. F. G.; Schrijer, F. F. J.</p>
<p>2017-04-01</p>
<p>A test case for pressure field reconstruction from particle image velocimetry (PIV) and <span class="hlt">Lagrangian</span> particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data which can realistically only be obtained for low-speed flows. Particle images were processed using tomographic PIV processing as well as the LPT algorithm `Shake-The-Box' (STB). Multiple pressure field reconstruction techniques have subsequently been applied to the PIV results (<span class="hlt">Eulerian</span> approach, iterative least-square pseudo-tracking, Taylor's hypothesis approach, and instantaneous Vortex-in-Cell) and LPT results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation, and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate reconstructed pressure fields could be obtained using LPT approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques proved to be critically sensitive to the amount of noise added in the present test case.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27575211','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27575211"><span>Influence of compressibility on the <span class="hlt">Lagrangian</span> statistics of vorticity-strain-rate interactions.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Danish, Mohammad; Sinha, Sawan Suman; Srinivasan, Balaji</p>
<p>2016-07-01</p>
<p>The objective of this study is to investigate the influence of compressibility on <span class="hlt">Lagrangian</span> statistics of vorticity and strain-rate interactions. The <span class="hlt">Lagrangian</span> statistics are extracted from "almost" time-continuous data sets of direct numerical simulations of compressible decaying isotropic turbulence by employing a cubic spline-based <span class="hlt">Lagrangian</span> particle tracker. We study the influence of compressibility on <span class="hlt">Lagrangian</span> statistics of alignment in terms of compressibility parameters-turbulent Mach number, normalized dilatation-rate, and flow topology. In comparison to incompressible turbulence, we observe that the presence of compressibility in a flow field weakens the alignment tendency of vorticity toward the largest strain-rate eigenvector. Based on the <span class="hlt">Lagrangian</span> statistics of alignment conditioned on dilatation and topology, we find that the weakened tendency of alignment observed in compressible turbulence is because of a special group of fluid particles that have an initially negligible dilatation-rate and are associated with stable-focus-stretching topology.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940010160','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940010160"><span>Non-recursive augmented <span class="hlt">Lagrangian</span> algorithms for the forward and inverse dynamics of constrained flexible multibodies</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bayo, Eduardo; Ledesma, Ragnar</p>
<p>1993-01-01</p>
<p>A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global <span class="hlt">Lagrangian</span> approach is used in <span class="hlt">formulating</span> the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930039947&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930039947&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing"><span><span class="hlt">Lagrangian</span> solution of supersonic real gas flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Loh, Ching-Yuen; Liou, Meng-Sing</p>
<p>1993-01-01</p>
<p>The present extention of a <span class="hlt">Lagrangian</span> approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the <span class="hlt">Lagrangian</span> form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1248278','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1248278"><span>Developing a Learning Algorithm-Generated Empirical Relaxer</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Mitchell, Wayne; Kallman, Josh; Toreja, Allen</p>
<p>2016-03-30</p>
<p>One of the main difficulties when running Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) simulations is determining how much to relax the mesh during the <span class="hlt">Eulerian</span> step. This determination is currently made by the user on a simulation-by-simulation basis. We present a Learning Algorithm-Generated Empirical Relaxer (LAGER) which uses a regressive random forest algorithm to automate this decision process. We also demonstrate that LAGER successfully relaxes a variety of test problems, maintains simulation accuracy, and has the potential to significantly decrease both the person-hours and computational hours needed to run a successful ALE simulation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26274277','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26274277"><span>Intermittent <span class="hlt">Lagrangian</span> velocities and accelerations in three-dimensional porous medium flow.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Holzner, M; Morales, V L; Willmann, M; Dentz, M</p>
<p>2015-07-01</p>
<p>Intermittency of <span class="hlt">Lagrangian</span> velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on <span class="hlt">Lagrangian</span> velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential <span class="hlt">Lagrangian</span> velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed <span class="hlt">Lagrangian</span> flow and transport behaviors.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..MAR.V1290M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..MAR.V1290M"><span><span class="hlt">Lagrangian</span> Approach to Study Catalytic Fluidized Bed Reactors</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration</p>
<p>2013-03-01</p>
<p><span class="hlt">Lagrangian</span> approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a <span class="hlt">Lagrangian</span> approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The <span class="hlt">Lagrangian</span> perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the <span class="hlt">Lagrangian</span> approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21517594','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21517594"><span><span class="hlt">Lagrangian</span> statistics and flow topology in forced two-dimensional turbulence.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K</p>
<p>2011-03-01</p>
<p>A study of the relationship between <span class="hlt">Lagrangian</span> statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a <span class="hlt">Lagrangian</span> approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the <span class="hlt">Lagrangian</span> Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the <span class="hlt">Lagrangian</span> velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the <span class="hlt">Lagrangian</span> acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the <span class="hlt">Lagrangian</span> curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JGP....60..857V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JGP....60..857V"><span>The <span class="hlt">Lagrangian</span>-Hamiltonian formalism for higher order field theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vitagliano, Luca</p>
<p>2010-06-01</p>
<p>We generalize the <span class="hlt">Lagrangian</span>-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order <span class="hlt">Lagrangian</span> field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JPhA...44L5203P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JPhA...44L5203P"><span><span class="hlt">Lagrangian</span>-Hamiltonian unified formalism for autonomous higher order dynamical systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso</p>
<p>2011-09-01</p>
<p>The <span class="hlt">Lagrangian</span>-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the <span class="hlt">Lagrangian</span> and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the <span class="hlt">Lagrangian</span>-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20140002508','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20140002508"><span>Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single Element LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar DWFDF Method</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Shih, Tsan-Hsing; Liu, Nan-Suey</p>
<p>2013-01-01</p>
<p>This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the <span class="hlt">Eulerian</span> scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the <span class="hlt">Eulerian</span> scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the <span class="hlt">Eulerian</span> scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22489841-lagrangian-hamiltonian-constraints-guiding-center-hamiltonian-theories','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22489841-lagrangian-hamiltonian-constraints-guiding-center-hamiltonian-theories"><span><span class="hlt">Lagrangian</span> and Hamiltonian constraints for guiding-center Hamiltonian theories</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Tronko, Natalia; Brizard, Alain J.</p>
<p></p>
<p>A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and <span class="hlt">Lagrangian</span> constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space <span class="hlt">Lagrangian</span> is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center <span class="hlt">Lagrangian</span> constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26328583','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26328583"><span>Dissipative inertial transport patterns near coherent <span class="hlt">Lagrangian</span> eddies in the ocean.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan</p>
<p>2015-08-01</p>
<p>Recent developments in dynamical systems theory have revealed long-lived and coherent <span class="hlt">Lagrangian</span> (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent <span class="hlt">Lagrangian</span> eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=510&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=510&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>PREFACE SPECIAL ISSUE ON MODEL EVALUATION: EVALUATION OF URBAN AND REGIONAL <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>The "Preface to the Special Edition on Model Evaluation: Evaluation of Urban and Regional <span class="hlt">Eulerian</span> Air Quality Models" is a brief introduction to the papers included in a special issue of Atmospheric Environment. The Preface provides a background for the papers, which have thei...</p>
</li>
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<ol class="result-class" start="481">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1919023P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1919023P"><span><span class="hlt">Lagrangian</span> Observations and Modeling of Marine Larvae</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Paris, Claire B.; Irisson, Jean-Olivier</p>
<p>2017-04-01</p>
<p>Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a <span class="hlt">Lagrangian</span> platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed <span class="hlt">Lagrangian</span> behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source <span class="hlt">Lagrangian</span> tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive <span class="hlt">Lagrangian</span> trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=75840&keyword=API&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=75840&keyword=API&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>DESCRIPTION OF ATMOSPHERIC TRANSPORT PROCESSES IN <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p>
<p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p>
<p></p>
<p></p>
<p>Key differences among many types of air quality models are the way atmospheric advection and turbulent diffusion processes are treated. Gaussian models use analytical solutions of the advection-diffusion equations. <span class="hlt">Lagrangian</span> models use a hypothetical air parcel concept effecti...</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27415358','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27415358"><span>Spectral-clustering approach to <span class="hlt">Lagrangian</span> vortex detection.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George</p>
<p>2016-06-01</p>
<p>One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of <span class="hlt">Lagrangian</span> trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent <span class="hlt">Lagrangian</span> vortices in several two- and three-dimensional flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA495081','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA495081"><span>Heterogeneous Teams of Autonomous Vehicles: Advanced Sensing & Control</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2009-03-01</p>
<p>Final Technical 3. DATES COVERED (From To) 7/1/05-12/31708 4. TITLE AND SUBTITLE Heterogeneous Teams of Autonomous Vehicles Advanced Sensing...assimilating data from underwater and surface autonomous vehicles in addition to the usual sources of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> systems into a small scale</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..SHK.D2004W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..SHK.D2004W"><span>Using Underwater Explosion and Cylinder Expansion Tests to Calibrate Afterburn Models for Aluminized Explosives</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Wedberg, Rasmus</p>
<p>2017-06-01</p>
<p>The study explores the combined use of underwater performance tests and cylinder expansion tests in order to parameterize detonation models for aluminized explosives which exhibit afterburning. The approach is suggested to be used in conjunction with thermochemical computation. A <span class="hlt">formulation</span> containing RDX and aluminum powder is considered and several charges with varying masses are submerged and detonated. Pressure gauges are employed at horizontal distances scaling with the charge diameter, and the specific shock wave energy is shown to increase with charge mass. This is attributed to the combustion of aluminum particles after the Chapman-Jouguet plane. Cylinder expansion tests are carried out using Photon Doppler Velocimetry to register the wall expansion velocity. The tests are modeled using a multi-material arbitrary <span class="hlt">Lagrangian-Eulerian</span> approach with the Guirguis-Miller model describing detonation with afterburning. The equation of state and afterburn rate law parameters are adjusted such that the model reproduces the results from the cylinder expansion and underwater tests. The approach seems promising, and might be valuable for aluminized explosive <span class="hlt">formulations</span> intended to be used in a variety of confinement conditions. Swedish Armed Forces.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920010138','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920010138"><span>A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Chen, C. P.; Jiang, Y.; Kim, Y. M.; Shang, H. M.</p>
<p>1991-01-01</p>
<p>The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are <span class="hlt">formulated</span> based on the <span class="hlt">Eulerian</span>-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is <span class="hlt">formulated</span> by a <span class="hlt">Lagrangian</span> tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...10..106B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...10..106B"><span><span class="hlt">Lagrangians</span> for generalized Argyres-Douglas theories</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Benvenuti, Sergio; Giacomelli, Simone</p>
<p>2017-10-01</p>
<p>We continue the study of <span class="hlt">Lagrangian</span> descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the <span class="hlt">Lagrangians</span> of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16860933','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16860933"><span>Performance estimation of a Venturi scrubber using a computational model for capturing dust particles with liquid spray.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Pak, S I; Chang, K S</p>
<p>2006-12-01</p>
<p>A Venturi scrubber has dispersed three-phase flow of gas, dust, and liquid. Atomization of a liquid jet and interaction between the phases has a large effect on the performance of Venturi scrubbers. In this study, a computational model for the interactive three-phase flow in a Venturi scrubber has been developed to estimate pressure drop and collection efficiency. The <span class="hlt">Eulerian-Lagrangian</span> method is used to solve the model numerically. Gas flow is solved using the <span class="hlt">Eulerian</span> approach by using the Navier-Stokes equations, and the motion of dust and liquid droplets, described by the Basset-Boussinesq-Oseen (B-B-O) equation, is solved using the <span class="hlt">Lagrangian</span> approach. This model includes interaction between gas and droplets, atomization of a liquid jet, droplet deformation, breakup and collision of droplets, and capture of dust by droplets. A circular Pease-Anthony Venturi scrubber was simulated numerically with this new model. The numerical results were compared with earlier experimental data for pressure drop and collection efficiency, and gave good agreements.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....5310411D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....5310411D"><span>Elimination of the Reaction Rate "Scale Effect": Application of the <span class="hlt">Lagrangian</span> Reactive Particle-Tracking Method to Simulate Mixing-Limited, Field-Scale Biodegradation at the Schoolcraft (MI, USA) Site</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ding, Dong; Benson, David A.; Fernández-Garcia, Daniel; Henri, Christopher V.; Hyndman, David W.; Phanikumar, Mantha S.; Bolster, Diogo</p>
<p>2017-12-01</p>
<p>Measured (or empirically fitted) reaction rates at groundwater remediation sites are typically much lower than those found in the same material at the batch or laboratory scale. The reduced rates are commonly attributed to poorer mixing at the larger scales. A variety of methods have been proposed to account for this scaling effect in reactive transport. In this study, we use the <span class="hlt">Lagrangian</span> particle-tracking and reaction (PTR) method to simulate a field bioremediation experiment at the Schoolcraft, MI site. A denitrifying bacterium, Pseudomonas Stutzeri strain KC (KC), was injected to the aquifer, along with sufficient substrate, to degrade the contaminant, carbon tetrachloride (CT), under anaerobic conditions. The PTR method simulates chemical reactions through probabilistic rules of particle collisions, interactions, and transformations to address the scale effect (lower apparent reaction rates for each level of upscaling, from batch to column to field scale). In contrast to a prior <span class="hlt">Eulerian</span> reaction model, the PTR method is able to match the field-scale experiment using the rate coefficients obtained from batch experiments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19820017704&hterms=fashion+models&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dfashion%2Bmodels','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19820017704&hterms=fashion+models&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dfashion%2Bmodels"><span>Quasi-Langrangian models of nascent thermals</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Rambaldi, S.; Randall, D. A.</p>
<p>1981-01-01</p>
<p>The motions in and around an isolated thermal were studied and rising motion in the core, and sinking motion on the outside were found; while the circulation resembled that of a vortex ring. In an entity cloud model, cloudy thermal is tracked, in a <span class="hlt">Lagrangian</span> fashion, as a discrete entity; the field of motion in and around the thermal is not explicitly simulated. Field of motion cloud models, in which the equations of motion are numerically integrated on an <span class="hlt">Eulerian</span> grid were developed. It is shown that the great potential of a hybrid cloud model can combine the simplicity of the entity models with the generality and flexibility of the field-of-motion models. A key problem to be overcome in the development of a hybrid model is the <span class="hlt">formulation</span> of a mathematical framework within which the cloud dynamics can be represented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900045170&hterms=pdf&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3D%253F%253F%253F%253F%253F%2B%253F%253F%253F%253F%253F%253F%253F%2Bpdf','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900045170&hterms=pdf&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3D%253F%253F%253F%253F%253F%2B%253F%253F%253F%253F%253F%253F%253F%2Bpdf"><span>The pdf approach to turbulent flow</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kollmann, W.</p>
<p>1990-01-01</p>
<p>This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible <span class="hlt">formulations</span> for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JGRD..122.1387D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGRD..122.1387D"><span><span class="hlt">Lagrangian</span> dynamics of the mistral during the HyMeX SOP2</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Drobinski, P.; Alonzo, B.; Basdevant, C.; Cocquerez, P.; Doerenbecher, A.; Fourrié, N.; Nuret, M.</p>
<p>2017-02-01</p>
<p>The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the <span class="hlt">Lagrangian</span> documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.7726D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.7726D"><span><span class="hlt">Lagrangian</span> dynamics of the mistral during the HyMeX SOP2</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Drobinski, Philippe; Alonzo, Bastien; Basdevant, Claude; Cocquerez, Philippe; Fourrié, Nadia; Nuret, Mathieu</p>
<p>2017-04-01</p>
<p>The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the <span class="hlt">Lagrangian</span> documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the <span class="hlt">Lagrangian</span> <span class="hlt">formulation</span> of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=thought+AND+experiments&pg=2&id=EJ912884','ERIC'); return false;" href="https://eric.ed.gov/?q=thought+AND+experiments&pg=2&id=EJ912884"><span>Gravity, Time, and <span class="hlt">Lagrangians</span></span></a></p>
<p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p>
<p>Huggins, Elisha</p>
<p>2010-01-01</p>
<p>Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the <span class="hlt">Lagrangian</span>. (Why would one…</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017NPGeo..24..379C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NPGeo..24..379C"><span>Insights into the three-dimensional <span class="hlt">Lagrangian</span> geometry of the Antarctic polar vortex</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba</p>
<p>2017-07-01</p>
<p>In this paper we study the three-dimensional (3-D) <span class="hlt">Lagrangian</span> structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using <span class="hlt">Lagrangian</span> descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of <span class="hlt">Lagrangian</span> transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the <span class="hlt">Lagrangian</span> structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex <span class="hlt">Lagrangian</span> patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JChPh.146l4115V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JChPh.146l4115V"><span>Performance of extended <span class="hlt">Lagrangian</span> schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton</p>
<p>2017-03-01</p>
<p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics <span class="hlt">formulation</span> in both the classical and LS-DFT regimes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28388116','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28388116"><span>Performance of extended <span class="hlt">Lagrangian</span> schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton</p>
<p>2017-03-28</p>
<p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics <span class="hlt">formulation</span> in both the classical and LS-DFT regimes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1414137-performance-extended-lagrangian-schemes-molecular-dynamics-simulations-classical-polarizable-force-fields-density-functional-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1414137-performance-extended-lagrangian-schemes-molecular-dynamics-simulations-classical-polarizable-force-fields-density-functional-theory"><span>Performance of extended <span class="hlt">Lagrangian</span> schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...</p>
<p>2017-03-28</p>
<p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics <span class="hlt">formulation</span> in both the classical and LS-DFT regimes.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1414137','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1414137"><span>Performance of extended <span class="hlt">Lagrangian</span> schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex</p>
<p></p>
<p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics <span class="hlt">formulation</span> in both the classical and LS-DFT regimes.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CorRe..34..339K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CorRe..34..339K"><span>Environmental and ecological controls of coral community metabolism on Palmyra Atoll</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Koweek, David; Dunbar, Robert B.; Rogers, Justin S.; Williams, Gareth J.; Price, Nichole; Mucciarone, David; Teneva, Lida</p>
<p>2015-03-01</p>
<p>Accurate predictions of how coral reefs may respond to global climate change hinge on understanding the natural variability to which these ecosystems are exposed and to which they contribute. We present high-resolution estimates of net community calcification (NCC) and net community production (NCP) from Palmyra Atoll, an uninhabited, near-pristine coral reef ecosystem in the central Pacific. In August-October 2012, we employed a combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> frameworks to establish high spatial (~2.5 km2) and temporal (hourly) resolution coral community metabolic estimates. <span class="hlt">Lagrangian</span> drifts, all conducted during daylight hours, resulted in NCC estimates of -51 to 116 mmol C m-2 h-1, although most NCC estimates were in the range of 0-40 mmol C m-2 h-1. <span class="hlt">Lagrangian</span> drift NCP estimates ranged from -7 to 67 mmol C m-2 h-1. In the <span class="hlt">Eulerian</span> setup, we present carbonate system parameters (dissolved inorganic carbon, total alkalinity, pH, and pCO2) at sub-hourly resolution through several day-night cycles and provide hourly NCC and NCP rate estimates. We compared diel cycles of all four carbonate system parameters to the offshore surface water (0-50 m depth) and show large departures from offshore surface water chemistry. Hourly <span class="hlt">Eulerian</span> estimates of NCC aggregated over the entire study ranged from 14 to 53 mmol C m-2 h-1, showed substantial variability during daylight hours, and exhibited a diel cycle with elevated NCC in the afternoons and depressed, but positive, NCC at night. The <span class="hlt">Eulerian</span> NCP range was very high (-55 to 177 mmol C m-2 h-1) and exhibited strong variability during daylight hours. Principal components analysis revealed that NCC and NCP were most closely aligned with diel cycle forcing, whereas the NCC/NCP ratio was most closely aligned with reef community composition. Our analysis demonstrates that ecological community composition is the primary determinant of coral reef biogeochemistry on a near-pristine reef and that reef biogeochemistry is</p>
</li>
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