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 Lagrangian 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://www.osti.gov/scitech/servlets/purl/15013468','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15013468"><span>A Dynamically Adaptive Arbitrary Lagrangian-<span class="hlt">Eulerian</span> Method for 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>2004-01-28</p>
<p>A new method that combines staggered grid Arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15013438','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15013438"><span>A Dynamically Adaptive Arbitrary Lagrangian-<span class="hlt">Eulerian</span> Method for 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>2002-10-19</p>
<p>A new method that combines staggered grid Arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.</p>
</li>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD0758010','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD0758010"><span>On the <span class="hlt">Eulerian</span> AFTON Equations for Axisymmetric Fluid Flow,</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p></p>
<p>The AFTON codes are based on a method for constructing finite difference equations that describe the evolution of classical fields, and more...by the AFTON 2A code, one of whose versions has been specialized for solution of the time-dependent Navier-Stokes equations for compressible flow, in...<span class="hlt">Eulerian</span> form. The version of AFTON 2A in question has now been used to compute many viscous compressible flow fields. This report discusses the</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/10170321','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/10170321"><span>A domain decomposition scheme for <span class="hlt">Eulerian</span> shock physics codes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bell, R.L.; Hertel, E.S. Jr.</p>
<p>1994-08-01</p>
<p>A new algorithm which allows for complex domain decomposition in <span class="hlt">Eulerian</span> codes was developed at Sandia National Laboratories. This new feature allows a user to customize the zoning for each portion of a calculation and to refine volumes of the computational space of particular interest This option is available in one, two, and three dimensions. The new technique will be described in detail and several examples of the effectiveness of this technique will also be discussed.</p>
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<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 Lagrangian formulation, 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 formulation 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 formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the Lagrangian 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 Lagrangian 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('http://www.osti.gov/scitech/servlets/purl/882177','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/882177"><span>SUDOKU A STORY & A <span class="hlt">SOLVER</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>GARDNER, P.R.</p>
<p>2006-04-01</p>
<p>Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The <span class="hlt">solver</span>, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my <span class="hlt">solver</span> successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19940002930&hterms=microsoft+corporation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dmicrosoft%2Bcorporation','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19940002930&hterms=microsoft+corporation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dmicrosoft%2Bcorporation"><span>ALPS - A LINEAR PROGRAM <span class="hlt">SOLVER</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Viterna, L. A.</p>
<p>1994-01-01</p>
<p>Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program <span class="hlt">Solver</span>, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP <span class="hlt">solvers</span> is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/921146','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/921146"><span>SIERRA framework version 4 : <span class="hlt">solver</span> services.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Williams, Alan B.</p>
<p>2005-02-01</p>
<p>Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to <span class="hlt">solver</span> libraries are collectively referred to as <span class="hlt">solver</span> services. This paper provides an overview of SIERRA's <span class="hlt">solver</span> services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19990008891','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19990008891"><span>Effects of Helicity on Lagrangian and <span class="hlt">Eulerian</span> Time Correlations in Turbulence</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Rubinstein, Robert; Zhou, Ye</p>
<p>1998-01-01</p>
<p>Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences <span class="hlt">Eulerian</span> time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on <span class="hlt">Eulerian</span> time correlations is nonzero. Fourier analysis shows that the helicity effect on <span class="hlt">Eulerian</span> time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890011564','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890011564"><span>Euler <span class="hlt">solvers</span> for transonic applications</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Vanleer, Bram</p>
<p>1989-01-01</p>
<p>The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler <span class="hlt">solvers</span> to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910011452','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910011452"><span>ALPS: A Linear Program <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Ferencz, Donald C.; Viterna, Larry A.</p>
<p>1991-01-01</p>
<p>ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP <span class="hlt">solvers</span>, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910035662&hterms=squire&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dsquire','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910035662&hterms=squire&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dsquire"><span>Lagrangian and <span class="hlt">Eulerian</span> statistics obtained from direct numerical simulations of homogeneous turbulence</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Squires, Kyle D.; Eaton, John K.</p>
<p>1991-01-01</p>
<p>Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and <span class="hlt">Eulerian</span> data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and <span class="hlt">Eulerian</span> velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the <span class="hlt">Eulerian</span> microscale, presumably due to the advection of the small scales by the large scales in the <span class="hlt">Eulerian</span> reference frame.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.ars.usda.gov/research/publications/publication/?seqNo115=307912','TEKTRAN'); return false;" href="http://www.ars.usda.gov/research/publications/publication/?seqNo115=307912"><span>Parallelizing alternating direction implicit <span class="hlt">solver</span> on GPUs</span></a></p>
<p><a target="_blank" href="https://www.ars.usda.gov/research/publications/find-a-publication/">USDA-ARS?s Scientific Manuscript database</a></p>
<p></p>
<p></p>
<p>We present a parallel Alternating Direction Implicit (ADI) <span class="hlt">solver</span> on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28269059','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28269059"><span>Vital sign monitoring utilizing <span class="hlt">Eulerian</span> video magnification and thermography.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Aubakir, Bauyrzhan; Nurimbetov, Birzhan; Tursynbek, Iliyas; Varol, Huseyin Atakan</p>
<p>2016-08-01</p>
<p>In this paper we present a proof of concept for non-contact extraction of vital signs using RGB and thermal images obtained from a smart phone. Using our method, heart rate, respiratory rate and forehead temperature can be measured concurrently. Face detection and tracking is leveraged in order to allow natural motion of patients. Heart rate is estimated via processing of visible band RGB video using <span class="hlt">Eulerian</span> Video Magnification technique. Respiratory rate and the temperature is measured using thermal video. Experiments conducted with 11 healthy subjects indicate that heart rate and respiration rate can be measured with 92 and 94 percent accuracy, respectively.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/5860418','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/5860418"><span>MESA: A 3-D <span class="hlt">Eulerian</span> hydrocode for penetration mechanics studies</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Mandell, D.A.; Holian, K.S.; Henninger, R.</p>
<p>1991-01-01</p>
<p>We describe an explicit, finite-difference hydrocode, called MESA, and compare calculations to metal and ceramic plate impacts with spall and to Taylor cylinder tests. The MESA code was developed with support from DARPA, the Army and the Marine Corps for use in armor/anti-armor problems primarily, but the code has been used for a number of other applications. MESA includes 2-D and 3-D <span class="hlt">Eulerian</span> hydrodynamics, a number of material strength and fracture models, and a programmed burn high explosives model. 15 refs., 4 figs.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880030086&hterms=entropy+lamb&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dentropy%2Blamb','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880030086&hterms=entropy+lamb&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dentropy%2Blamb"><span>Prospects for <span class="hlt">Eulerian</span> CFD analysis of helicopter vortex flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Drela, Mark; Murman, Earll M.</p>
<p>1987-01-01</p>
<p>The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel <span class="hlt">Eulerian</span>/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDR34006I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDR34006I"><span>Lagrangian and <span class="hlt">Eulerian</span> statistics in homogeneous, anisotropic flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Iyer, Kartik; Bonaccorso, Fabio; Toschi, Federico; Biferale, Luca</p>
<p>2016-11-01</p>
<p>We report results from highly resolved direct numerical simulations of anisotropic homogeneous flows using up to 20483 collocations points. We examine a turbulent Kolmogorov flow with randomly correlated phases in order to recover space homogeneity on average. We present <span class="hlt">Eulerian</span> and Lagrangian measurements concerning the universality of isotropic and anisotropic contributions using a systematic decomposition based on the eigenfunctions of the SO (3) group of rotations in three dimensions. Additionally, we discuss absolute dispersion statistics of particles in flows subjected to different large-scale anisotropies. ERC ADG NewTURB 2013.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDE17001I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDE17001I"><span>Improved Stiff ODE <span class="hlt">Solvers</span> for Combustion CFD</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Imren, A.; Haworth, D. C.</p>
<p>2016-11-01</p>
<p>Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) <span class="hlt">solver</span> to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE <span class="hlt">solvers</span> for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE <span class="hlt">solver</span> couples with the CFD algorithm. In this work, a fresh look at stiff ODE <span class="hlt">solvers</span> is taken that includes how the <span class="hlt">solver</span> is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based <span class="hlt">solvers</span> in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19563427','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19563427"><span>A parallel PCG <span class="hlt">solver</span> for MODFLOW.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Dong, Yanhui; Li, Guomin</p>
<p>2009-01-01</p>
<p>In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) <span class="hlt">solver</span> with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the <span class="hlt">solver</span> transit to a parallel program smoothly one block of code at a time. The parallel PCG <span class="hlt">solver</span>, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG <span class="hlt">solver</span> are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG <span class="hlt">solver</span>, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG <span class="hlt">solver</span> code needs to be maintained in the MODFLOW source tree.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/982821','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/982821"><span><span class="hlt">Eulerian</span> hydrocode modeling of a dynamic tensile extrusion experiment (u)</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Burkett, Michael W; Clancy, Sean P</p>
<p>2009-01-01</p>
<p><span class="hlt">Eulerian</span> hydrocode simulations utilizing the Mechanical Threshold Stress flow stress model were performed to provide insight into a dynamic extrusion experiment. The dynamic extrusion response of copper (three different grain sizes) and tantalum spheres were simulated with MESA, an explicit, 2-D <span class="hlt">Eulerian</span> continuum mechanics hydrocode and compared with experimental data. The experimental data consisted of high-speed images of the extrusion process, recovered extruded samples, and post test metallography. The hydrocode was developed to predict large-strain and high-strain-rate loading problems. Some of the features of the features of MESA include a high-order advection algorithm, a material interface tracking scheme and a van Leer monotonic advection-limiting. The Mechanical Threshold Stress (MTS) model was utilized to evolve the flow stress as a function of strain, strain rate and temperature for copper and tantalum. Plastic strains exceeding 300% were predicted in the extrusion of copper at 400 m/s, while plastic strains exceeding 800% were predicted for Ta. Quantitative comparisons between the predicted and measured deformation topologies and extrusion rate were made. Additionally, predictions of the texture evolution (based upon the deformation rate history and the rigid body rotations experienced by the copper during the extrusion process) were compared with the orientation imaging microscopy measurements. Finally, comparisons between the calculated and measured influence of the initial texture on the dynamic extrusion response of tantalum was performed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003PASP..115..303T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003PASP..115..303T"><span>A Primer on <span class="hlt">Eulerian</span> Computational Fluid Dynamics for Astrophysics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Trac, Hy; Pen, Ue-Li</p>
<p>2003-03-01</p>
<p>We present a pedagogical review of some of the methods employed in <span class="hlt">Eulerian</span> computational fluid dynamics (CFD). Fluid mechanics is governed by the Euler equations, which are conservation laws for mass, momentum, and energy. The standard approach to <span class="hlt">Eulerian</span> CFD is to divide space into finite volumes or cells and store the cell-averaged values of conserved hydro quantities. The integral Euler equations are then solved by computing the flux of the mass, momentum, and energy across cell boundaries. We review both first-order and second-order flux assignment schemes. All linear schemes are either dispersive or diffusive. The nonlinear, second-order accurate total variation diminishing (TVD) approach provides high-resolution capturing of shocks and prevents unphysical oscillations. We review the relaxing TVD scheme, a simple and robust method to solve systems of conservation laws such as the Euler equations. A three-dimensional relaxing TVD code is applied to the Sedov-Taylor blast-wave test. The propagation of the blast wave is accurately captured and the shock front is sharply resolved. We apply a three-dimensional self-gravitating hydro code to simulating the formation of blue straggler stars through stellar mergers and present some numerical results. A sample three-dimensional relaxing TVD code is provided in the Appendix.</p>
</li>
</ol>
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<ol class="result-class" start="101">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980237451','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980237451"><span><span class="hlt">Eulerian</span>-Lagrangian Simulations of Transonic Flutter Instabilities</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bendiksen, Oddvar O.</p>
<p>1994-01-01</p>
<p>This paper presents an overview of recent applications of <span class="hlt">Eulerian</span>-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an <span class="hlt">Eulerian</span> to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AnGeo..29...97V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AnGeo..29...97V"><span>Inductive ionospheric <span class="hlt">solver</span> for magnetospheric MHD simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vanhamäki, H.</p>
<p>2011-01-01</p>
<p>We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric <span class="hlt">solvers</span> currently in use, the new <span class="hlt">solver</span> takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive <span class="hlt">solver</span> is similar to the electrostatic <span class="hlt">solvers</span>, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive <span class="hlt">solver</span> is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).</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</span>-Lagrangian 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, L.F.; Hornberger, G.Z.</p>
<p>2000-01-01</p>
<p>This report documents the U.S. Geological Survey <span class="hlt">Eulerian</span>-Lagrangian 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 formulation 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 formulation. 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 <span class="hlt">solvers</span> 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('http://hdl.handle.net/2060/19950005164','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950005164"><span>A coupled <span class="hlt">Eulerian</span>/Lagrangian method for the solution of three-dimensional vortical flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Felici, Helene Marie</p>
<p>1992-01-01</p>
<p>A coupled <span class="hlt">Eulerian</span>/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard <span class="hlt">Eulerian</span> finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the <span class="hlt">Eulerian</span> time-marching procedure and provides a correction of the <span class="hlt">Eulerian</span> solution. In turn, the <span class="hlt">Eulerian</span> solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the <span class="hlt">Eulerian</span> solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard <span class="hlt">Eulerian</span> finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with <span class="hlt">Eulerian</span> solutions on finer grids. The use of the combined <span class="hlt">Eulerian</span>/Lagrangian scheme results in substantially lower grid resolution requirements than the standard <span class="hlt">Eulerian</span> scheme for a given solution accuracy.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992mit..reptT....F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992mit..reptT....F"><span>A coupled <span class="hlt">Eulerian</span>/Lagrangian method for the solution of three-dimensional vortical flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Felici, Helene Marie</p>
<p>1992-06-01</p>
<p>A coupled <span class="hlt">Eulerian</span>/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard <span class="hlt">Eulerian</span> finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the <span class="hlt">Eulerian</span> time-marching procedure and provides a correction of the <span class="hlt">Eulerian</span> solution. In turn, the <span class="hlt">Eulerian</span> solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the <span class="hlt">Eulerian</span> solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard <span class="hlt">Eulerian</span> finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with <span class="hlt">Eulerian</span> solutions on finer grids. The use of the combined <span class="hlt">Eulerian</span>/Lagrangian scheme results in substantially lower grid resolution requirements than the standard <span class="hlt">Eulerian</span> scheme for a given solution accuracy.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992PhDT........30F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992PhDT........30F"><span>A Coupled <span class="hlt">Eulerian</span>/lagrangian Method for the Solution of Three-Dimensional Vortical Flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Felici, Helene Marie</p>
<p>1992-01-01</p>
<p>A coupled <span class="hlt">Eulerian</span>/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard <span class="hlt">Eulerian</span> finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the <span class="hlt">Eulerian</span> time-marching procedure and provides a correction of the <span class="hlt">Eulerian</span> solution. In turn, the <span class="hlt">Eulerian</span> solution is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the <span class="hlt">Eulerian</span> solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters', take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard <span class="hlt">Eulerian</span> finite-volume methods. The combined solution procedure is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of a turbulent inlet velocity profile, the swirling flow in a pipe, the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with <span class="hlt">Eulerian</span> solutions on finer grids. The use of the combined <span class="hlt">Eulerian</span>/Lagrangian scheme results in substantially lower grid resolution requirements than the standard <span class="hlt">Eulerian</span> scheme for a given solution accuracy. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910023149','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910023149"><span>An approximate Riemann <span class="hlt">solver</span> for hypervelocity flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Jacobs, Peter A.</p>
<p>1991-01-01</p>
<p>We describe an approximate Riemann <span class="hlt">solver</span> for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The <span class="hlt">solver</span> is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the <span class="hlt">solver</span> performs well.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/936247','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/936247"><span>Using SPARK as a <span class="hlt">Solver</span> for Modelica</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.</p>
<p>2008-06-30</p>
<p>Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK <span class="hlt">solver</span> has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK <span class="hlt">solver</span> is competitive with Dymola, which is believed to provide the best <span class="hlt">solver</span> for Modelica.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/433387','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433387"><span>New iterative <span class="hlt">solvers</span> for the NAG Libraries</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Salvini, S.; Shaw, G.</p>
<p>1996-12-31</p>
<p>The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative <span class="hlt">solvers</span> for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative <span class="hlt">solvers</span>, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add <span class="hlt">solvers</span>, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26764851','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26764851"><span>Full <span class="hlt">Eulerian</span> lattice Boltzmann model for conjugate heat transfer.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong</p>
<p>2015-12-01</p>
<p>In this paper a full <span class="hlt">Eulerian</span> lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4820586','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4820586"><span>Noninvasive Free Flap Monitoring Using <span class="hlt">Eulerian</span> Video Magnification</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Liu, Yuan Fang; Vuong, Christopher; Walker, Paul Charles; Peterson, Nathaniel Ray; Inman, Jared Christian; Filho, Pedro Alcantara Andrade; Lee, Steve Choon-Sung</p>
<p>2016-01-01</p>
<p><span class="hlt">Eulerian</span> Video Magnification (EVM) can enhance subtle changes in videos to reveal what was once invisible to the naked eye. In this proof of concept study, we investigated using EVM as a novel form of free flap monitoring. Free flaps with skin paddles were filmed in the operating room with manipulation of their pedicles. In a representative 77-year-old female who received a latissimus dorsi-serratus-rib composite free flap, EVM was able to detect blockage of arterial or venous supply instantaneously, providing a visible representation through degree of color change in videos. EVM has the potential to serve as a powerful free flap monitoring tool with the benefit of being noninvasive, sensitive, easy-to-use, and nearly cost-free. PMID:27092284</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22220571','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22220571"><span>Hamiltonian magnetohydrodynamics: Lagrangian, <span class="hlt">Eulerian</span>, and dynamically accessible stability—Theory</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Andreussi, T.; Morrison, P. J.; Pegoraro, F.</p>
<p>2013-09-15</p>
<p>Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of <span class="hlt">Eulerian</span> variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.</p>
</li>
<li>
<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 Lagrangian <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 Lagrangian <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 Lagrangian 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 Lagrangian 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1247151','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1247151"><span>Adaptive reconnection-based arbitrary Lagrangian <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>2015-07-21</p>
<p>We present a new adaptive Arbitrary Lagrangian <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 Lagrangian 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 Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE 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.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880061851&hterms=Beats+waves&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DBeats%2Bwaves','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880061851&hterms=Beats+waves&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DBeats%2Bwaves"><span><span class="hlt">Eulerian</span> measurements of horizontal accelerations in shoaling gravity waves</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Elgar, Steve; Guza, R. T.; Freilich, M. H.</p>
<p>1988-01-01</p>
<p>Laboratory and field measurements of suspended sediment in the nearshore suggest that fluid accelerations are an important factor in sediment transport by oscillatory waves. Here, <span class="hlt">Eulerian</span> accelerations of the cross-shore velocity are calculated from measurements of velocity obtained by an array of bottom-mounted electromagnetic flow meters spanning a natural surf zone. Large shoreward accelerations of brief duration are associated with the steep front faces of both near-breaking and breaking waves. Weaker offshore accelerations of longer duration occur during passage of the more gently sloped rear faces. The acceleration field is thus strongly skewed in the shoreward direction. Power spectra and bispectra indicate, as expected, that statistics of the acceleration field are significantly influenced by high-frequency motions but are rather insensitive to surf beat.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525063','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525063"><span>Relativistic perturbations in ΛCDM: <span class="hlt">Eulerian</span> and Lagrangian approaches</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Villa, Eleonora; Rampf, Cornelius E-mail: cornelius.rampf@port.ac.uk</p>
<p>2016-01-01</p>
<p>We study the relativistic dynamics of a pressure-less and irrotational fluid of dark matter (CDM) with a cosmological constant (Λ), up to second order in cosmological perturbation theory. In our analysis we also account for vector and tensor perturbations and include primordial non-Gaussianity. We consider three gauges: the synchronous-comoving gauge, the Poisson gauge and the total matter gauge, where the first is the unique relativistic Lagrangian frame of reference, and the latters are convenient gauge choices for <span class="hlt">Eulerian</span> frames. Our starting point is the metric and fluid variables in the Poisson gauge up to second order. We then perform the gauge transformations to the synchronous-comoving gauge and subsequently to the total matter gauge. Our expressions for the metrics, densities, velocities, and the gauge generators are novel and coincide with known results in the limit of a vanishing cosmological constant.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4351671','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4351671"><span>Techniques to derive geometries for image-based <span class="hlt">Eulerian</span> computations</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Dillard, Seth; Buchholz, James; Vigmostad, Sarah; Kim, Hyunggun; Udaykumar, H.S.</p>
<p>2014-01-01</p>
<p>Purpose The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based <span class="hlt">Eulerian</span> fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted. Design/methodology/approach Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures. Findings While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics. Originality/value It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an <span class="hlt">Eulerian</span> setting. PMID</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1095954','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1095954"><span>Development and deployment of constitutive softening routines in <span class="hlt">Eulerian</span> hydrocodes.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Fuller, Timothy Jesse; Dewers, Thomas A.; Swan, Matthew Scot</p>
<p>2013-03-01</p>
<p>The state of the art in failure modeling enables assessment of crack nucleation, propagation, and progression to fragmentation due to high velocity impact. Vulnerability assessments suggest a need to track material behavior through failure, to the point of fragmentation and beyond. This eld of research is particularly challenging for structures made of porous quasi-brittle materials, such as ceramics used in modern armor systems, due to the complex material response when loading exceeds the quasi-brittle material's elastic limit. Further complications arise when incorporating the quasi-brittle material response in multi-material <span class="hlt">Eulerian</span> hydrocode simulations. In this report, recent e orts in coupling a ceramic materials response in the post-failure regime with an <span class="hlt">Eulerian</span> hydro code are described. Material behavior is modeled by the Kayenta material model [2] and Alegra as the host nite element code [14]. Kayenta, a three invariant phenomenological plasticity model originally developed for modeling the stress response of geologic materials, has in recent years been used with some success in the modeling of ceramic and other quasi-brittle materials to high velocity impact. Due to the granular nature of ceramic materials, Kayenta allows for signi cant pressures to develop due to dilatant plastic ow, even in shear dominated loading where traditional equations of state predict little or no pressure response. When a material's ability to carry further load is compromised, Kayenta allows the material's strength and sti ness to progressively degrade through the evolution of damage to the point of material failure. As material dilatation and damage progress, accommodations are made within Alegra to treat in a consistent manner the evolving state.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130001703','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130001703"><span>Extension of the Time-Spectral Approach to Overset <span class="hlt">Solvers</span> for Arbitrary Motion</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.</p>
<p>2012-01-01</p>
<p> demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian <span class="hlt">solvers</span> for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed <span class="hlt">Eulerian</span> mesh and mesh points in the <span class="hlt">Eulerian</span> mesh interior to the solid body are removed (cut or blanked), leaving a hole in the <span class="hlt">Eulerian</span> mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian <span class="hlt">solver</span> with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW <span class="hlt">solver</span> and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset <span class="hlt">solver</span> for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW <span class="hlt">solver</span> will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUFMGP51A1357K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUFMGP51A1357K"><span>Novel Scalable 3-D MT Inverse <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kuvshinov, A. V.; Kruglyakov, M.; Geraskin, A.</p>
<p>2016-12-01</p>
<p>We present a new, robust and fast, three-dimensional (3-D) magnetotelluric (MT) inverse <span class="hlt">solver</span>. As a forward modelling engine a highly-scalable <span class="hlt">solver</span> extrEMe [1] is used. The (regularized) inversion is based on an iterative gradient-type optimization (quasi-Newton method) and exploits adjoint sources approach for fast calculation of the gradient of the misfit. The inverse <span class="hlt">solver</span> is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT (single-site and/or inter-site) responses, and supports massive parallelization. Different parallelization strategies implemented in the code allow for optimal usage of available computational resources for a given problem set up. To parameterize an inverse domain a mask approach is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to high-performance clusters demonstrate practically linear scalability of the code up to thousands of nodes. 1. Kruglyakov, M., A. Geraskin, A. Kuvshinov, 2016. Novel accurate and scalable 3-D MT forward <span class="hlt">solver</span> based on a contracting integral equation method, Computers and Geosciences, in press.</p>
</li>
</ol>
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<ol class="result-class" start="121">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950010045','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950010045"><span>Equation <span class="hlt">solvers</span> for distributed-memory computers</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Storaasli, Olaf O.</p>
<p>1994-01-01</p>
<p>A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation <span class="hlt">solvers</span> with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/984939','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/984939"><span>A comparison of Lagrangian/<span class="hlt">Eulerian</span> approaches for tracking the kinematics of high deformation solid motion.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad</p>
<p>2009-09-01</p>
<p>The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/<span class="hlt">Eulerian</span> or a pure <span class="hlt">Eulerian</span> modeling framework must be introduced. We discuss and contrast several Lagrangian/<span class="hlt">Eulerian</span> approaches for keeping track of the details of material kinematics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002JIntS...5...25L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002JIntS...5...25L"><span>A Note on the Total Number of Double <span class="hlt">Eulerian</span> Circuits in Multigraphs</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Liskovets, Valery</p>
<p>2002-12-01</p>
<p>We formulate explicitly and discuss a simple new enumerative formula for double (directed) <span class="hlt">eulerian</span> circuits in n-edged labeled multigraphs. The formula follows easily from a recent 2-parametric formula of B. Lass.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=splitting+AND+water&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="http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=splitting+AND+water&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</span>-LAGRANGIAN 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</span>-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6138230','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6138230"><span>Multi-dimensional arbitrary Lagrangian-<span class="hlt">Eulerian</span> method for dynamic fluid-structure interaction. [LMFBR</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wang, C.Y.; Zeuch, W.R.</p>
<p>1982-01-01</p>
<p>This paper describes an arbitrary Lagrangian-<span class="hlt">Eulerian</span> method for analyzing fluid-structure interactions in fast-reactor containment with complex internal structures. The fluid transient can be calculated either implicitly or explicitly, using a finite-difference mesh with vertices that may be moved with the fluid (Lagrangian), held fixed (<span class="hlt">Eulerian</span>), or moved in any other prescribed manner (hybrid Lagrangian <span class="hlt">Eulerian</span>). The structural response is computed explicitly by two nonlinear, elastic-plastic finite-element modules formulated in corotational coordinates. Interaction between fluid and structure is accounted for by enforcing the interface boundary conditions. The method has convincing advantages in treating complicated phenomena such as flow through perforated structures, large material distortions, flow around corners and irregularities, and highly contorted fluid boundaries. Several sample problems are given to illustrate the effectiveness of this arbitrary Lagrangian-<span class="hlt">Eulerian</span> method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21418120','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21418120"><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; Qian Jianliang</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 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://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=numerical+AND+methods+AND+application&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&CFID=90806395&CFTOKEN=93168155','EPA-EIMS'); return false;" href="http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=numerical+AND+methods+AND+application&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&CFID=90806395&CFTOKEN=93168155"><span>AN <span class="hlt">EULERIAN</span>-LAGRANGIAN 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</span>-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130011909','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130011909"><span>Imposing a Lagrangian Particle Framework on an <span class="hlt">Eulerian</span> Hydrodynamics Infrastructure in Flash</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.</p>
<p>2012-01-01</p>
<p>In many astrophysical simulations, both <span class="hlt">Eulerian</span> and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have <span class="hlt">Eulerian</span> discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement <span class="hlt">Eulerian</span> framework to enable such simulations. The discretization of the field variables is <span class="hlt">Eulerian</span>, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22047620','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22047620"><span>IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN <span class="hlt">EULERIAN</span> HYDRODYNAMICS INFRASTRUCTURE IN FLASH</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.</p>
<p>2012-08-01</p>
<p>In many astrophysical simulations, both <span class="hlt">Eulerian</span> and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have <span class="hlt">Eulerian</span> discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement <span class="hlt">Eulerian</span> framework to enable such simulations. The discretization of the field variables is <span class="hlt">Eulerian</span>, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.326..290L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.326..290L"><span>High-order <span class="hlt">Eulerian</span> incompressible smoothed particle hydrodynamics with transition to Lagrangian free-surface motion</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lind, S. J.; Stansby, P. K.</p>
<p>2016-12-01</p>
<p>The incompressible Smoothed Particle Hydrodynamics (ISPH) method is derived in <span class="hlt">Eulerian</span> form with high-order smoothing kernels to provide increased accuracy for a range of steady and transient internal flows. Periodic transient flows, in particular, demonstrate high-order convergence and accuracies approaching, for example, spectral mesh-based methods. The improved accuracies are achieved through new high-order Gaussian kernels applied over regular particle distributions with time stepping formally up to 2nd order for transient flows. The <span class="hlt">Eulerian</span> approach can be easily extended to model free surface flows by merging from <span class="hlt">Eulerian</span> to Lagrangian regions in an Arbitrary-Lagrangian-<span class="hlt">Eulerian</span> (ALE) fashion, and a demonstration with periodic wave propagation is presented. In the long term, it is envisaged that the method will greatly increase the accuracy and efficiency of SPH methods, while retaining the flexibility of SPH in modelling free surface and multiphase flows.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDL12009R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDL12009R"><span><span class="hlt">Eulerian</span>-Lagrangian Simulation of an Explosive Dispersal of Particles</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Rollin, Bertrand; Ouellet, Frederick; Koneru, Rahul; Annamalai, Subramanian</p>
<p>2016-11-01</p>
<p>Explosive dispersal of solid particles can be observed in a wide variety of contexts, notably in natural phenomenon such as volcanic eruptions or in engineering applications such as detonation of multiphase explosives. As the initial blast wave crosses the surrounding layer of particles, compaction occurs shortly before particles disperse radially outward at high speed. During the dispersion phase, complex multiphase interactions occurs between particles and detonation products of the explosive. Using a <span class="hlt">Eulerian</span>-Lagrangian approach, namely point particle simulations, we study the case of a bed of particles of cylindrical shape surrounding an explosive chord. Our interest lies in predicting the behavior of particles after detonation. In particular, capturing and describing the mechanisms responsible for late-time formation of stable particle jets is sought. Therefore, detonation of the explosive material is not simulated. Instead an equivalent energy source is used to initiate the simulation. We present a detailed description of our approach to solving this problem, and our most recent progress in the analysis of particles explosive dispersal. This work was supported by the U.S. DoE, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.</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>Lagrangian 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 Lagrangian 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://adsabs.harvard.edu/abs/2013PhPl...20i2111P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhPl...20i2111P"><span><span class="hlt">Eulerian</span> simulations of collisional effects on electrostatic plasma waves</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pezzi, Oreste; Valentini, Francesco; Perrone, Denise; Veltri, Pierluigi</p>
<p>2013-09-01</p>
<p>The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attack, both from the theoretical and the numerical point of view. In this paper, a <span class="hlt">Eulerian</span> time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear forms. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. O'Neil, Phys. Plasmas 14, 112110 (2007)]. Finally, for the study of collisional plasmas, a recipe to set the simulation parameters in order to prevent the filamentation problem can be provided, by exploiting the property of velocity diffusion operators to smooth out small velocity scales.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22220578','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22220578"><span><span class="hlt">Eulerian</span> simulations of collisional effects on electrostatic plasma waves</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pezzi, Oreste; Valentini, Francesco; Perrone, Denise; Veltri, Pierluigi</p>
<p>2013-09-15</p>
<p>The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attack, both from the theoretical and the numerical point of view. In this paper, a <span class="hlt">Eulerian</span> time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear forms. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. O'Neil, Phys. Plasmas 14, 112110 (2007)]. Finally, for the study of collisional plasmas, a recipe to set the simulation parameters in order to prevent the filamentation problem can be provided, by exploiting the property of velocity diffusion operators to smooth out small velocity scales.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001AGUSM...A42A05H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001AGUSM...A42A05H"><span>Comparison between <span class="hlt">Eulerian</span> and Lagrangian Atmospheric Transport Models</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Heinrich, P.; Grillon, Y.</p>
<p>2001-05-01</p>
<p>Two numerical atmospheric models are tested and compared both in backward and forward modes to study the transport and dispersion of radioactive gases in the framework of the Comprehensive Test Ban Treaty. The first one (LMDZ) has been developed at the Laboratoire de Meteorologie Dynamique in Paris,it calculates <span class="hlt">eulerian</span> large-scale advection based upon finite-volume methods and parametrization of turbulent mixing and convection. The second one (HYSPLIT), developed by the Air Resources Laboratory of NOAA, is lagrangian and calculated 3D trajectories of particules, taking also into account dispersion due to wind shear. Concentrations of particules are compared at stations of the CTBT network for a fictitious source in the Pacific Ocean, that is assumed to be punctual in time and space. In the backward mode, concentrations are calculated and compared over 15 days from a point source at Tahiti to determine the field of regard for this station. Sensitivity tests are carried out by varying the spatial resolution of models.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..1714193O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..1714193O"><span>Currents in the Dead Sea: Lagrangian and <span class="hlt">Eulerian</span> observations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav</p>
<p>2015-04-01</p>
<p>The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (<span class="hlt">Eulerian</span>) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA540238','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA540238"><span>A Lagrangian-<span class="hlt">Eulerian</span> Approach to Modeling Homogeneous Condensation in High Density Flows (POSTPRINT)</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2011-01-01</p>
<p>Homogeneous Condensation in High Density Gas Expansions (Postprint) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Ryan Jansen ...Prescribed by ANSI Std. 239.18 A Lagrangian–<span class="hlt">Eulerian</span> approach to modeling homogeneous condensation in high density gas expansions Ryan Jansen , Natalia...Lagrangian–<span class="hlt">Eulerian</span> approach to modeling homogeneous condensation in high density gas expansions Ryan Jansen ,1 Natalia Gimelshein,2 Sergey Gimelshein,2</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA476972','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA476972"><span>Space Weather Applications of the UAF <span class="hlt">Eulerian</span> Parallel Polar Ionosphere Model (EPPIM)</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2006-06-01</p>
<p>list in Figure 1) and from other facilities (for instance, HAARP digizonde at Gakona, Alaska). Space Weather Applications of the UAF <span class="hlt">Eulerian</span>...RTO-MP-IST-056 11 - 1 UNCLASSIFIED/UNLIMITED UNCLASSIFIED/UNLIMITED Space Weather Applications of the UAF <span class="hlt">Eulerian</span> Parallel Polar Ionosphere...series of geophysical indices is capable of providing useful space weather forecasts. Further improvement of the forecasts by applying data</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013OcDyn..63..565W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013OcDyn..63..565W"><span>Difference between the Lagrangian trajectories and <span class="hlt">Eulerian</span> residual velocity fields in the southwestern Yellow Sea</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Wang, Bin; Hirose, Naoki; Moon, Jae-Hong; Yuan, Dongliang</p>
<p>2013-05-01</p>
<p>The responses to tidal and/or wind forces of Lagrangian trajectories and <span class="hlt">Eulerian</span> residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward <span class="hlt">Eulerian</span> residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward <span class="hlt">Eulerian</span> residual current rather than following it. Additional sensitivity experiments reveal that the influence of the <span class="hlt">Eulerian</span> tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the <span class="hlt">Eulerian</span> tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the <span class="hlt">Eulerian</span> residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1993cfd..proc..511N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1993cfd..proc..511N"><span>Implicit compressible flow <span class="hlt">solvers</span> on 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>Nagaoka, Makoto; Horinouchi, Nariaki</p>
<p>1993-09-01</p>
<p>An implicit <span class="hlt">solver</span> for compressible flows using Bi-CGSTAB method is proposed. The Euler equations are discretized with the delta-form by the finite volume method on the cell-centered triangular unstructured meshes. The numerical flux is calculated by Roe's upwind scheme. The linearized simultaneous equations with the irregular nonsymmetric sparse matrix are solved by the Bi-CGSTAB method with the preconditioner of incomplete LU factorization. This method is also vectorized by the multi-colored ordering. Although the <span class="hlt">solver</span> requires more computational memory, it shows faster and more robust convergence than the other conventional methods: three-stage Runge-Kutta method, point Gauss-Seidel method, and Jacobi method for two-dimensional inviscid steady flows.</p>
</li>
</ol>
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<ol class="result-class" start="141">
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/986082','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/986082"><span>Implicit Riemann <span class="hlt">solvers</span> for the Pn equations.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Mehlhorn, Thomas Alan; McClarren, Ryan; Brunner, Thomas A.; Holloway, James Paul</p>
<p>2005-03-01</p>
<p>The spherical harmonics (P{sub n}) approximation to the transport equation for time dependent problems has previously been treated using Riemann <span class="hlt">solvers</span> and explicit time integration. Here we present an implicit time integration method for the P n equations using Riemann <span class="hlt">solvers</span>. Both first-order and high-resolution spatial discretization schemes are detailed. One facet of the high-resolution scheme is that a system of nonlinear equations must be solved at each time step. This nonlinearity is the result of slope reconstruction techniques necessary to avoid the introduction of artifical extrema in the numerical solution. Results are presented that show auspicious agreement with analytical solutions using time steps well beyond the CFL limit.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1168984','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1168984"><span>Aleph Field <span class="hlt">Solver</span> Challenge Problem Results Summary</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Hooper, Russell; Moore, Stan Gerald</p>
<p>2015-01-01</p>
<p>Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core <span class="hlt">solver</span> capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field <span class="hlt">solver</span> via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950016514','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950016514"><span>A perspective on unstructured grid flow <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Venkatakrishnan, V.</p>
<p>1995-01-01</p>
<p>This survey paper assesses the status of compressible Euler and Navier-Stokes <span class="hlt">solvers</span> on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22273973','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22273973"><span>Domain decomposition for the SPN <span class="hlt">solver</span> MINOS</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques</p>
<p>2012-07-01</p>
<p>In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS <span class="hlt">solver</span> of the APOLLO3 (R) code. (authors)</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017SoftX...6..124W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017SoftX...6..124W"><span>The Openpipeflow Navier-Stokes <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Willis, Ashley P.</p>
<p></p>
<p>Pipelines are used in a huge range of industrial processes involving fluids, and the ability to accurately predict properties of the flow through a pipe is of fundamental engineering importance. Armed with parallel MPI, Arnoldi and Newton-Krylov <span class="hlt">solvers</span>, the Openpipeflow code can be used in a range of settings, from large-scale simulation of highly turbulent flow, to the detailed analysis of nonlinear invariant solutions (equilibria and periodic orbits) and their influence on the dynamics of the flow.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012TTSP...41..495J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012TTSP...41..495J"><span>Domain Decomposition for the SPN <span class="hlt">Solver</span> MINOS</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques</p>
<p>2012-12-01</p>
<p>In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS <span class="hlt">solver</span> of the APOLLO3® code.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA588626','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA588626"><span>Gerris Flow <span class="hlt">Solver</span>: Implementation and Application</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2013-05-12</p>
<p>Zienkiewicz, 1966). It is the <span class="hlt">solver</span> for the Imperial College Ocean Model (ICOM), which uses 3D adaptive mesh methods (Ford et al., 2004). The finite...method (Popinet, 2003). The 3D Gerris model was used to study air turbulence associated with a complex shape with good match to observations (Popinet...et al., 2004). The Ocean module of Gerris was described by Popinet and Rickard (2004) as an adaptive, finite-volume, 3D , incompressible, N-S fluid</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019201','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019201"><span>A multigrid <span class="hlt">solver</span> for the semiconductor equations</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bachmann, Bernhard</p>
<p>1993-01-01</p>
<p>We present a multigrid <span class="hlt">solver</span> for the exponential fitting method. The <span class="hlt">solver</span> is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid <span class="hlt">solvers</span>, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20938489','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20938489"><span>Differential geometry based solvation model I: <span class="hlt">Eulerian</span> formulation.</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>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 salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an <span class="hlt">Eulerian</span> formulation 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('http://adsabs.harvard.edu/abs/2015MNRAS.450.3319L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015MNRAS.450.3319L"><span>Voids in modified gravity reloaded: <span class="hlt">Eulerian</span> void assignment</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lam, Tsz Yan; Clampitt, Joseph; Cai, Yan-Chuan; Li, Baojiu</p>
<p>2015-07-01</p>
<p>We revisit the excursion set approach to calculate void abundances in chameleon-type modified gravity theories, which was previously studied by Clampitt, Cai & Li. We focus on properly accounting for the void-in-cloud effect, i.e. the growth of those voids sitting in overdense regions may be restricted by the evolution of their surroundings. This effect may change the distribution function of voids hence affect predictions on the differences between modified gravity (MG) and general relativity (GR). We show that the thin-shell approximation usually used to calculate the fifth force is qualitatively good but quantitatively inaccurate. Therefore, it is necessary to numerically solve the fifth force in both overdense and underdense regions. We then generalize the <span class="hlt">Eulerian</span>-void-assignment method of Paranjape, Lam & Sheth to our modified gravity model. We implement this method in our Monte Carlo simulations and compare its results with the original Lagrangian methods. We find that the abundances of small voids are significantly reduced in both MG and GR due to the restriction of environments. However, the change in void abundances for the range of void radii of interest for both models is similar. Therefore, the difference between models remains similar to the results from the Lagrangian method, especially if correlated steps of the random walks are used. As Clampitt et al., we find that the void abundance is much more sensitive to MG than halo abundances. Our method can then be a faster alternative to N-body simulations for studying the qualitative behaviour of a broad class of theories. We also discuss the limitations and other practical issues associated with its applications.</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> formulation</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 Lagrangian formulation of the surface energy into an <span class="hlt">Eulerian</span> formulation 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('http://adsabs.harvard.edu/abs/2016PhRvF...1f4404C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvF...1f4404C"><span><span class="hlt">Eulerian</span> formulation of the interacting particle representation model of 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>Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca</p>
<p>2016-10-01</p>
<p>The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the confines of a one-point model. In the original formulation [Kassinos and Reynolds, Center for Turbulence Research: Annual Research Briefs, 31-51 (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is reformulated in an <span class="hlt">Eulerian</span> framework, and evolution equations are developed for the marginal probability density functions (PDFs). <span class="hlt">Eulerian</span> methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with <span class="hlt">Eulerian</span> simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new <span class="hlt">Eulerian</span> solution method are thoroughly analyzed. The sensitivity of the <span class="hlt">Eulerian</span> simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between <span class="hlt">Eulerian</span> and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new <span class="hlt">Eulerian</span> solution method and the original Lagrangian approach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MS%26E..232a2032G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MS%26E..232a2032G"><span>A fluid-structure interaction <span class="hlt">solver</span> for the fluid flow through reed type valves</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>González, I.; Naseri, A.; Rigola, J.; Pérez-Segarra, C. D.; Oliva, A.</p>
<p>2017-08-01</p>
<p>Suction and discharge processes with self actuated valves have a major influence in efficiency and reliability of hermetic reciprocating compressors. Understanding the operation completely in order to enhance compressor’s design needs precise prediction of the fluid-structure interaction complexities involved in these processes. This paper presents a comprehensive description of a numerical methodology to account for the coupled behaviour of a reed valve and a turbulent flow. The method is based on a partitioned semi-implicit scheme that only strongly couples the fluid pressure term to the structural <span class="hlt">solver</span>. A three-dimensional CFD analysis with LES turbulence modelling is used for the flow while a combination of plate theory and mode summation method is used for the solid. The dynamically changing domains are tackled by means of lagrangian and arbitrary lagrangian-<span class="hlt">eulerian</span> approaches for the solid and the fluid, respectively. The whole model is compared with experimental data at Reynolds number 10, 000, showing good agreement in lift amplitude and deformation fluctuations. Finally, as an illustrative case, results regarding lift, pressures, force and effective areas are compared with those of a valve with wider gland.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.326..312C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.326..312C"><span>A multi-dimensional finite volume cell-centered direct ALE <span class="hlt">solver</span> for hydrodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Clair, G.; Ghidaglia, J.-M.; Perlat, J.-P.</p>
<p>2016-12-01</p>
<p>In this paper we describe a second order multi-dimensional scheme, belonging to the class of direct Arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) methods, for the solution of non-linear hyperbolic systems of conservation law. The scheme is constructed upon a cell-centered explicit Lagrangian <span class="hlt">solver</span> completed with an edge-based upwinded formulation of the numerical fluxes, computed from the MUSCL-Hancock method, to obtain a full ALE formulation. Numerical fluxes depend on nodal grid velocities which are either set or computed to avoid most of the mesh problems typically encountered in purely Lagrangian simulations. In order to assess the robustness of the scheme, most results proposed in this paper have been obtained by computing the grid velocities as a fraction of the Lagrangian nodal velocities, the ratio being set before running the test case. The last part of the paper describes preliminary results about the triple point test case run in the ALE framework by computing the grid velocities with the fully adaptive Large Eddy Limitation (L.E.L.) method proposed in [1]. Such a method automatically computes the grid velocities at each node defining the mesh from the local characteristics of the flow. We eventually discuss the advantages and the drawback of the coupling.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.270..432P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.270..432P"><span>Approximate Riemann <span class="hlt">solvers</span> for the Godunov SPH (GSPH)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Puri, Kunal; Ramachandran, Prabhu</p>
<p>2014-08-01</p>
<p>The Godunov Smoothed Particle Hydrodynamics (GSPH) method is coupled with non-iterative, approximate Riemann <span class="hlt">solvers</span> for solutions to the compressible Euler equations. The use of approximate <span class="hlt">solvers</span> avoids the expensive solution of the non-linear Riemann problem for every interacting particle pair, as required by GSPH. In addition, we establish an equivalence between the dissipative terms of GSPH and the signal based SPH artificial viscosity, under the restriction of a class of approximate Riemann <span class="hlt">solvers</span>. This equivalence is used to explain the anomalous “wall heating” experienced by GSPH and we provide some suggestions to overcome it. Numerical tests in one and two dimensions are used to validate the proposed Riemann <span class="hlt">solvers</span>. A general SPH pairing instability is observed for two-dimensional problems when using unequal mass particles. In general, Ducowicz Roe's and HLLC approximate Riemann <span class="hlt">solvers</span> are found to be suitable replacements for the iterative Riemann <span class="hlt">solver</span> in the original GSPH scheme.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21167776','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21167776"><span><span class="hlt">Eulerian</span> Gaussian beams for Schroedinger equations in the semi-classical regime</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Leung, Shingyu Qian Jianliang</p>
<p>2009-05-01</p>
<p>We propose Gaussian-beam based <span class="hlt">Eulerian</span> methods to compute semi-classical solutions of the Schroedinger equation. Traditional Gaussian beam type methods for the Schroedinger equation are based on the Lagrangian ray tracing. Based on the first <span class="hlt">Eulerian</span> Gaussian beam framework proposed in Leung et al. [S. Leung, J. Qian, R. Burridge, <span class="hlt">Eulerian</span> Gaussian beams for high frequency wave propagation, Geophysics 72 (2007) SM61-SM76], we develop a new <span class="hlt">Eulerian</span> Gaussian beam method which uses global Cartesian coordinates, level-set based implicit representation and Liouville equations. The resulting method gives uniformly distributed phases and amplitudes in phase space simultaneously. To obtain semi-classical solutions to the Schroedinger equation with different initial wave functions, we only need to slightly modify the summation formula. This yields a very efficient method for computing semi-classical solutions to the Schroedinger equation. For instance, in the one-dimensional case the proposed algorithm requires only O(sNm{sup 2}) operations to compute s different solutions with s different initial wave functions under the influence of the same potential, where N=O(1/h),h is the Planck constant, and m<<N is the number of computed beams which depends on h weakly. Numerical experiments indicate that this <span class="hlt">Eulerian</span> Gaussian beam approach yields accurate semi-classical solutions even at caustics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1793o0008D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1793o0008D"><span>Modeling and simulation challenges in <span class="hlt">Eulerian</span>-Lagrangian computations of 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>Diggs, Angela; Balachandar, S.</p>
<p>2017-01-01</p>
<p>The present work addresses the numerical methods required for particle-gas and particle-particle interactions in <span class="hlt">Eulerian</span>-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an <span class="hlt">Eulerian</span> grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an <span class="hlt">Eulerian</span> quantity associated with the flow. In Grid-Based (GB) methods, the volume fraction is first obtained within each cell as an <span class="hlt">Eulerian</span> quantity and then interpolated to each particle. In Particle-Based (PB) methods, the particle volume fraction is obtained at each particle and then projected onto the <span class="hlt">Eulerian</span> grid. Traditionally, GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of PB methods. By evaluating the total error and its components we compare the performance of GB and PB methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20787463','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20787463"><span>Efficient decoupling schemes with bounded controls based on <span class="hlt">Eulerian</span> orthogonal arrays</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wocjan, Pawel</p>
<p>2006-06-15</p>
<p>The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control, Viola and Knill proposed a method called '<span class="hlt">Eulerian</span> decoupling' that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the local structure of internal couplings and couplings to an environment that typically occur in multipartite quantum systems. In this paper we define a combinatorial structure called <span class="hlt">Eulerian</span> orthogonal array. It merges the desirable properties of orthogonal arrays and <span class="hlt">Eulerian</span> cycles in Cayley graphs (that are the basis of <span class="hlt">Eulerian</span> decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be used to remove both internal couplings and couplings to an environment of a multipartite quantum system. Furthermore, we show how to construct <span class="hlt">Eulerian</span> orthogonal arrays having good parameters in order to obtain efficient decoupling schemes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24h2509S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24h2509S"><span><span class="hlt">Eulerian</span> approach to bounce-transit and drift resonance with magnetic drifts in tokamaks</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Shaing, K. C.; Seol, J.; Chu, M. S.; Sabbagh, S. A.</p>
<p>2017-08-01</p>
<p>Bounce-transit and drift resonance can be important to plasma confinement in tokamaks with a broken symmetry. The resonance usually is either treated by integrating along the unperturbed orbits or calculated using an action-angle approach. An <span class="hlt">Eulerian</span> approach has been developed to take into account the momentum conservation property of the Coulomb collision operator. The difference between the <span class="hlt">Eulerian</span> approach and other approaches is in the thermodynamic forces of the transport fluxes, and the corresponding toroidal plasma viscosity. The mass and heat flows that are parallel to the equilibrium magnetic field B appear in the thermodynamic forces in the <span class="hlt">Eulerian</span> approach. However, in the existing <span class="hlt">Eulerian</span> approach, only the E × B drift is kept in the theory; the magnetic drifts, i.e., ∇B , and curvature drifts are neglected by adopting the large aspect ratio assumption, where E is the electric field and B = |B|. Here, the <span class="hlt">Eulerian</span> approach is extended to include the magnetic drifts, which is important for energetic alpha particles as well, to calculate neoclassical toroidal plasma viscosity in finite aspect ratio tokamaks. The relation to the nonlinear plasma viscosity in the plateau regime will also be discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20150022164','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20150022164"><span>Updates to the NEQAIR Radiation <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Cruden, Brett A.; Brandis, Aaron M.</p>
<p>2014-01-01</p>
<p>The NEQAIR code is one of the original heritage <span class="hlt">solvers</span> for radiative heating prediction in aerothermal environments, and is still used today for mission design purposes. This paper discusses the implementation of the first major revision to the NEQAIR code in the last five years, NEQAIR v14.0. The most notable features of NEQAIR v14.0 are the parallelization of the radiation computation, reducing runtimes by about 30×, and the inclusion of mid-wave CO2 infrared radiation.</p>
</li>
</ol>
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<ol class="result-class" start="161">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1990tmsf.proc...25H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1990tmsf.proc...25H"><span>Some topics of Navier-Stokes <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Honma, H.; Nishikawa, N.</p>
<p>1990-03-01</p>
<p>The process of numerical simulation consists of selection of some items: a mathematical model, a numerical scheme, the level of the computer, and post processing. From this point of view, recent numerical studies of viscous flows are described especially for the fluid engineering laboratories in the Chiba University. The examples of simulations are Mach reflection on a wedge using a kinetic model equation and a cylinder-plate juncture flow using incompressible Navier Stokes equation. Some attempts at graphic monitoring of fluid mechanical calculations are also shown for some combinations of computers with Computational Fluid Dynamics (CFD) <span class="hlt">solvers</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/10179588','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/10179588"><span>A finite different field <span class="hlt">solver</span> for dipole modes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Nelson, E.M.</p>
<p>1992-08-01</p>
<p>A finite element field <span class="hlt">solver</span> for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The <span class="hlt">solver</span> is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field <span class="hlt">solver</span> URMEL.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1326627','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1326627"><span>A 3D approximate maximum likelihood localization <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p></p>
<p>2016-09-23</p>
<p>A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with acoustic transmitters and vocalizing marine mammals to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives and support Marine Renewable Energy. An approximate maximum likelihood <span class="hlt">solver</span> was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature.</p>
</li>
<li>
<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</span>-Lagrangian 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</span>-Lagrangian 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 Lagrangian 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 Lagrangian 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22858466','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22858466"><span>Simulation on gasification of forestry residues in fluidized beds by <span class="hlt">Eulerian</span>-Lagrangian approach.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Xie, Jun; Zhong, Wenqi; Jin, Baosheng; Shao, Yingjuan; Liu, Hao</p>
<p>2012-10-01</p>
<p>A comprehensive three-dimensional numerical model is developed to simulate forestry residues gasification in a fluidized bed reactor using <span class="hlt">Eulerian</span>-Lagrangian approach. The complex granular flow behaviors and chemical reaction characteristics are addressed simultaneously. The model uses an <span class="hlt">Eulerian</span> method for fluid phase and a discrete particle method for solid phase, which takes particle contact force into account. Heterogeneous and homogenous reaction rates are solved on the <span class="hlt">Eulerian</span> grid. The numerical model is employed to study the gasification performance in a lab-scale pine gasifier. A series of simulations have been performed with some critical parameters including temperature, equivalence ratio and steam to biomass ratio. The model predicts product gas composition and carbon conversion efficiency in good agreement with experimental data. The formation and development of flow regimes, profiles of particle species, and distributions of gas compositions inside the reactor are also discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985ATJDS.107..258P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985ATJDS.107..258P"><span>Representation of measured ejector characteristics by simple <span class="hlt">Eulerian</span> bond graph models</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Paynter, H. M.</p>
<p>1985-12-01</p>
<p>For some time, a purely fluidic type of pump or compressor has existed. This device possesses no solid moving parts. Such an ejector of jet-pump employs the momentum of a high velocity jet from the drive flow to entrain and pressurize a secondary suction flow stream. One application of such ejectors is related to an employment by the nuclear industry. Certain accidents have drawn attention to the grossly inadequate data base for ejectors operating under extreme pathological conditions including reverse flows. In connection with these developments, extensive tests were conducted. The present paper uses primarily data obtained in these tests. Attention is given to an analysis of the test results, aspects of bond graph representation, internal <span class="hlt">Eulerian</span> flows satisfying a condition of <span class="hlt">Eulerian</span> similitude, a canonical model, moduli functions, a near-perfect <span class="hlt">Eulerian</span> device, and constant and variable paramter models. The considered tests and studies made it possible to establish a structured performance model for ejectors.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913150M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913150M"><span>Explicit <span class="hlt">solvers</span> in an implicit code</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Martinez Montesinos, Beatriz; Kaus, Boris J. P.; Popov, Anton</p>
<p>2017-04-01</p>
<p>Many geodynamic processes occur over long timescales (millions of years), and are best solved with implicit <span class="hlt">solvers</span>. Yet, some processes, such as hydrofracking, or wave propagation, occur over smaller timescales. In those cases, it might be advantageous to use an explicit rather than an implicit approach as it requires significantly less memory and computational costs. Here, we discuss our ongoing work to include explicit <span class="hlt">solvers</span> in the parallel software package LaMEM (Lithosphere and Mantle Evolution Model). As a first step, we focus on modelling seismic wave propagation in heterogeneous 3D poro-elasto-plastic models. To do that, we add inertial terms to the momentum equations as well as elastic compressibility to the mass conservation equations in an explicit way using the staggered grid finite difference discretization method. Results are similar to that of existing wave propagation codes and are capable to simulate wave propagation in heterogeneous media. To simulate geomechanical problems, timestep restrictions posed by the seismic wave speed are usually too severe to allow simulating deformation on a timescale of months-years. The classical (FLAC) method introduces a mass-density scaling in which a non-physical (larger) density is employed in the momentum equations. We will discuss how this method fits simple benchmarks for elastic and elastoplastic deformation. As an application, we use the code to model different complex media subject to compression and we investigate how mass scaling influence in our results.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..SHK.H4002D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..SHK.H4002D"><span>Modeling and Numerical Challenges in <span class="hlt">Eulerian</span>-Lagrangian Computations of Shock-driven 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>Diggs, Angela; Balachandar, Sivaramakrishnan</p>
<p>2015-06-01</p>
<p>The present work addresses the numerical methods required for particle-gas and particle-particle interactions in <span class="hlt">Eulerian</span>-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an <span class="hlt">Eulerian</span> grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an <span class="hlt">Eulerian</span> quantity associated with the flow. In <span class="hlt">Eulerian</span> Projection (EP) methods, the volume fraction is first obtained within each cell as an <span class="hlt">Eulerian</span> quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the <span class="hlt">Eulerian</span> grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.</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://www.osti.gov/scitech/servlets/purl/433367','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433367"><span>Experiences with linear <span class="hlt">solvers</span> for oil reservoir simulation problems</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.</p>
<p>1996-12-31</p>
<p>This talk will focus on practical experiences with iterative linear <span class="hlt">solver</span> algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear <span class="hlt">solver</span> algorithms for these types of problems. The results of numerical experiments will be presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..MARX27003K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..MARX27003K"><span>A real-time impurity <span class="hlt">solver</span> for DMFT</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kim, Hyungwon; Aron, Camille; Han, Jong E.; Kotliar, Gabriel</p>
<p></p>
<p>Dynamical mean-field theory (DMFT) offers a non-perturbative approach to problems with strongly correlated electrons. The method heavily relies on the ability to numerically solve an auxiliary Anderson-type impurity problem. While powerful Matsubara-frequency <span class="hlt">solvers</span> have been developed over the past two decades to tackle equilibrium situations, the status of real-time impurity <span class="hlt">solvers</span> that could compete with Matsubara-frequency <span class="hlt">solvers</span> and be readily generalizable to non-equilibrium situations is still premature. We present a real-time <span class="hlt">solver</span> which is based on a quantum Master equation description of the dissipative dynamics of the impurity and its exact diagonalization. As a benchmark, we illustrate the strengths of our <span class="hlt">solver</span> in the context of the equilibrium Mott-insulator transition of the one-band Hubbard model and compare it with iterative perturbation theory (IPT) method. Finally, we discuss its direct application to a nonequilibrium situation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930030449&hterms=competitive+advantages&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dcompetitive%2Badvantages','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930030449&hterms=competitive+advantages&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dcompetitive%2Badvantages"><span>Shape reanalysis and sensitivities utilizing preconditioned iterative boundary <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Guru Prasad, K.; Kane, J. H.</p>
<p>1992-01-01</p>
<p>The computational advantages associated with the utilization of preconditined iterative equation <span class="hlt">solvers</span> are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative <span class="hlt">solvers</span> are compared with those obtained via direct <span class="hlt">solvers</span> and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation <span class="hlt">solvers</span> in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct <span class="hlt">solvers</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1307472','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1307472"><span>General purpose nonlinear system <span class="hlt">solver</span> based on Newton-Krylov method.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p></p>
<p>2013-12-01</p>
<p>KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation <span class="hlt">Solvers</span> [1]. KINSOL is a general-purpose nonlinear system <span class="hlt">solver</span> based on Newton-Krylov and fixed-point <span class="hlt">solver</span> technologies [2].</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/433333','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433333"><span>Optimising a parallel conjugate gradient <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Field, M.R.</p>
<p>1996-12-31</p>
<p>This work arises from the introduction of a parallel iterative <span class="hlt">solver</span> to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019070','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019070"><span>Linear iterative <span class="hlt">solvers</span> for implicit ODE methods</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Saylor, Paul E.; Skeel, Robert D.</p>
<p>1990-01-01</p>
<p>The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation <span class="hlt">solvers</span>. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/5466577','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/5466577"><span><span class="hlt">Eulerian</span> simulation of the perforation of aluminum plates by nondeforming projectiles</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Silling, S.A.</p>
<p>1992-03-01</p>
<p>A new algorithm for the treatment of sliding interfaces between solids with or without friction in an <span class="hlt">Eulerian</span> wavecode is described. The algorithm has been implemented in the two-dimensional version of the CTH code. The code was used to simulate penetration and perforation of aluminum plates by rigid, conical-nosed tungsten projectiles. Comparison with experimental data is provided.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/505173','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/505173"><span><span class="hlt">Eulerian</span>-Lagrangian localized adjoint methods for reactive transport in groundwater</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ewing, R.E.; Wang, Hong</p>
<p>1996-12-31</p>
<p>In this paper, we present <span class="hlt">Eulerian</span>-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=static+AND+dynamic&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&CFID=78001885&CFTOKEN=57287486','EPA-EIMS'); return false;" href="http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=static+AND+dynamic&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&CFID=78001885&CFTOKEN=57287486"><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>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010A%26A...522A.102S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010A%26A...522A.102S"><span>A 3D radiative transfer framework . VII. Arbitrary velocity fields in the <span class="hlt">Eulerian</span> frame</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Seelmann, A. M.; Hauschildt, P. H.; Baron, E.</p>
<p>2010-11-01</p>
<p>Aims: A solution of the radiative-transfer problem in 3D with arbitrary velocity fields in the <span class="hlt">Eulerian</span> frame is presented. The method is implemented in our 3D radiative transfer framework and used in the PHOENIX/3D code. It is tested by comparison to our well-tested 1D co-moving frame radiative transfer code, where the treatment of a monotonic velocity field is implemented in the Lagrangian frame. The <span class="hlt">Eulerian</span> formulation does not need much additional memory and is useable on state-of-the-art computers, even large-scale applications with 1000's of wavelength points are feasible. Methods: In the <span class="hlt">Eulerian</span> formulation of the problem, the photon is seen by the atom at a Doppler-shifted wavelength depending on its propagation direction, which leads to a Doppler-shifted absorption and emission. This leads to a different source function and a different Λ^* operator in the radiative transfer equations compared to the static case. Results: The results of the <span class="hlt">Eulerian</span> 3D spherical calculations are compared to our well-tested 1D Lagrangian spherical calculations, the agreement is, up to vmax = 1 × 103 km s-1 very good. Test calculation in other geometries are also shown.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/432879','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/432879"><span>Implementation of a friction model in an <span class="hlt">Eulerian</span> viscoplastic formulation for steady flow</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Dawson, P.R.; Boyce, D.E.</p>
<p>1996-04-01</p>
<p>The goal of this project was to implement the routines necessary to use the friction model of Wilson and Korzekwa into the finite element analysis program {ital hickory}, in the case of an <span class="hlt">Eulerian</span> reference frame. {ital hickory} is a deformation simulation code based on finite element modeling of viscoplastic deformation When using {ital hickory}, time-dependent problems are modeled from a Lagrangian reference frame; while steady-state problems are modeled from an <span class="hlt">Eulerian</span> reference frame. The friction model had been implemented in earlier versions of {ital hickory}, for use with a Lagrangian reference frame. Additional modifications were required, however, to extend this capability to the case of an <span class="hlt">Eulerian</span> reference frame. That is the subject of this report. The necessary modifications were related to the time integration of the friction state variables. The application of an <span class="hlt">Eulerian</span> reference frame to study a steady-state flow requires that each specified boundary segment be a streamline of the flow. As such, an initial value for each state variable must be given at the first point of the streamline, and subsequent values must be determined by previous values by integration along the streamline. Additional routines were added to {ital hickory} to implement the streamline integration along the boundary. A plane strain rolling problem was used both to test the implementation and as a source of comparison among friction models.</p>
</li>
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<ol class="result-class" start="181">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA016944','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA016944"><span>SMITE - A Second Order <span class="hlt">Eulerian</span> Code for Hydrodynamic and Elastic-Plastic Problems</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>1975-08-01</p>
<p>et al Mathematical Applications Group, Incorporated Prepared for: Ballistic Research Laboratories August 1975 DISTRIBI,TED BY: mi] National...SMITE - A SECOND ORDER <span class="hlt">EULERIAN</span> CODE FOR HYDRODYNAMIC AND ELASTIC-PLASTIC PROBLEMS Prepared by Mathematical Applications Group, Inc. 3...AODRcis jMathematical Applications Group, Inc. 13 Westchester Plaza IFlmsford, New York 10523 10. PROGRAM ELEMENT, PROJECT, TASK AREA t WORK</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=Model+AND+Transport+AND+Research+AND+Operational&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="http://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=Model+AND+Transport+AND+Research+AND+Operational&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>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007JMPSo..55..338X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007JMPSo..55..338X"><span>Thermodynamic laws and consistent <span class="hlt">Eulerian</span> formulation of finite elastoplasticity with thermal effects</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Xiao, Heng; Bruhns, Otto T.; Meyers, Albert</p>
<p>2007-02-01</p>
<p>Recently it has been demonstrated that, on the basis of the separation D=De+Dp arising from the split of the stress power and two consistency criteria for objective <span class="hlt">Eulerian</span> rate formulations, it is possible to establish a consistent <span class="hlt">Eulerian</span> rate formulation of finite elastoplasticity in terms of the Kirchhoff stress and the stretching, without involving additional deformation-like variables labelled "elastic" or "plastic". It has further been demonstrated that this consistent formulation leads to a simple essential structure implied by the work postulate, namely, both the normality rule for plastic flow Dp and the convexity of the yield surface in Kirchhoff stress space. Here, we attempt to place such an <span class="hlt">Eulerian</span> formulation on the thermodynamic grounds by extending it to a general case with thermal effects, where the consistency requirements are treated in a twofold sense. First, we propose a general constitutive formulation based on the foregoing separation as well as the two consistency criteria. This is accomplished by employing the corotational logarithmic rate and by incorporating an exactly integrable <span class="hlt">Eulerian</span> rate equation for De for thermo-elastic behaviour. Then, we study the consistency of the formulation with thermodynamic laws. Towards this goal, simple forms of restrictions are derived, and consequences are discussed. It is shown that the proposed <span class="hlt">Eulerian</span> formulation is free in the sense of thermodynamic consistency. Namely, a Helmholtz free energy function in explicit form may be found such that the restrictions from the thermodynamic laws can be fulfilled with positive internal dissipation for arbitrary forms of constitutive functions included in the constitutive formulation. In particular, that is the case for the foregoing essential constitutive structure in the purely mechanical case. These results eventually lead to a complete, explicit constitutive theory for coupled fields of deformation, stress and temperature in thermo</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1104761','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1104761"><span>Comparison of open-source linear programming <span class="hlt">solvers</span>.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph</p>
<p>2013-10-01</p>
<p>When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming <span class="hlt">solvers</span>. In such cases, one option is to use an open-source linear programming <span class="hlt">solver</span>. A survey of linear programming tools was conducted to identify potential open-source <span class="hlt">solvers</span>. From this survey, four open-source <span class="hlt">solvers</span> were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The <span class="hlt">solvers</span> considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source <span class="hlt">solver</span> outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source <span class="hlt">solver</span> considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.345..330B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.345..330B"><span>An iterative <span class="hlt">solver</span> for the 3D Helmholtz equation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir</p>
<p>2017-09-01</p>
<p>We develop a frequency-domain iterative <span class="hlt">solver</span> for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our <span class="hlt">solver</span> has been verified by benchmarking against exact solutions and a time-domain <span class="hlt">solver</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22039740','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22039740"><span>A non-conforming 3D spherical harmonic transport <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Van Criekingen, S.</p>
<p>2006-07-01</p>
<p>A new 3D transport <span class="hlt">solver</span> for the time-independent Boltzmann transport equation has been developed. This <span class="hlt">solver</span> is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this <span class="hlt">solver</span> is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AIPC.1501..429Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AIPC.1501..429Z"><span>GPU accelerated kinetic <span class="hlt">solvers</span> for rarefied 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>Zabelok, Sergey A.; Kolobov, Vladimir I.; Arslanbekov, Robert R.</p>
<p>2012-11-01</p>
<p>GPU-acceleration is applied to the Boltzmann <span class="hlt">solver</span> with adaptive Cartesian mesh in the Unified Flow <span class="hlt">Solver</span> framework. NVIDIA CUDA technology is used with threads being grouped in thread blocks by points of Korobov sequences in each cell for computing the collision integral and by points in coordinate space for the free-molecular flow stage. GPU-accelerated Boltzmann <span class="hlt">solver</span> with octree Cartesian mesh has been tested on several computer systems. Speedup of several times for GPU-based code compared to single-core CPU computations on the same machines has been observed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/15089447','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/15089447"><span>Influence of <span class="hlt">Eulerian</span> and Lagrangian scales on the relative dispersion properties in Lagrangian stochastic models of turbulence.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Maurizi, A; Pagnini, G; Tampieri, F</p>
<p>2004-03-01</p>
<p>The influence of <span class="hlt">Eulerian</span> and Lagrangian scales on the turbulent relative dispersion is investigated through a three-dimensional <span class="hlt">Eulerian</span> consistent Lagrangian stochastic model. As a general property of this class of models, it is found to depend solely on a parameter beta based on the Kolmogorov constants C(K) and C0. This parameter represents the ratio between the Lagrangian and <span class="hlt">Eulerian</span> scales and is related to the intrinsic inhomogeneity of the relative dispersion process. In particular, the quantity g*=g/C(0) (where g is the Richardson constant) and the temporal extension of the t(3) regime are found to be strongly dependent on the value adopted for beta.</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-Lagrangian-<span class="hlt">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 <span class="hlt">solver</span> 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 <span class="hlt">solver</span> 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-Lagrangian-<span class="hlt">Eulerian</span> (ALE) schemes, where a space-time conservation formulation 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://hdl.handle.net/2060/20080048189','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20080048189"><span>Flow <span class="hlt">Solver</span> for Incompressible Rectangular Domains</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kalb, Virginia L.</p>
<p>2008-01-01</p>
<p>This is an extension of the Flow <span class="hlt">Solver</span> for Incompressible 2-D Drive Cavity software described in the preceding article. It solves the Navier-Stokes equations for incompressible flow using finite differencing on a uniform, staggered grid. There is a runtime choice of either central differencing or modified upwinding for the convective term. The domain must be rectangular, but may have a rectangular walled region within it. Currently, the position of the interior region and exterior boundary conditions are changed by modifying parameters in the code and recompiling. These features make it possible to solve a variety of classical fluid flow problems such as an L-shaped cavity, channel flow, or wake flow past a square cylinder. The code uses fourth-order Runge-Kutta time-stepping and overall second-order spatial accuracy. This software permits the walled region to be positioned such that flow past a square cylinder, an L-shaped cavity, and the flow over a back-facing step can all be solved by reconfiguration. Also, this extension has an automatic detection of periodicity, as well as use of specialized data structure for ease of configuring domain decomposition and computing convergence in overlap regions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000046785','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000046785"><span>Advanced Multigrid <span class="hlt">Solvers</span> for Fluid Dynamics</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Brandt, Achi</p>
<p>1999-01-01</p>
<p>The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD <span class="hlt">solvers</span>. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/763231','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/763231"><span>Elliptic <span class="hlt">Solvers</span> for Adaptive Mesh Refinement Grids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.</p>
<p>1999-06-03</p>
<p>We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic <span class="hlt">solver</span>. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900020588','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900020588"><span>Generic task problem <span class="hlt">solvers</span> in Soar</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Johnson, Todd R.; Smith, Jack W., Jr.; Chandrasekaran, B.</p>
<p>1989-01-01</p>
<p>Two trends can be discerned in research in problem solving architectures in the last few years. On one hand, interest in task-specific architectures has grown, wherein types of problems of general utility are identified, and special architectures that support the development of problem solving systems for those types of problems are proposed. These architectures help in the acquisition and specification of knowledge by providing inference methods that are appropriate for the type of problem. However, knowledge based systems which use only one type of problem solving method are very brittle, and adding more types of methods requires a principled approach to integrating them in a flexible way. Contrasting with this trend is the proposal for a flexible, general architecture contained in the work on Soar. Soar has features which make it attractive for flexible use of all potentially relevant knowledge or methods. But as the theory Soar does not make commitments to specific types of problem <span class="hlt">solvers</span> or provide guidance for their construction. It was investigated how task-specific architectures can be constructed in Soar to retain as many of the advantages as possible of both approaches. Examples were used from the Generic Task approach for building knowledge based systems. Though this approach was developed and applied for a number of problems, the ideas are applicable to other task-specific approaches as well.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050177239','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050177239"><span>LSPRAY: Lagrangian Spray <span class="hlt">Solver</span> for Applications With Parallel Computing and Unstructured Gas-Phase Flow <span class="hlt">Solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Raju, Manthena S.</p>
<p>1998-01-01</p>
<p>Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., 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) <span class="hlt">solver</span>. The LSPRAY <span class="hlt">solver</span> accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase <span class="hlt">solvers</span>. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/433334','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433334"><span>Parallel iterative <span class="hlt">solvers</span> and preconditioners using approximate hierarchical methods</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Grama, A.; Kumar, V.; Sameh, A.</p>
<p>1996-12-31</p>
<p>In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES <span class="hlt">solver</span> for Boundary Element Methods. The <span class="hlt">solver</span> uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our <span class="hlt">solver</span> yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our <span class="hlt">solver</span>. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20040110968&hterms=web+performance&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dweb%2Bperformance','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20040110968&hterms=web+performance&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dweb%2Bperformance"><span>Performance of NASA Equation <span class="hlt">Solvers</span> on Computational Mechanics Applications</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Storaasli, Olaf O.</p>
<p>1996-01-01</p>
<p>This paper describes the performance of a new family of NASA-developed equation <span class="hlt">solvers</span> used for large-scale (i.e. 551,705 equations) structural analysis. To minimize computer time and memory, the <span class="hlt">solvers</span> are divided by application and matrix characteristics (sparse/dense, real/complex, symmetric/nonsymmetric, size: in-core/out of core) and exploit the hardware features of current and future computers. In this paper, the equation <span class="hlt">solvers</span>, which are written in FORTRAN, and are therefore easily transportable, are shown to be faster than specialized computer library routines utilizing assembly code. Twenty NASA structural benchmark models with NASA <span class="hlt">solver</span> timings reside on World Wide Web with a challenge to beat them.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009LNCS.5759...64S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009LNCS.5759...64S"><span>Experiences Running a Parallel Answer Set <span class="hlt">Solver</span> on Blue Gene</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Schneidenbach, Lars; Schnor, Bettina; Gebser, Martin; Kaminski, Roland; Kaufmann, Benjamin; Schaub, Torsten</p>
<p></p>
<p>This paper presents the concept of parallelisation of a <span class="hlt">solver</span> for Answer Set Programming (ASP). While there already exist some approaches to parallel ASP solving, there was a lack of a parallel version of the powerful clasp <span class="hlt">solver</span>. We implemented a parallel version of clasp based on message-passing. Experimental results on Blue Gene P/L indicate the potential of such an approach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21301157','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21301157"><span>RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN <span class="hlt">SOLVER</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.</p>
<p>2010-05-01</p>
<p>We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann <span class="hlt">solver</span>. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our <span class="hlt">solver</span> is very robust. When compared with a family of simpler <span class="hlt">solvers</span> that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our <span class="hlt">solver</span> turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD <span class="hlt">solver</span>. The amount of operations needed by the FWD <span class="hlt">solver</span> makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010ApJS..188....1A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010ApJS..188....1A"><span>Relativistic Magnetohydrodynamics: Renormalized Eigenvectors and Full Wave Decomposition Riemann <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Antón, Luis; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Aloy, Miguel A.; Mimica, Petar</p>
<p>2010-05-01</p>
<p>We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann <span class="hlt">solver</span>. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our <span class="hlt">solver</span> is very robust. When compared with a family of simpler <span class="hlt">solvers</span> that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our <span class="hlt">solver</span> turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD <span class="hlt">solver</span>. The amount of operations needed by the FWD <span class="hlt">solver</span> makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUFMSH21C2551T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUFMSH21C2551T"><span><p>A Full <span class="hlt">Eulerian</span> Vlasov-Maxwell Study of Turbulent Dynamics and Dissipation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>TenBarge, J. M.; Juno, J.; Hakim, A.</p>
<p>2016-12-01</p>
<p>The development of a detailed understanding of turbulence in magnetized plasmas has been a long standing goal of the broader scientific community, both as a fundamental physics process and because of its applicability to a wide variety of phenomena. Turbulence in a magnetized plasma is the primary mechanism responsible for transforming energy at large injection scales into small-scale motions, which are ultimately dissipated as heat in systems such as the solar corona and wind. At large scales, the turbulence is well described by fluid models of the plasma; however, understanding the processes responsible for heating a weakly collisional plasma such as the solar wind requires a kinetic description. We present the first fully kinetic <span class="hlt">Eulerian</span> Vlasov-Maxwell study of turbulence using the Gkeyll simulation code. We focus on the pristine distribution function dynamics that are possible with the <span class="hlt">Eulerian</span> approach. We also present the signatures and form of dissipation as diagnosed via field-particle correlation functions.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15005665','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15005665"><span>Comparison of Direct <span class="hlt">Eulerian</span> Godunov and Lagrange Plus Remap, Artificial Viscosity Schemes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pember, R B; Anderson, R W</p>
<p>2001-03-30</p>
<p>The authors compare two algorithms for solving the equations of unsteady inviscid compressible flow in an <span class="hlt">Eulerian</span> frame: a staggered grid, Lagrange plus remap artificial viscosity scheme and a cell-centered, direct <span class="hlt">Eulerian</span> higher-order Godunov scheme. They use the two methods to compute solutions to a number of one- and two-dimensional problems. The results show the accuracy of the two schemes to be generally equivalent. In a 1984 survey paper by Woodward and Colella, the Lagrange plus remap approach did not compare favorably with the higher-order Godunov methodology. They examine, therefore, how certain features of the staggered grid scheme considered here contribute to its improved accuracy. The critical features are shown to be the use of a monotonic artificial viscosity in the Lagrange step and, in the remap step, the use of a corner transport upwind scheme with van Leer limiters in conjunction with separate advection of internal and kinetic energies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JCoPh.230..596S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JCoPh.230..596S"><span>A full <span class="hlt">Eulerian</span> finite difference approach for solving fluid-structure coupling problems</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>2011-02-01</p>
<p>A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation [Hirt, Nichols, J. Comput. Phys. 39 (1981) 201], which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the <span class="hlt">Eulerian</span> frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full <span class="hlt">Eulerian</span> method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1999PhDT........72D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999PhDT........72D"><span>Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-<span class="hlt">Eulerian</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>Darlington, Rebecca Mattson</p>
<p></p>
<p>This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian <span class="hlt">Eulerian</span> (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over <span class="hlt">Eulerian</span> simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17257815','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17257815"><span>Transient molecular electro-optics Cartesian rotation vector versus <span class="hlt">Eulerian</span> angles.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Evensen, Tom Richard; Elgsaeter, Arnljot; Naess, Stine Nalum</p>
<p>2007-04-15</p>
<p>Comparing the Euler angles, the classical choice of generalized coordinates describing the three rotational degrees of freedom of a rigid body, and the Cartesian rotation vector, we show that they both have their advantages and disadvantages in kinetic theory and Brownian dynamics analysis of molecular electro-optics. The <span class="hlt">Eulerian</span> angles often yield relatively simple, yet singular, equations of motion, while their counterparts expressed in terms of Cartesian rotation vector are non-singular but more complex. In a special case, we show that the generalized force associated with the Cartesian rotation vector equals the torque. In addition, we introduce a new graphical approach to qualitatively track how changes in the <span class="hlt">Eulerian</span> angles affect the Cartesian rotation vector.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..DFD.G3002X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..DFD.G3002X"><span><span class="hlt">Eulerian</span> CFD modeling and X-ray validation of non-evaporating diesel spray</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Xue, Qingluan; Som, Sibendu; Quan, Shaoping; Pomraning, Eric; Senecal, P. K.</p>
<p>2013-11-01</p>
<p>This work implemented an <span class="hlt">Eulerian</span> single-phase approach by Vallet et al. into CFD software (Convergent) for diesel spray simulations. This <span class="hlt">Eulerian</span> approach considers liquid and gas phase as a complex mixture of a single flow with a highly variable density to describe the near nozzle dense sprays. The mean density is obtained form the Favre-averaged liquid mass fraction. Liquid mass fraction is transported with a model for the turbulent liquid diffusion flux into the gas. A mean gradient-based model is employed for the diffusion flux in this study. A non-evaporating diesel spray was measured using x-ray radiography at Argonne National Laboratory. The quantitative and time-resolved data of liquid penetration and mass distribution in the dense spray region are used to validate this approach. The different turbulence models are also used for the simulations. The comparison between the simulated results and experimental data and the turbulence model effect are discussed.</p>
</li>
<li>
<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 Lagrangian 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 formulated as systems of hyperbolic conservation laws. The other is SPHC, a smoothed particle hydrodynamics code produced by Stellingwerf Consulting. Use of the Lagrangian 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhPl...23j2112A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhPl...23j2112A"><span>Hamiltonian magnetohydrodynamics: Lagrangian, <span class="hlt">Eulerian</span>, and dynamically accessible stability—Examples with translation symmetry</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Andreussi, T.; Morrison, P. J.; Pegoraro, F.</p>
<p>2016-10-01</p>
<p>Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, <span class="hlt">Eulerian</span> (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate <span class="hlt">Eulerian</span> equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22373509','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22373509"><span>Cosmological dynamics: from the <span class="hlt">Eulerian</span> to the Lagrangian frame. Part I. Newtonian approximation</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Villa, Eleonora; Maino, Davide; Matarrese, Sabino E-mail: sabino.matarrese@pd.infn.it</p>
<p>2014-06-01</p>
<p>We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the <span class="hlt">Eulerian</span> and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the <span class="hlt">Eulerian</span> to the Lagrangian frame in the Newtonian approximation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15013106','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15013106"><span>Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-<span class="hlt">Eulerian</span> method</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Darlington, Rebecca Mattson</p>
<p>1999-12-01</p>
<p>This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian <span class="hlt">Eulerian</span> (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over <span class="hlt">Eulerian</span> simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..17.9796O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..17.9796O"><span>Benchmarking transport <span class="hlt">solvers</span> for fracture flow problems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Olkiewicz, Piotr; Dabrowski, Marcin</p>
<p>2015-04-01</p>
<p>Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in geothermal systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. For example, geothermal energy is primarily transported by the flow of the heated water or steam rather than by the thermal diffusion. The geometry of the fracture network and the distribution of the mean apertures of individual fractures are the key parameters with regard to the fracture network transmissivity. Transport in fractures can occur through the combination of advection and diffusion processes like in the case of dissolved chemical components. The local distribution of the fracture aperture may play an important role for both flow and transport processes. In this work, we benchmark various numerical <span class="hlt">solvers</span> for flow and transport processes in a single fracture in 2D and 3D. Fracture aperture distributions are generated by a number of synthetic methods. We examine a single-phase flow of an incompressible viscous Newtonian fluid in the low Reynolds number limit. Periodic boundary conditions are used and a pressure difference is imposed in the background. The velocity field is primarly found using the Stokes equations. We systematically compare the obtained velocity field to the results obtained by solving the Reynolds equation. This allows us to examine the impact of the aperture distribution on the permeability of the medium and the local velocity distribution for two different mathematical descriptions of the fracture flow. Furthermore, we analyse the impact of aperture distribution on the front characteristics such as the standard deviation and the fractal dimension for systems in 2D and 3D.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940008729','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940008729"><span>A robust multilevel simultaneous eigenvalue <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Costiner, Sorin; Taasan, Shlomo</p>
<p>1993-01-01</p>
<p>Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid <span class="hlt">solver</span>. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1999PhDT........16U','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999PhDT........16U"><span>An advanced implicit <span class="hlt">solver</span> for MHD</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Udrea, Bogdan</p>
<p></p>
<p>A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann <span class="hlt">solver</span> for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20100024470','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20100024470"><span>A Comparative Study of Randomized Constraint <span class="hlt">Solvers</span> for Random-Symbolic Testing</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo</p>
<p>2009-01-01</p>
<p>The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint <span class="hlt">solvers</span> are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the <span class="hlt">solver</span> does not support. This paper proposes and evaluates several randomized <span class="hlt">solvers</span> to address this issue. We compare the effectiveness of a symbolic <span class="hlt">solver</span> (CVC3), a random <span class="hlt">solver</span>, three hybrid <span class="hlt">solvers</span> (i.e., mix of random and symbolic), and two heuristic search <span class="hlt">solvers</span>. We evaluate the <span class="hlt">solvers</span> on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other <span class="hlt">solvers</span> for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the <span class="hlt">solvers</span> are complementary.</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 Lagrangian 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>codes are parallelized using message passing interface (MPI) based on domain decomposition. For SPH , graphics processing unit (GPU) computing, which is...aims at developing a numerical capability using a Lagrangian Smoothed Particle Hydrodynamics ( SPH ) method and an <span class="hlt">Eulerian</span> Level-Set Method (LSM) for...the SPH and LSM with environmental input provided by coupled wind and wave simulations at far field; (2) Use the numerical method developed in (1</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006AGUFM.H34A..06S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006AGUFM.H34A..06S"><span>Lagrangian and <span class="hlt">Eulerian</span> Methods for the Identification of Water Vapour Sources and Transport</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Sodemann, H.; Schwierz, C.; Wernli, H.</p>
<p>2006-12-01</p>
<p>Diagnostics of the hydrological cycle are an important component of detection and attribution of climate variability. The hydrological cycle is a key component of the climate system, but due to the scale of evaporation and condensation processes, NWP models rely heavily on parameterizations. Evaluations of reanalysis datasets show biases of the hydrological cycle that are created during data assimilation, rendering these data one of the less reliable components of reanalysis products. We present two novel approaches to identify the sources and transport paths of atmospheric water vapor from analysis or reanalysis data, one of Lagrangian, and one of <span class="hlt">Eulerian</span> nature. The Lagrangian method is based on back-trajectories, and diagnoses the evaporative sources of water vapor in high spatial detail. The method is exemplified with an examination of the inter-annual variability of the moisture sources for winter-time precipitation in Greenland, and the seasonality of the moisture sources for Alpine precipitation, based on ECMWF's ERA-40 reanalysis data. The <span class="hlt">Eulerian</span> method makes use of a regional climate model that has been fitted with a mass-conservative water vapor tracer. This provides a novel possibility to evaluate the representation of the model's hydrological cycle in detail, and on a regional scale. The capabilities of the <span class="hlt">Eulerian</span> method are exemplified with an identification of the moisture sources of the August 2002 flood, one of the strongest flood events in Central Europe in recent decades. A comparison of the two method indicates different preferential areas of application: the Lagrangian method being more suitable for gaining a large-scale picture, while the <span class="hlt">Eulerian</span> method could provide detailed process understanding and be useful for NWP model evaluation. This in turn implies that a complementary view could potentially be gained when using such methods for evaluation purposes in combination with new observational data of the atmospheric hydrological cycle.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=applicable+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dapplicable%2Bmethods','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=applicable+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dapplicable%2Bmethods"><span>Extension of rezoned <span class="hlt">Eulerian</span>-Lagrangian 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</span>-Lagrangian 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26871161','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26871161"><span>Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and <span class="hlt">Eulerian</span> accelerations and passive scalar dynamics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie</p>
<p>2016-01-01</p>
<p>The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and <span class="hlt">Eulerian</span> accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and <span class="hlt">Eulerian</span> accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the <span class="hlt">Eulerian</span> acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and <span class="hlt">Eulerian</span> accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both <span class="hlt">Eulerian</span> and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the <span class="hlt">Eulerian</span> acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its <span class="hlt">Eulerian</span> time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the <span class="hlt">Eulerian</span> time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA441412','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA441412"><span>Prediction and Analysis of Material Response to Impact and Shock Loading Using a Sharp-Interface <span class="hlt">Eulerian</span> Methodology</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2005-12-01</p>
<p>IMPACT AND 5b. GRANT NUMBER SHOCK LOADING USING A SHARP-INTERFACE <span class="hlt">EULERIAN</span> METHODOLOGY 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER H. S...ABSTRACT Numerical methods and a computer code have been developed for the simulation of multimaterial interactions in a general setting...by ANSI Std. Z39.18 FINAL REPORT PREDICTION AND ANALYSIS OF MATERIAL RESPONSE TO IMPACT AND SHOCK LOADING USING A SHARP-INTERFACE <span class="hlt">EULERIAN</span> METHODOLOGY</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JMFM...18..783P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JMFM...18..783P"><span>An <span class="hlt">Eulerian</span>-Lagrangian Form for the Euler Equations in Sobolev Spaces</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pooley, Benjamin C.; Robinson, James C.</p>
<p>2016-12-01</p>
<p>In 2000 Constantin showed that the incompressible Euler equations can be written in an "<span class="hlt">Eulerian</span>-Lagrangian" form which involves the back-to-labels map (the inverse of the trajectory map for each fixed time). In the same paper a local existence result is proved in certain Hölder spaces {C^{1,μ}}. We review the <span class="hlt">Eulerian</span>-Lagrangian formulation of the equations and prove that given initial data in H s for {n ≥ 2} and {s > n/2+1}, a unique local-in-time solution exists on the n-torus that is continuous into H s and C 1 into H s-1. These solutions automatically have C 1 trajectories. The proof here is direct and does not appeal to results already known about the classical formulation. Moreover, these solutions are regular enough that the classical and <span class="hlt">Eulerian</span>-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1049955','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1049955"><span>Unit physics performance of a mix model in <span class="hlt">Eulerian</span> fluid computations</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Vold, Erik; Douglass, Rod</p>
<p>2011-01-25</p>
<p>In this report, we evaluate the performance of a K-L drag-buoyancy mix model, described in a reference study by Dimonte-Tipton [1] hereafter denoted as [D-T]. The model was implemented in an <span class="hlt">Eulerian</span> multi-material AMR code, and the results are discussed here for a series of unit physics tests. The tests were chosen to calibrate the model coefficients against empirical data, principally from RT (Rayleigh-Taylor) and RM (Richtmyer-Meshkov) experiments, and the present results are compared to experiments and to results reported in [D-T]. Results show the <span class="hlt">Eulerian</span> implementation of the mix model agrees well with expectations for test problems in which there is no convective flow of the mass averaged fluid, i.e., in RT mix or in the decay of homogeneous isotropic turbulence (HIT). In RM shock-driven mix, the mix layer moves through the <span class="hlt">Eulerian</span> computational grid, and there are differences with the previous results computed in a Lagrange frame [D-T]. The differences are attributed to the mass averaged fluid motion and examined in detail. Shock and re-shock mix are not well matched simultaneously. Results are also presented and discussed regarding model sensitivity to coefficient values and to initial conditions (IC), grid convergence, and the generation of atomically mixed volume fractions.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..DFDM18003F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..DFDM18003F"><span><span class="hlt">Eulerian</span> models for particle trajectory crossing in turbulent flows over a large range of Stokes numbers</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Fox, Rodney O.; Vie, Aymeric; Laurent, Frederique; Chalons, Christophe; Massot, Marc</p>
<p>2012-11-01</p>
<p>Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, <span class="hlt">Eulerian</span> methods can be used to solve for the moments of the NDF resulting in an unclosed <span class="hlt">Eulerian</span> system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the <span class="hlt">Eulerian</span> models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. Research carried out at the Center for Turbulence Research 2012 Summer Program.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1988JGR....93.2389B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1988JGR....93.2389B"><span>The effect of diffusion on tracer puffs simulated by a regional scale <span class="hlt">Eulerian</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>Brost, Richard A.; Haagenson, Philip L.; Kuo, Ying-Hwa</p>
<p>1988-03-01</p>
<p>On a spatial scale of up to 1,100 km and a temporal scale of up to 36 hours, we used <span class="hlt">Eulerian</span> models to simulate the transport and diffusion of a passive tracer released from a point source near the surface. An <span class="hlt">Eulerian</span> tracer model was driven by meteorological analysis of 6-hour rawinsonde data supplemented by the simulations of an <span class="hlt">Eulerian</span> mesoscale meteorological model. The tracer model simulations were compared with 6-hour integrated samples collected at 86 surface stations during the Cross-Appalachian Tracer Experiment (CAPTEX) for six different releases. We examined the effect of the parameterizations of vertical and horizontal sub-grid scale turbulent transport and the finite difference advection scheme on the simulations of concentration and the trajectories of the center of mass of the tracer at the surface. We found that the simulated trajectory error was sensitive to the vertical eddy diffusivity but insensitive to the advection scheme and hence insensitive to (horizontal) numerical diffusion. Using 70-km horizontal resolution, only the most sophisticated advection scheme tested here (Prather, 1986) simulated a tracer puff with a horizontal area that was not too large during the first 36 hours after a point source release. The other schemes tested (Russell and Lerner, 1981; a simplified version of Smolarkiewicz, 1983) had enough numerical diffusion that the simulated horizontal tracer puffs were larger than the observed puffs. There were considerable differences in the capability of the tracer models to simulate individual releases, particularly for quantitative comparisons of simulated and observed concentrations.</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('http://adsabs.harvard.edu/abs/2011MSSP...25..344O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011MSSP...25..344O"><span><span class="hlt">Eulerian</span> laser Doppler vibrometry: Online blade damage identification on a multi-blade test rotor</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Oberholster, A. J.; Heyns, P. S.</p>
<p>2011-01-01</p>
<p>Laser Doppler vibrometry enables the telemetry-free measurement of online turbomachinery blade vibration. Specifically, the <span class="hlt">Eulerian</span> or fixed reference frame implementation of laser vibrometry provides a practical solution to the condition monitoring of rotating blades. The short data samples that are characteristic of this measurement approach do however negate the use of traditional frequency domain signal processing techniques. It is therefore necessary to employ techniques such as time domain analysis and non-harmonic Fourier analysis to obtain useful information from the blade vibration signatures. The latter analysis technique allows the calculation of phase angle trends which can be used as indicators of blade health deterioration, as has been shown in previous work for a single-blade rotor. This article presents the results from tests conducted on a five-blade axial-flow test rotor at different rotor speeds and measurement positions. With the aid of artificial neural networks, it is demonstrated that the parameters obtained from non-harmonic Fourier analysis and time domain signal processing on <span class="hlt">Eulerian</span> laser Doppler vibrometry signals can successfully be used to identify and quantify blade damage from among healthy blades. It is also shown that the natural frequencies of individual blades can be approximated from the <span class="hlt">Eulerian</span> signatures recorded during rotor run-up and run-down.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.304..189D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.304..189D"><span>On the computation of the Baer-Nunziato model using ALE formulation with HLL- and HLLC-type <span class="hlt">solvers</span> towards fluid-structure interactions</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Daude, F.; Galon, P.</p>
<p>2016-01-01</p>
<p>Computation of compressible two-phase flows with the unsteady compressible Baer-Nunziato model in conjunction with the moving grid approach is discussed in this paper. Both HLL- and HLLC-type Finite-Volume methods are presented and implemented in the context of Arbitrary Lagrangian-<span class="hlt">Eulerian</span> formulation in a multidimensional framework. The construction of suitable numerical methods is linked to proper approximations of the non-conservative terms on moving grids. The HLL discretization follows global conservation properties such as free-stream preservation and uniform pressure and velocity profiles preservation on moving grids. The HLLC <span class="hlt">solver</span> initially proposed by Tokareva and Toro [1] for the Baer-Nunziato model is based on an approximate solution of local Riemann problems containing all the characteristic fields present in the exact solution. Both ;subsonic; and ;supersonic; configurations are considered in the construction of the present HLLC <span class="hlt">solver</span>. In addition, an adaptive 6-wave HLLC scheme is also proposed for computational efficiency. The methods are first assessed on a variety of 1-D Riemann problems including both fixed and moving grids applications. The methods are finally tested on 2-D and 3-D applications: 2-D Riemann problems, a 2-D shock-bubble interaction and finally a 3-D fluid-structure interaction problem with a good agreement with the experiments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2423440','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2423440"><span>Quantitative analysis of numerical <span class="hlt">solvers</span> for oscillatory biomolecular system models</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Quo, Chang F; Wang, May D</p>
<p>2008-01-01</p>
<p>Background This article provides guidelines for selecting optimal numerical <span class="hlt">solvers</span> for biomolecular system models. Because various parameters of the same system could have drastically different ranges from 10-15 to 1010, the ODEs can be stiff and ill-conditioned, resulting in non-unique, non-existing, or non-reproducible modeling solutions. Previous studies have not examined in depth how to best select numerical <span class="hlt">solvers</span> for biomolecular system models, which makes it difficult to experimentally validate the modeling results. To address this problem, we have chosen one of the well-known stiff initial value problems with limit cycle behavior as a test-bed system model. Solving this model, we have illustrated that different answers may result from different numerical <span class="hlt">solvers</span>. We use MATLAB numerical <span class="hlt">solvers</span> because they are optimized and widely used by the modeling community. We have also conducted a systematic study of numerical <span class="hlt">solver</span> performances by using qualitative and quantitative measures such as convergence, accuracy, and computational cost (i.e. in terms of function evaluation, partial derivative, LU decomposition, and "take-off" points). The results show that the modeling solutions can be drastically different using different numerical <span class="hlt">solvers</span>. Thus, it is important to intelligently select numerical <span class="hlt">solvers</span> when solving biomolecular system models. Results The classic Belousov-Zhabotinskii (BZ) reaction is described by the Oregonator model and is used as a case study. We report two guidelines in selecting optimal numerical <span class="hlt">solver(s</span>) for stiff, complex oscillatory systems: (i) for problems with unknown parameters, ode45 is the optimal choice regardless of the relative error tolerance; (ii) for known stiff problems, both ode113 and ode15s are good choices under strict relative tolerance conditions. Conclusions For any given biomolecular model, by building a library of numerical <span class="hlt">solvers</span> with quantitative performance assessment metric, we show that it is possible</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005Ap%26SS.299....1N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005Ap%26SS.299....1N"><span>A Comparison of Stiff ODE <span class="hlt">Solvers</span> for Astrochemical Kinetics Problems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nejad, Lida A. M.</p>
<p>2005-09-01</p>
<p>The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE <span class="hlt">solver</span> packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE <span class="hlt">solvers</span>. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct <span class="hlt">solver</span> routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of <span class="hlt">solvers</span>, the ordering and the chosen options. It is also shown that though a particular <span class="hlt">solver</span> with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another <span class="hlt">solver</span> can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70033100','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70033100"><span><span class="hlt">Eulerian</span>-Lagrangian 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 Lagrangian 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 Lagrangian 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('http://hdl.handle.net/2060/19980003439','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980003439"><span>Euler/Navier-Stokes <span class="hlt">Solvers</span> Applied to Ducted Fan Configurations</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Keith, Theo G., Jr.; Srivastava, Rakesh</p>
<p>1997-01-01</p>
<p>Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic <span class="hlt">solvers</span> based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler <span class="hlt">solvers</span> capture significant physics of the flowfield and are reasonably fast. An aerodynamic <span class="hlt">solver</span> Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this <span class="hlt">solver</span> has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic <span class="hlt">solver</span> based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic <span class="hlt">solver</span> was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these <span class="hlt">solvers</span> were applied to several test cases and validated against experimental data, where available.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008JCoPh.227.6448K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JCoPh.227.6448K"><span>Comparison between Lagrangian and mesoscopic <span class="hlt">Eulerian</span> modelling approaches for inertial particles suspended in decaying isotropic turbulence</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.</p>
<p>2008-06-01</p>
<p>The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic <span class="hlt">Eulerian</span> approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic <span class="hlt">Eulerian</span> and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040070802','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040070802"><span>EUPDF-II: An <span class="hlt">Eulerian</span> Joint Scalar Monte Carlo PDF Module : 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.; Liu, Nan-Suey (Technical Monitor)</p>
<p>2004-01-01</p>
<p>EUPDF-II provides the solution for the species and temperature fields based on an evolution equation for PDF (Probability Density Function) and it is developed mainly 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 CFD and spray <span class="hlt">solvers</span>. The <span class="hlt">solver</span> accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with an understanding of the various models involved in the PDF formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other <span class="hlt">solvers</span>. The source code of EUPDF-II will be available with National Combustion Code (NCC) as a complete package.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1243136-performance-models-spike-banded-linear-system-solver','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1243136-performance-models-spike-banded-linear-system-solver"><span>Performance Models for the Spike Banded Linear System <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...</p>
<p>2011-01-01</p>
<p>With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system <span class="hlt">solvers</span> and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the <span class="hlt">solvers</span> and preconditioners. There has been some work in the past on characterizing performance of the iterative <span class="hlt">solvers</span> themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded <span class="hlt">solvers</span>, banded preconditioners are capable of significantly faster time-to-solution. Our banded <span class="hlt">solver</span>, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike <span class="hlt">solver</span>, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our <span class="hlt">solver</span>, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our <span class="hlt">solver</span>. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our <span class="hlt">solver</span>. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.303..455Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.303..455Z"><span>Adaptive kinetic-fluid <span class="hlt">solvers</span> for heterogeneous computing architectures</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir</p>
<p>2015-12-01</p>
<p>We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow <span class="hlt">Solver</span> (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid <span class="hlt">solvers</span> based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24 × 24 × 24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann <span class="hlt">solver</span> using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) <span class="hlt">solver</span>, and a mesoscopic <span class="hlt">solver</span> based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.8749K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.8749K"><span>The novel high-performance 3-D MT inverse <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey</p>
<p>2016-04-01</p>
<p>We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse <span class="hlt">solver</span>. The <span class="hlt">solver</span> is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the <span class="hlt">solver</span>. As a forward modelling engine a modern scalable <span class="hlt">solver</span> extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse <span class="hlt">solver</span> is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.344....1A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.344....1A"><span>An adaptive fast multipole accelerated Poisson <span class="hlt">solver</span> for complex geometries</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Askham, T.; Cerfon, A. J.</p>
<p>2017-09-01</p>
<p>We present a fast, direct and adaptive Poisson <span class="hlt">solver</span> for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the <span class="hlt">solver</span> relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient ;black box; fast <span class="hlt">solver</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110008375','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110008375"><span>Overset Techniques for Hypersonic Multibody Configurations with the DPLR <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Hyatt, Andrew James; Prabhu, Dinesh K.; Boger, David A.</p>
<p>2010-01-01</p>
<p>Three unit problems in shock-shock/shock-boundary layer interactions are considered in the evaluation overset techniques with the Data Parallel Line Relaxation (DPLR) computational fluid dynamics <span class="hlt">solver</span>, a three dimensional Navier-Stokes <span class="hlt">solver</span> . The unit problems considered are those of two stacked hemispherical cylinders (of different diameters and lengths, and at various orientations relative to each other or relative to the nozzle axis) tested in a hypersonic wind tunnel. These problems are taken as representative of a Two-Stage-To-Orbit design. The objective of the present presentation would be to discuss the techniques used to develop suitable overset grid systems and then evaluate their respective solutions by comparing to corresponding point matched grid solutions and experimental data. Both successful and unsuccessful techniques would be discussed. All solutions would be calculated using the DPLR <span class="hlt">solver</span> and SUGGAR will be used to develop the domain connectivity information.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030065951','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030065951"><span>General Equation Set <span class="hlt">Solver</span> for Compressible and Incompressible Turbomachinery Flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Sondak, Douglas L.; Dorney, Daniel J.</p>
<p>2002-01-01</p>
<p>Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow <span class="hlt">solvers</span>. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery <span class="hlt">solvers</span>. An unsteady GES turbomachinery flow <span class="hlt">solver</span> has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28600242','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28600242"><span>Advanced Fast 3D Electromagnetic <span class="hlt">Solver</span> for Microwave Tomography Imaging.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Simonov, Nikolai; Kim, Bo-Ra; Lee, Kwang-Jae; Jeon, Soon-Ik; Son, Seong-Ho</p>
<p>2017-06-07</p>
<p>This paper describes a fast forward electromagnetic <span class="hlt">solver</span> (FFS) for the image reconstruction algorithm of our microwave tomography (MT) system. Our apparatus is a preclinical prototype of a biomedical imaging system, designed for the purpose of early breast cancer detection. It operates in the 3-6 GHz frequency band using a circular array of probe antennas immersed in a matching liquid; it produces image reconstructions of the permittivity and conductivity profiles of the breast under examination. Our reconstruction algorithm solves the electromagnetic inverse problem and takes into account the real electromagnetic properties of the probe antenna array as well as the influence of the patient's body and that of the upper metal screen sheet. This FFS algorithm is much faster than conventional electromagnetic simulation <span class="hlt">solvers</span>. In comparison, in the same PC, the CST <span class="hlt">solver</span> takes ~45 min, while the FFS takes ~1 s of effective simulation time for the same electromagnetic model of a numerical breast phantom.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007JCoPh.227...12K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007JCoPh.227...12K"><span>Numerical comparison of Riemann <span class="hlt">solvers</span> for astrophysical hydrodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Klingenberg, Christian; Schmidt, Wolfram; Waagan, Knut</p>
<p>2007-11-01</p>
<p>The idea of this work is to compare a new positive and entropy stable approximate Riemann <span class="hlt">solver</span> by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann <span class="hlt">solver</span> into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann <span class="hlt">solver</span> increases the computational speed without significant loss of accuracy.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020087941','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020087941"><span>Two <span class="hlt">Solvers</span> for Tractable Temporal Constraints with Preferences</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)</p>
<p>2002-01-01</p>
<p>A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time on the basis of preferences. Soft temporal constraints problems allow to describe in a natural way scenarios where events happen over time and preferences are associated to event distances and durations. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. We describe two <span class="hlt">solvers</span> based on two different approaches for solving the same tractable subclass. For each <span class="hlt">solver</span> we present the theoretical results it stands on, a description of the algorithm and some experimental results. The random generator used to build the problems on which tests are performed is also described. Finally, we compare the two <span class="hlt">solvers</span> highlighting the tradeoff between performance and representational power.</p>
</li>
</ol>
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<ol class="result-class" start="241">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AdWR...99...15B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AdWR...99...15B"><span>A comparison of <span class="hlt">Eulerian</span> and Lagrangian transport and non-linear reaction algorithms</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 A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel</p>
<p>2017-01-01</p>
<p>When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and <span class="hlt">Eulerian</span> (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen <span class="hlt">Eulerian</span> methods incur no error when simulating advection, shows that both the <span class="hlt">Eulerian</span> and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050182013','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050182013"><span>Numerical System <span class="hlt">Solver</span> Developed for the National Cycle Program</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Binder, Michael P.</p>
<p>1999-01-01</p>
<p>As part of the National Cycle Program (NCP), a powerful new numerical <span class="hlt">solver</span> has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP <span class="hlt">solver</span> is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998JChEd..75..119H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998JChEd..75..119H"><span>Nonlinear Least Squares Curve Fitting with Microsoft Excel <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Harris, Daniel C.</p>
<p>1998-01-01</p>
<p>"<span class="hlt">Solver</span>" is a powerful tool in the Microsoft Excel spreadsheet that provides a simple means of fitting experimental data to nonlinear functions. The procedure is so easy to use and its mode of operation is so obvious that it is excellent for students to learn the underlying principle of lease squares curve fitting. This article introduces the method of fitting nonlinear functions with <span class="hlt">Solver</span> and extends the treatment to weighted least squares and to the estimation of uncertainties in the least-squares parameters.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1116976','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1116976"><span>An Easy Method To Accelerate An Iterative Algebraic Equation <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Yao, Jin</p>
<p>2014-01-06</p>
<p>This article proposes to add a simple term to an iterative algebraic equation <span class="hlt">solver</span> with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation <span class="hlt">solver</span> with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005AGUFM.V31D0647P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005AGUFM.V31D0647P"><span>Preliminary Benchmarking of Plinian Eruption Simulations Using an Adaptive Grid <span class="hlt">Eulerian</span> Technique</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Peterson, A. H.; Ogden, D. E.; Wohletz, K. H.; Gisler, G.; Glatzmaier, G. A.</p>
<p>2005-12-01</p>
<p>The SAGE (SAIC Adaptive Grid <span class="hlt">Eulerian</span>) code is an <span class="hlt">Eulerian</span> hydrodynamics numerical technique employing adaptive mesh refinement at each cycle for every cell in 1-, 2-, and 3-D grids. It is primarily designed to solve high deformation flow of multiple materials and thus provides important capabilities for simulating volcanic eruption phenomena. Its multimaterial equation of state libraries includes a comprehensive coverage of water from solid ice through two-phase liquid and vapor to supercritical states approaching the Hugoniot, and extremely important aspect for simulating volcanic gases in general. In development are strength and failure rules that model non-Newtonian fluid/solid deformation. Because of the low effective sound speeds of eruptive mixtures, the facts that SAGE uses a piecewise, linear, multi-material, Gudonov numerical method to resolve shocks with second-order precision and exactly conserves mass, momentum, and energy, are a highly desirable attributes. Although this code has been previously used to simulate a volcanic eruption (i.e., eruption through a crater lake at Ruapehu volcano by Morrissey and Gisler), we are embarking in an effort to benchmark the code with CFDLib, a well-validated arbitrary Lagrangian-<span class="hlt">Eulerian</span> code developed at Los Alamos National Laboratory. Through this effort we expect to better understand the strengths and weaknesses, the limitations, and provide direction for important enhancement of SAGE, and potentially provide the volcanological community with a powerful alternative to numerical codes currently available. At this point in our benchmarking, we demonstrate some results for fluid convection within a chamber and fluid jetting through a conduit.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003EAEJA.....3410M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003EAEJA.....3410M"><span>Assimilation of drifter observations for the reconstruction of <span class="hlt">eulerian</span> circulation field.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Molcard, A.; Ozgokmen, T.; Piterbarg, L.; Griffa, A.</p>
<p>2003-04-01</p>
<p>In light of the increasing number of drifting buoys in the ocean, and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in <span class="hlt">Eulerian</span> models is investigated. A new and general rigorous approach is developed based on optimal interpolation methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin-experiments using a reduced-gravity, quasi-geostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation and uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of <span class="hlt">Eulerian</span> data, such as fixed-point velocities. Overall the results are very favorable for the assimilation of Lagrangian observations to improve the <span class="hlt">Eulerian</span> velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in the range of 20-50% of the Lagrangian integral time scale of the flow field. The method is extended to primitive equation ocean models by using a dynamical relationship between velocity components and layer thickness based on geostrophy. The method is implemented in an idealized MICOM of midlatitude circulation, and performances of three different techniques, Pseudo-Lagrangian OI, Lagrangian OI and Pseudo-Lagrangian Kalman Filter (based on Chin et al., 1999) are compared using a comprehensive set of experiments. The main finding of this study is that two different strategies of data assimilation are simultaneously supported: (i) the strategy of adopting well</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/936675','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/936675"><span>An Arbitrary Lagrangian-<span class="hlt">Eulerian</span> Discretization of MHD on 3D Unstructured Grids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Rieben, R N; White, D A; Wallin, B K; Solberg, J M</p>
<p>2006-06-12</p>
<p>We present an arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and <span class="hlt">Eulerian</span> advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to <span class="hlt">Eulerian</span> advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70016242','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70016242"><span>Stability analysis of <span class="hlt">Eulerian</span>-Lagrangian methods for the one-dimensional shallow-water equations</span></a></p>
<p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p>
<p>Casulli, V.; Cheng, R.T.</p>
<p>1990-01-01</p>
<p>In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined <span class="hlt">Eulerian</span>-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit <span class="hlt">Eulerian</span>-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the <span class="hlt">Eulerian</span>-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhDT.......346M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhDT.......346M"><span>Computational Transonic Flutter Solutions for Cranked Wings by the Direct <span class="hlt">Eulerian</span>-Lagrangian Method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mellquist, Erik Charles</p>
<p></p>
<p>In this dissertation, a three-dimensional computational aeroelastic simulation for cranked, highly-swept wings is developed, and solutions are presented for several wing models. The computational model is a fully nonlinear coupled fluid-structure simulation based on the Direct <span class="hlt">Eulerian</span>-Lagrangian coupling methodology. The wing is modeled using nonlinear modified von Karman plate finite elements. Large deformation is accounted for through the use of element-attached local coordinate systems referenced to a single global coordinate system. The fluid is modeled using the mixed <span class="hlt">Eulerian</span>-Lagrangian formulation of the classical Euler equations and is discretized using a Galerkin finite element approach on an unstructured tetrahedral mesh. The fluid and structural models are coupled by the Direct <span class="hlt">Eulerian</span>-Lagrangian method where the finite-element shape functions and the local element coordinate systems are used to describe the fluid-structure boundary without approximation. Time synchronization and spatial accuracy are maintained to ensure accurate exchange of energy between the fluid and the structure. The computational solutions exhibit multiple types of aeroelastic response including transonic limit cycle flutter at a wide range of dynamic pressures, subsonic and supersonic bending-torsion flutter at higher dynamic pressures and a wide range of Mach numbers, and limit cycle oscillation dependent on both Mach number and angle of attack. Shock motion dependent on wing deformation is shown to play a major role in determining the response of the wings, and, depending on the flow conditions, can either stabilize or destabilize the response. Results from the simulations correlate closely with observed wind tunnel test responses.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040031690','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040031690"><span>A <span class="hlt">Eulerian</span>-Lagrangian Model to Simulate Two-Phase/Particulate Flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Apte, S. V.; Mahesh, K.; Lundgren, T.</p>
<p>2003-01-01</p>
<p>Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an <span class="hlt">Eulerian</span>-Lagrangian technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on <span class="hlt">Eulerian</span>-Lagrangian technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on <span class="hlt">Eulerian</span>-Lagrangian techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011GMD.....4..317K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011GMD.....4..317K"><span>Simulation of variability in atmospheric carbon dioxide using a global coupled <span class="hlt">Eulerian</span> - Lagrangian 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>Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.</p>
<p>2011-04-01</p>
<p>This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global <span class="hlt">Eulerian</span> model and a global Lagrangian particle dispersion model, to improve the reproducibility of tracer-gas variations affected by the near-field surface emissions and transport around observation sites. The ability to resolve variability in atmospheric composition on an hourly time-scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and from upcoming space-based observations. The coupled model yields an increase in the horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling computationally efficient global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at three sites: two operated by the National Oceanic and Atmospheric Administration, USA, and one operated by the National Institute for Environmental Studies, Japan. As the goal of this study is limited to introducing the new modeling approach, we selected a transport simulation at these three sites to demonstrate how the model may perform at various geographical areas. The coupled model provides improved agreement between modeled and observed CO2 concentrations in comparison to the <span class="hlt">Eulerian</span> model. In an area where variability in CO2 concentration is dominated by a fossil fuel signal, the correlation coefficient between modeled and observed concentrations increases by between 0.05 to 0.1 from the original values of 0.5-0.6 achieved with the <span class="hlt">Eulerian</span> model.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JGRG..119.2018U','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JGRG..119.2018U"><span>Inferring methane fluxes at a larch forest using Lagrangian, <span class="hlt">Eulerian</span>, and hybrid inverse models</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ueyama, Masahito; Takanashi, Satoru; Takahashi, Yoshiyuki</p>
<p>2014-10-01</p>
<p>Measuring methane (CH4) flux at upland forests is challenging due to high levels of heterogeneity in upscaling chamber measurements and the detection limits of currently available micrometeorological methods. We estimated CH4 fluxes in an upland forest from vertical concentration profiles using three different inverse multilayer models: the Lagrangian localized near field theory, <span class="hlt">Eulerian</span>, and hybrid Lagrangian-<span class="hlt">Eulerian</span> models. The approach could estimate spatially representative fluxes, and use of higher gradients within canopies than above them could minimize uncertainties associated with sensor noises. Comparing fluxes by the models and measurements by the micrometeorological hyperbolic relaxed eddy accumulation and chamber methods, daytime fluxes were reasonably reproduced, but nighttime fluxes were overestimated most likely due to an underestimation of stable conditions and storage effects. The models and measurements show that the forest acted as a CH4 sink during the study period, and the soil acted as the dominant sink. The estimated sink increased with increasing soil temperatures and decreasing soil water content. The CH4 sink estimated during the study period were 1.5 ± 0.2 nmol m-2 s-1 by the micrometeorological method, 2.4 ± 0.5 nmol m-2 s-1 by chambers, 2.8 ± 1.1 nmol m-2 s-1 by the Lagrangian model, 2.7 ± 1.0 nmol m-2 s-1 by the <span class="hlt">Eulerian</span> model, and 3.7 ± 2.8 nmol m-2 s-1 by the hybrid model. The performance of the Lagrangian and hybrid models increased when the CH4 sink/source was assumed to only exist in the soil.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EUCAS...5..109S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EUCAS...5..109S"><span>Arbitrary Lagrangian-<span class="hlt">Eulerian</span> approach in reduced order modeling of a flow with a moving boundary</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Stankiewicz, W.; Roszak, R.; Morzyński, M.</p>
<p>2013-06-01</p>
<p>Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DFDL13001L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DFDL13001L"><span>A second order Lagrangian <span class="hlt">Eulerian</span> momentum bounded 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>Le Chenadec, Vincent; Pitsch, Heinz</p>
<p>2011-11-01</p>
<p>A Lagrangian <span class="hlt">Eulerian</span> framework relying on both Level Set and Volume of Fluid methods is presented in the context of multiphase flow computations. The resulting interface capturing scheme is shown to preserve planarity, and to conserve mass exactly for solenoidal and linear velocity fields. A novel fractional step approach for the incompressible Navier Stokes equation is also presented. The proposed scheme relies on a consistent transport of volume fraction and momentum fields, which also preserves velocity boundedness. A sharp interface projection step is derived accordingly. The algorithm is shown to conserve momentum exactly for solenoidal linear velocity, and to lead to robust computations. Supported by NASA under Subsonic Fixed Wing project.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFM.A33A0186S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFM.A33A0186S"><span>Inverse modeling of global atmospheric carbon dioxide by Global <span class="hlt">Eulerian</span>-Lagrangian Coupled Atmospheric Model (GELCA)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Dlugokencky, E. J.; Tans, P. P.; Maksyutov, S. S.</p>
<p>2013-12-01</p>
<p>Global monthly CO2 flux distributions for 2001-2011 were estimated using an atmospheric inverse modeling system, which is based on combination of two transport models, called GELCA (Global <span class="hlt">Eulerian</span>-Lagrangian Coupled Atmospheric model). This coupled model approach has several advantages over inversions to a single model alone: the use of Lagrangian particle dispersion model (LPDM) to simulate the transport in the vicinity of the observation points enables us to avoid numerical diffusion of <span class="hlt">Eulerian</span> models, and is suitable to represent observations at high spatial and temporal resolutions. The global background concentration field generated by an <span class="hlt">Eulerian</span> model is used as time-variant boundary conditions for an LPDM that performs backward simulations from each receptor point (observation event). In the GELCA inversion system, National Institute for Environmental Studies-Transport Model (NIES-TM) version 8.1i was used as an <span class="hlt">Eulerian</span> global transport model coupled with FLEXPART version 8.0 as an LPDM. The meteorological fields for driving both models were taken from JMA Climate Data Assimilation System (JCDAS) with a spatial resolution of 1.25° x 1.25°, 40 vertical levels and a temporal resolution of 6 hours. Our prior CO2 fluxes consist of daily terrestrial biospheric fluxes, monthly oceanic fluxes, monthly biomass burning emissions, and monthly fossil fuel CO2 emissions. We employed a Kalman Smoother optimization technique with fixed lag of 3 months, estimating monthly CO2 fluxes for 42 land and 22 ocean regions. We have been using two different global networks of CO2 observations. The Observation Package (ObsPack) data products contain more measurement information in space and time than the NOAA global cooperative air sampling network which basically consists of approximately weekly sampling at background sites. The global total flux and its large-scale distribution optimized with two different global observation networks agreed overall with other previous</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015OEng....5...37L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015OEng....5...37L"><span>Modeling erosion in a centrifugal pump in an <span class="hlt">Eulerian</span>-Lagrangian frame using OpenFOAM®</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lopez, Alejandro; Stickland, Matthew; Dempster, William</p>
<p>2015-07-01</p>
<p>Erosion induced by solid particle impingement is a very commonwear mechanism in turbomachinery and Computational Fluid Dynamics is one of the most widely used tools for its prediction. In this article, erosion is modeled in one of the channels of a centrifugal pump using OpenFOAM®,which is an Open Source CFD package. A review of some of the most commonly used erosion models is carried out in an <span class="hlt">Eulerian</span>-Lagrangian frame along with a comparative study of the erosion rates obtained with each model. Results yielded some disparities between models due to the different factors taken into consideration. The mesh is then deformed to obtain the resulting eroded geometry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUSMOS22A..07A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUSMOS22A..07A"><span>Turbidity Current Transport using DEM and FEM: a Hybrid Lagrangian-<span class="hlt">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>Alves, J. L.; Guevara, N. O., Jr.; Silva, C. E.; Alves, F. T.; Gazoni, L. C.; Coutinho, A.; Camata, J.; Elias, R. N.; Paraizo, P.</p>
<p>2013-05-01</p>
<p>In this work we describe a contribution to the study of turbidity transport in scales smaller than TFM (two-fluid models), The intent of the work, part of a large scale simulation project, is to assess local, small scale parameters and their upscaling. The hybrid model is based on a Lagrangian-<span class="hlt">Eulerian</span> approach under a class of the so called Unresolved Discrete Particle Method (UDPM). In this approach, a Lagrangian description is used for the particle system employing the Discrete Element Method (DEM) while a fixed <span class="hlt">Eulerian</span> mesh is used for the fluid phase modeled by finite element method (FEM), Fluid motion is governed by Navier-Stokes equations which are solved by an appropriate FEM implementation. Closure equation are used to compute drag and lift forces over the particles in the DEM framework. Volume averaged momentum sink terms are included in the fluid equations. The resulting coupled DEM-FEM model is integrated in time with a subcycling scheme. The aforementioned scheme was applied in the simulation of a sedimentation basin as depicted in figures 1 and 2 to investigate flow and deposition features of the suspension in a finer scale. For this purpose a submodel of the basin was generated. Mapping variables back and forth the <span class="hlt">Eulerian</span> (finite element) model and the Lagrangian (discrete element) model were performed during the subcycled integration of the hybrid model. References: [1] Hoomans, B.P.B., Kuipers, J.A.M., Swaaij, van W.P.M," Granular dynamics Simulation of segregation phenomena in bubbling gas-fluidised beds", Powder Technology, V 109, Issues 1-3, 3 April 2000, pp 41-48; [2] Cho, S.H., Choi,H.G, Yoo, J.Y.,"Direct numerical simulation of fluid flow laden with many particles", International Journal of Multiphase Flow, V 31, Issue 4, April 2005, pp 435-451;; Sedimentation basin: sectioning the turbidity plume in the <span class="hlt">Eulerian</span> FE model for setting up the discrete particle model. ; Sedimentation Basin: section of the turbidity plume displaying the</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DPPB10007M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DPPB10007M"><span>On Hamiltonian Magnetohydrodynamics: Lagrangian, <span class="hlt">Eulerian</span>, and Dynamically Accessible Stability - Applications with Translation Symmetry</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Morrison, P. J.; Andreussi, T.; Pegoraro, F.</p>
<p>2016-10-01</p>
<p>In a series of papers we have investigated general properties of equilibria and their stability in each of the Lagrangian, <span class="hlt">Eulerian</span>, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. DOE DE-FG02-04ER-54742.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1613975C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1613975C"><span>A fast <span class="hlt">Eulerian</span> multiphase flow model for volcanic ash plumes: turbulence, heat transfer and particle non-equilibrium dynamics.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Cerminara, Matteo; Esposti Ongaro, Tomaso; Carlo Berselli, Luigi</p>
<p>2014-05-01</p>
<p>We have developed a compressible multiphase flow model to simulate the three-dimensional dynamics of turbulent volcanic ash plumes. The model describes the eruptive mixture as a polydisperse fluid, composed of different types of gases and particles, treated as interpenetrating <span class="hlt">Eulerian</span> phases. Solid phases represent the discrete ash classes into which the total granulometric spectrum is discretized, and can differ by size and density. The model is designed to quickly and accurately resolve important physical phenomena in the dynamics of volcanic ash plumes. In particular, it can simulate turbulent mixing (driving atmospheric entrainment and controlling the heat transfer), thermal expansion (controlling the plume buoyancy), the interaction between solid particles and volcanic gas (including kinetic non-equilibrium effects) and the effects of compressibility (over-pressured eruptions and infrasonic measurements). The model is based on the turbulent dispersed multiphase flow theory for dilute flows (volume concentration <0.001, implying that averaged inter-particle distance is larger than 10 diameters) where particle collisions are neglected. Moreover, in order to speed up the code without losing accuracy, we make the hypothesis of fine particles (Stokes number <0.2 , i.e., volcanic ash particles finer then a millimeter), so that we are able to consider non-equilibrium effects only at the first order. We adopt LES formalism (which is preferable in transient regimes) for compressible flows to model the non-linear coupling between turbulent scales and the effect of sub-grid turbulence on the large-scale dynamics. A three-dimensional numerical code has been developed basing on the OpenFOAM computational framework, a CFD open source parallel software package. Numerical benchmarks demonstrate that the model is able to capture important non-equilibrium phenomena in gas-particle mixtures, such as particle clustering and ejection from large-eddy turbulent structures, as well</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/EJ242959.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/EJ242959.pdf"><span>Intellectual Abilities That Discriminate Good and Poor Problem <span class="hlt">Solvers</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>Meyer, Ruth Ann</p>
<p>1981-01-01</p>
<p>This study compared good and poor fourth-grade problem <span class="hlt">solvers</span> on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1060752','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1060752"><span>Navier-Stokes <span class="hlt">Solvers</span> and Generalizations for Reacting Flow Problems</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Elman, Howard C</p>
<p>2013-01-27</p>
<p>This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and <span class="hlt">solvers</span> for models of computational fluid dynamics (CFD).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=memory+AND+visualization&pg=5&id=EJ242959','ERIC'); return false;" href="https://eric.ed.gov/?q=memory+AND+visualization&pg=5&id=EJ242959"><span>Intellectual Abilities That Discriminate Good and Poor Problem <span class="hlt">Solvers</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>Meyer, Ruth Ann</p>
<p>1981-01-01</p>
<p>This study compared good and poor fourth-grade problem <span class="hlt">solvers</span> on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDE27001A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDE27001A"><span>PSH3D fast Poisson <span class="hlt">solver</span> for petascale DNS</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Adams, Darren; Dodd, Michael; Ferrante, Antonino</p>
<p>2016-11-01</p>
<p>Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the <span class="hlt">solver</span>. We have developed a parallel <span class="hlt">solver</span> of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear <span class="hlt">solver</span> in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS <span class="hlt">solver</span> does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/EJ1124786.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/EJ1124786.pdf"><span>Thinking Process of Naive Problem <span class="hlt">Solvers</span> to Solve Mathematical Problems</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>Mairing, Jackson Pasini</p>
<p>2017-01-01</p>
<p>Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem <span class="hlt">solvers</span>. This research aimed to describe…</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AIPC.1786e0006C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AIPC.1786e0006C"><span>Hypersonic simulations using open-source CFD and DSMC <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.</p>
<p>2016-11-01</p>
<p>Hypersonic hybrid hydrodynamic-molecular gas flow <span class="hlt">solvers</span> are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics <span class="hlt">solver</span> named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD <span class="hlt">solver</span>. In this paper, further testing is performed, in particular with the CFD <span class="hlt">solver</span>, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CompM.tmp...41H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CompM.tmp...41H"><span>A new fast direct <span class="hlt">solver</span> for the boundary 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>Huang, S.; Liu, Y. J.</p>
<p>2017-04-01</p>
<p>A new fast direct linear equation <span class="hlt">solver</span> for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct <span class="hlt">solver</span> stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct <span class="hlt">solver</span> based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct <span class="hlt">solver</span> can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2854862','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2854862"><span>Assessment of Linear Finite-Difference Poisson-Boltzmann <span class="hlt">Solvers</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>Wang, Jun; Luo, Ray</p>
<p>2009-01-01</p>
<p>CPU time and memory usage are two vital issues that any numerical <span class="hlt">solvers</span> for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference <span class="hlt">solvers</span> with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient <span class="hlt">solvers</span>, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical <span class="hlt">solvers</span> for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1231076','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1231076"><span>Coordinate Projection-based <span class="hlt">Solver</span> for ODE with Invariants</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Serban, Radu</p>
<p>2008-04-08</p>
<p>CPODES is a general purpose (serial and parallel) <span class="hlt">solver</span> for systems of ordinary differential equation (ODE) with invariants. It implements a coordinate projection approach using different types of projection (orthogonal or oblique) and one of several methods for the decompositon of the Jacobian of the invariant equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009JDE...247..447G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009JDE...247..447G"><span>Time-varying Riemann <span class="hlt">solvers</span> for conservation laws on networks</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Garavello, Mauro; Piccoli, Benedetto</p>
<p></p>
<p>We consider a conservation law on a network and generic Riemann <span class="hlt">solvers</span> at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1237557','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1237557"><span>Parallel <span class="hlt">Solver</span> for H(div) Problems Using Hybridization and AMG</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Lee, Chak S.; Vassilevski, Panayot S.</p>
<p>2016-01-15</p>
<p>In this paper, a scalable parallel <span class="hlt">solver</span> is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The <span class="hlt">solver</span> is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) <span class="hlt">solvers</span>, the hybridization <span class="hlt">solver</span> does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the <span class="hlt">solver</span>. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG <span class="hlt">solvers</span> designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed <span class="hlt">solver</span> provides a promising alternative to ADS, a state-of-the-art <span class="hlt">solver</span> [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008AtmEn..42.2415D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008AtmEn..42.2415D"><span>Estimation of the Lagrangian Kolmogorov constant from <span class="hlt">Eulerian</span> measurements for distinct Reynolds number with application to pollution dispersion model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Degrazia, Gervásio Annes; Welter, Guilherme Sausen; Wittwer, Adrián Roberto; da Costa Carvalho, Jonas; Roberti, Débora Regina; Acevedo, Otávio Costa; Moraes, Osvaldo L. L.; de Campos Velho, Haroldo F.</p>
<p></p>
<p>An expression that allows the determination of the Lagrangian Kolmogorov structure function constant C0 from the knowledge of the constant CS associated to the second order <span class="hlt">Eulerian</span> velocity structure function and the γ numerical coefficient relating the <span class="hlt">Eulerian</span> spectra constant to the Lagrangian one, is suggested. Experimental data from both wind tunnel and atmospheric boundary layer observation were used to determine CS. The study agrees with the universal nature of the <span class="hlt">Eulerian</span> CS constant for fully developed turbulence. The analysis leads to an estimate of C0≅5.09±0.93, in agreement with previous studies. This estimated value has been employed in a Lagrangian stochastic dispersion model to simulate the observed concentration obtained from classical diffusion experiments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20782553','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20782553"><span>Velocity-space resolution, entropy production, and upwind dissipation in <span class="hlt">Eulerian</span> gyrokinetic simulations</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Candy, J.; Waltz, R.E.</p>
<p>2006-03-15</p>
<p>Equations which describe the evolution of volume-averaged gyrokinetic entropy are derived and added to GYRO [J. Candy and R.E. Waltz, J. Comput. Phys. 186, 545 (2003)], a <span class="hlt">Eulerian</span> gyrokinetic turbulence simulation code. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor energy flux is significantly changed by a 16-fold increase (from 32 to 512 grid points per cell) in the number of grid points in the two-dimensional velocity space. Third, the measured flux is invariant to an eightfold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that <span class="hlt">Eulerian</span> gyrokinetic codes miss important velocity-space structure. The issues of density and energy conservation and their relation to negligible second-order effects such as the parallel nonlinearity are also discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890001792','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890001792"><span>Modeling of combustion processes of stick propellants via combined <span class="hlt">Eulerian</span>-Lagrangian approach</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.</p>
<p>1988-01-01</p>
<p>This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined <span class="hlt">Eulerian</span>-Lagrangian approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the <span class="hlt">Eulerian</span> approach is obtained; governing equations for the stick propellants are formulated using the Lagrangian approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20879325','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20879325"><span>Simulation of brain mass effect with an arbitrary Lagrangian and <span class="hlt">Eulerian</span> FEM.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Chen, Yasheng; Ji, Songbai; Wu, Xunlei; An, Hongyu; Zhu, Hongtu; Shen, Dinggang; Lin, Weili</p>
<p>2010-01-01</p>
<p>Estimation of intracranial stress distribution caused by mass effect is critical to the management of hemorrhagic stroke or brain tumor patients, who may suffer severe secondary brain injury from brain tissue compression. Coupling with physiological parameters that are readily available using MRI, eg, tissue perfusion, a non-invasive, quantitative and regional estimation of intracranial stress distribution could offer a better understanding of brain tissue's reaction under mass effect. A quantitative and sound measurement serving this particular purpose remains elusive due to multiple challenges associated with biomechanical modeling of the brain. One such challenge for the conventional Lagrangian frame based finite element method (LFEM) is that the mesh distortion resulted from the expansion of the mass effects can terminate the simulation prematurely before the desired pressure loading is achieved. In this work, we adopted an arbitrary Lagrangian and <span class="hlt">Eulerian</span> FEM method (ALEF) with explicit dynamic solutions to simulate the expansion of brain mass effects caused by a pressure loading. This approach consists of three phases: 1) a Lagrangian phase to deform mesh like LFEM, 2) a mesh smoothing phase to reduce mesh distortion, and 3) an <span class="hlt">Eulerian</span> phase to map the state variables from the old mesh to the smoothed one. In 2D simulations with simulated geometries, this approach is able to model substantially larger deformations compared to LFEM. We further applied this approach to a simulation with 3D real brain geometry to quantify the distribution of von Mises stress within the brain.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFD.G4006B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFD.G4006B"><span>Towards Modeling Local Foam Drainage Using the Arbitrary Lagrangian <span class="hlt">Eulerian</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>Brandon, Andrew; Ananth, Ramagopal</p>
<p>2014-11-01</p>
<p>Liquid drainage in foams is a multi-scale, multi-dimensional phenomena that is tied directly to how well a foam performs. For example, the amount of metal within a metal foam after it solidifies affects the strength of the foam and the amount of liquid within an aqueous fire fighting foam determines how effective it is at extinguishing a fire. Liquid drainage is driven by gravity and is governed by the liquid's density and viscosity as well as the surface tension at the liquid gas interface. There are numerous one dimensional, single phase models that approximate liquid drainage by employing a global description but there are no multidimensional models that use a local description. In this presentation, I will describe an ongoing effort to develop a two dimensional, multiphase, Arbitrary Lagrangian <span class="hlt">Eulerian</span> model for the study of local liquid drainage in foams. I will present an improved algorithm for the solution of the incompressible fluid equations in the Arbitrary Lagrangian <span class="hlt">Eulerian</span> method, the novel method used for moving the domain in time, and results from this model development effort.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007APS..DFD.EC008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007APS..DFD.EC008C"><span>Two-way Interaction of Lagrangian Bubble Dynamics and <span class="hlt">Eulerian</span> Mixture Flow Field</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Choi, Jin-Keun; Hsiao, Chao-Tsung; Chahine, Georges</p>
<p>2007-11-01</p>
<p>Although under simple flow conditions a well dispersed bubble cloud in a liquid can be modeled with an <span class="hlt">Eulerian</span> continuum model, the fine scale interactions between the two phases, the potential non-uniformities and high bubble concentrations in stiff gradient regions of complex flows can only be represented by more detailed numerical models such as Lagrangian tracking of individual bubbles. To meet both needs of describing individual bubbles and of including the collective effects in the two-phase continuum, we have developed a method coupling in a two-way fashion the two approaches. The bubble dynamics and tracking scheme is based on extensive studies on bubble dynamics and interactions at Dynaflow and is based on a Surface Averaged Pressure spherical model using a modified incompressible Rayleigh-Plesset equation or a modified compressible Gilmore equation. The bubbles presence in the <span class="hlt">Eulerian</span> flow field is considered through a variable medium density formulation resulting from the instantaneous bubble population distribution in the field. The developed method is applicable to many practical flows in pipes, jets, pumps, propellers, ships, and the ocean. We present the method and its application to waterjet thrust augmentation by bubble injection.</p>
</li>
<li>
<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 formulated 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 Lagrangian formulation. 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010GMDD....3.2051K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010GMDD....3.2051K"><span>Simulation of atmospheric carbon dioxide variability with a global coupled <span class="hlt">Eulerian</span>-Lagrangian 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>Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.</p>
<p>2010-11-01</p>
<p>This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global <span class="hlt">Eulerian</span> model and a global Lagrangian particle dispersion model, for reproducibility of tracer gas variation affected by near field around observation sites. The ability to resolve variability in atmospheric composition on an hourly time scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and upcoming space-based observations. The coupled model yields increased horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at two sites operated by the National Oceanic and Atmospheric Administration, USA and one site operated by National Institute for Environmental Studies, Japan. As the purpose of this study is limited to demonstration of the new modeling approach, we select a small subset of 3 sites to highlight use of the model in various geographical areas. To explore the capability of the coupled model in simulating synoptic-scale meteorological phenomena, we calculate the correlation coefficients and variance ratios between deseasonalized model-simulated and observed CO2 concentrations. Compared with the <span class="hlt">Eulerian</span> model alone, the coupled model yields improved agreement between modeled and observed CO2 concentrations.</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 formulation, 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('http://adsabs.harvard.edu/abs/2010APS..DFD.GU008N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010APS..DFD.GU008N"><span>Full-<span class="hlt">Eulerian</span> fluid-structure coupling simulation of hyperelastic 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>Nagano, Naohiro; Sugiyama, Kazuyasu; Takeuchi, Shintaro; Satoshi, II; Takagi, Shu; Matsumoto, Yoichiro</p>
<p>2010-11-01</p>
<p>A full-<span class="hlt">Eulerian</span> simulation for coupling a Newtonian fluid and hyperelastic material is conducted. The system involves an interaction problem between the fluid and hyperelastic walls and is driven by pressure difference, mimicking a blood flow in a blood vessel. A single set of the governing equations for the fluid and solid is employed, and a volume-of-fluid idea is employed to describe a multi-component geometry. The solid stress is defined in <span class="hlt">Eulerian</span> frame by using a left Cauchy-Green deformation tensor, and the temporal change in the solid deformation is described by updating the tensor. The method employs a uniform fixed grid system for both fluid and solid and it does not require any mesh generation or reconstruction, aiming at facilitating the practical bio-mechanical fluid-structure analysis based on a medical image. The validity of the simulation results is established through comparison with a theoretical prediction. As an application of the present method, pulsating flows are simulated to demonstrate a nonlinear behavior of the flow rate on the pulsating amplitude, and an effect of employing an anisotropic hyperelastic material is discussed.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MS%26E..145b2017I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MS%26E..145b2017I"><span>Numerical Simulation of the Friction Stir Welding Process Using Coupled <span class="hlt">Eulerian</span> Lagrangian Method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.</p>
<p>2016-08-01</p>
<p>Friction Stir Welding (FSW) is a solid state joining process that relies on frictional heating and plastic deformation realized at the interaction between a non-consumable welding tool that rotates on the contact surfaces of the combined parts. The experiments are often time consuming and costly. To overcome these problems, numerical analysis has frequently been used in last years. Several simplified numerical models were designed to elucidate various aspects of the complex thermo-mechanical phenomena associated with FSW. This research investigates a thermo-mechanical finite element model based on Coupled <span class="hlt">Eulerian</span> Lagrangian method to simulate the friction stir welding of the AA 6082-T6 alloy. Abaqus/cae software is used in order to simulate the welding stage of the Friction Stir Welding process. This paper presents the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Coupled <span class="hlt">Eulerian</span> Lagrangian method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CoPhC.215...49J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CoPhC.215...49J"><span>Block-structured grids in full velocity space for <span class="hlt">Eulerian</span> gyrokinetic simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Jarema, D.; Bungartz, H. J.; Görler, T.; Jenko, F.; Neckel, T.; Told, D.</p>
<p>2017-06-01</p>
<p>Global, i.e., full-torus, gyrokinetic simulations play an important role in exploring plasma microturbulence in magnetic fusion devices with strong radial variations. In the presence of steep temperature profiles, grid-based <span class="hlt">Eulerian</span> approaches can become quite challenging as the correspondingly varying velocity space structures need to be accommodated and sufficiently resolved. A rigid velocity space grid then requires a very high number of discretization nodes resulting in enormous computational costs. To tackle this issue and reduce the computational demands, we introduce block-structured grids in the all velocity space dimensions. The construction of these grids is based on a general approach, making them suitable for various <span class="hlt">Eulerian</span> implementations. In the current study, we explain the rationale behind the presented approach, detail the implementation, and provide simulation results obtained with the block-structured grids. The achieved reduction in the number of computational nodes depends on the temperature profile and simulation scenario provided. In the test cases at hand, about ten times fewer grid points are required for nonlinear simulations performed with block-structured grids in the plasma turbulence code GENE (http://genecode.org). With the speed-up found to scale almost exactly reciprocal to the number of grid points, the new implementation greatly reduces the computational costs and therefore opens new possibilities for applications of this software package.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.297...13T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.297...13T"><span>Multiscale Universal Interface: A concurrent framework for coupling heterogeneous <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em</p>
<p>2015-09-01</p>
<p>Concurrently coupled numerical simulations using heterogeneous <span class="hlt">solvers</span> are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for <span class="hlt">solver</span>-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-<span class="hlt">solver</span> information exchange irrespective of the <span class="hlt">solvers</span>' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and <span class="hlt">solvers</span>. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22465652','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22465652"><span>Multiscale Universal Interface: A concurrent framework for coupling heterogeneous <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em</p>
<p>2015-09-15</p>
<p>Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous <span class="hlt">solvers</span> are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for <span class="hlt">solver</span>-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-<span class="hlt">solver</span> information exchange irrespective of the <span class="hlt">solvers</span>' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and <span class="hlt">solvers</span>. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/223853','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/223853"><span>Migration of vectorized iterative <span class="hlt">solvers</span> to distributed memory architectures</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pommerell, C.; Ruehl, R.</p>
<p>1994-12-31</p>
<p>Both necessity and opportunity motivate the use of high-performance computers for iterative linear <span class="hlt">solvers</span>. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative <span class="hlt">solvers</span> have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative <span class="hlt">solvers</span> currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative <span class="hlt">solvers</span> and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative <span class="hlt">solvers</span> rather than reimplementing everything for each new machine, or even for each new architecture.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20100018532','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20100018532"><span>Decision Engines for Software Analysis Using Satisfiability Modulo Theories <span class="hlt">Solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Bjorner, Nikolaj</p>
<p>2010-01-01</p>
<p>The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) <span class="hlt">solvers</span>. Z3 is a state-of-the-art SMT <span class="hlt">solver</span>. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT <span class="hlt">solvers</span>, including the <span class="hlt">solver</span> Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT <span class="hlt">solvers</span>. Proceedings</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CoPhC.203..122Q','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CoPhC.203..122Q"><span>Efficient three-dimensional Poisson <span class="hlt">solvers</span> in open rectangular conducting pipe</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Qiang, Ji</p>
<p>2016-06-01</p>
<p>Three-dimensional (3D) Poisson <span class="hlt">solver</span> plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson <span class="hlt">solvers</span> for a charged particle beam in an open rectangular conducting pipe. These three <span class="hlt">solvers</span> include a spectral integrated Green function (IGF) <span class="hlt">solver</span>, a 3D spectral <span class="hlt">solver</span>, and a 3D integrated Green function <span class="hlt">solver</span>. These <span class="hlt">solvers</span> effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF <span class="hlt">solver</span> and the 3D IGF <span class="hlt">solver</span> scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral <span class="hlt">solver</span> scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three <span class="hlt">solvers</span> using several numerical examples and discuss the advantageous regime of each <span class="hlt">solver</span> in the physical application.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007JPhA...40.7411B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007JPhA...40.7411B"><span>Blocked edges on <span class="hlt">Eulerian</span> maps and mobiles: application to spanning trees, hard particles and the Ising model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Bouttier, J.; Di Francesco, P.; Guitter, E.</p>
<p>2007-07-01</p>
<p>We introduce <span class="hlt">Eulerian</span> maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on <span class="hlt">Eulerian</span> triangulations or the Ising model on quadrangulations.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017FlDyR..49e5507Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017FlDyR..49e5507Z"><span>Accurate signal reconstruction for higher order Lagrangian–<span class="hlt">Eulerian</span> back-coupling in multiphase turbulence</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zwick, D.; Sakhaee, E.; Balachandar, S.; Entezari, A.</p>
<p>2017-10-01</p>
<p>Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the <span class="hlt">Eulerian</span> frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the <span class="hlt">Eulerian</span> grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to</p>
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<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>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AIPC.1740d0003V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AIPC.1740d0003V"><span><span class="hlt">Eulerian</span> frequency analysis of structural vibrations from high-speed video</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Venanzoni, Andrea; De Ryck, Laurent; Cuenca, Jacques</p>
<p>2016-06-01</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 Lagrangian 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 motion 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 content</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22608639','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22608639"><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; De Ryck, Laurent; Cuenca, Jacques</p>
<p>2016-06-28</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 Lagrangian 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 motion 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 content</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1001682','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1001682"><span>Benchmarking ICRF Full-wave <span class="hlt">Solvers</span> for ITER</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS</p>
<p>2011-01-06</p>
<p>Abstract Benchmarking of full-wave <span class="hlt">solvers</span> for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave <span class="hlt">solver</span> groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160003617','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160003617"><span>A Nonlinear Modal Aeroelastic <span class="hlt">Solver</span> for FUN3D</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.</p>
<p>2016-01-01</p>
<p>A nonlinear structural <span class="hlt">solver</span> has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear <span class="hlt">solver</span> is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20140008915','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20140008915"><span>Verification and Validation Studies for the LAVA CFD <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.</p>
<p>2013-01-01</p>
<p>The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) <span class="hlt">solver</span> is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the <span class="hlt">solver</span> and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.</p>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1226960','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1226960"><span>Parallel Auxiliary Space AMG <span class="hlt">Solver</span> for $H(div)$ Problems</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Kolev, Tzanio V.; Vassilevski, Panayot S.</p>
<p>2012-12-18</p>
<p>We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence <span class="hlt">solver</span> (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell <span class="hlt">solver</span> AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110012000','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110012000"><span>An Upwind <span class="hlt">Solver</span> for the National Combustion Code</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Sockol, Peter M.</p>
<p>2011-01-01</p>
<p>An upwind <span class="hlt">solver</span> is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new <span class="hlt">solver</span> has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/881896','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/881896"><span>On improving linear <span class="hlt">solver</span> performance: a block variant of GMRES</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Baker, A H; Dennis, J M; Jessup, E R</p>
<p>2004-05-10</p>
<p>The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear <span class="hlt">solver</span> algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear <span class="hlt">solver</span> algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/918322','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/918322"><span>LDRD report : parallel repartitioning for optimal <span class="hlt">solver</span> performance.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Heaphy, Robert; Devine, Karen Dragon; Preis, Robert; Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar</p>
<p>2004-02-01</p>
<p>We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear <span class="hlt">solvers</span> and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos <span class="hlt">solver</span> framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/793986','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/793986"><span>Elliptic <span class="hlt">Solvers</span> with Adaptive Mesh Refinement on Complex Geometries</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Phillip, B.</p>
<p>2000-07-24</p>
<p>Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic <span class="hlt">solvers</span> such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic <span class="hlt">solvers</span>.</p>
</li>
</ol>
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<ol class="result-class" start="301">
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910056100&hterms=pointwise&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dpointwise','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910056100&hterms=pointwise&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dpointwise"><span>A 3-D upwind Euler <span class="hlt">solver</span> for unstructured meshes</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Barth, Timothy J.</p>
<p>1991-01-01</p>
<p>A three-dimensional finite-volume upwind Euler <span class="hlt">solver</span> is developed for unstructured meshes. The finite-volume scheme solves for solution variables at vertices of the mesh and satisfies the integral conservation law on nonoverlapping polyhedral control volumes surrounding vertices of the mesh. The schene achieves improved solution accuracy by assuming a piecewise linear variation of the solution in each control volume. This improved spatial accuracy hinges heavily upon the calculation of the solution gradient in each control volume given pointwise values of the solution at vertices of the mesh. Several algorithms are discussed for obtaining these gradients. Details concerning implementation procedures and data structures are discussed. Sample calculations for inviscid Euler flow about isolated aircraft wings at subsonic and transonic speeds are compared with established Euler <span class="hlt">solvers</span> as well as experiment.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..GECQR1087S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..GECQR1087S"><span>A spectral Poisson <span class="hlt">solver</span> for kinetic plasma simulation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf</p>
<p>2011-10-01</p>
<p>Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson <span class="hlt">solver</span> for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral <span class="hlt">solver</span> we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/10131138','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/10131138"><span>A functional implementation of the Jacobi eigen-<span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Boehm, A.P.W.; Hiromoto, R.E.</p>
<p>1993-02-01</p>
<p>In this paper, we describe the systematic development of two implementations of the Jacobi eigen-<span class="hlt">solver</span> and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel ``group-rotations`` algorithm first described by Sameh. Our version of this algorithm requires 0(n{sup 3}) operations, whereas Sameh`s original version requires 0(n{sup 4}) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-<span class="hlt">solvers</span> to the functional sub-set of the language.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/6606632','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/6606632"><span>A functional implementation of the Jacobi eigen-<span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E. )</p>
<p>1993-01-01</p>
<p>In this paper, we describe the systematic development of two implementations of the Jacobi eigen-<span class="hlt">solver</span> and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel group-rotations'' algorithm first described by Sameh. Our version of this algorithm requires 0(n[sup 3]) operations, whereas Sameh's original version requires 0(n[sup 4]) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-<span class="hlt">solvers</span> to the functional sub-set of the language.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1324039','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1324039"><span>Scalable Out-of-Core <span class="hlt">Solvers</span> on Xeon Phi Cluster</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>D'Azevedo, Ed F; Chan, Ki Shing; Su, Shiquan; Wong, Kwai</p>
<p>2015-01-01</p>
<p>This paper documents the implementation of a distributive out-of-core (OOC) <span class="hlt">solver</span> for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC <span class="hlt">solver</span> is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.</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/2016AIPC.1769j0007T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AIPC.1769j0007T"><span>Two dimensional Coupled <span class="hlt">Eulerian</span> Lagrangian (CEL) model for banded structure prediction in friction stir welding with trigonal tool</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tongne, A.; Robe, H.; Desrayaud, C.; Jahazi, M.; Feulvarch, E.</p>
<p>2016-10-01</p>
<p>A finite element model has been developed by means of a coupled <span class="hlt">Eulerian</span>-Lagrangian approach. The banded structure which is related to the periodical material deposition is predicted in two dimensions as the experimental investigation shows that, during FSW with trigonal tool, the material flow operates mainly in the welded plates plan.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/5179133','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/5179133"><span>Lagrangian and <span class="hlt">Eulerian</span> diffusion study in the coastal surface layers. Progress report, July 1, 1979-June 30, 1980</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Carter, H H; Okubo, A; Wilson, R E; Sanderson, B; Pritchard, D W</p>
<p>1980-07-01</p>
<p>This research project addresses a fundamental problem in turbulence theory, the relation between Lagrangian and <span class="hlt">Eulerian</span> statistics, by carrying out, analyzing, and interpreting a set of field experiments in the coastal waters off the south shore of Long Island. The study will not only provide information on the relation between the Lagrangian and <span class="hlt">Eulerian</span> autocorrelations but also between the various experimental methods for quantitatively estimating turbulent diffusion. Two experiments, one in summer and one in winter, consisting of simultaneous measurements of dye diffusion, drogue dispersion, and <span class="hlt">Eulerian</span> current velocities in a typical coastal locale were planned. In order to ensure a match between the Lagrangian (drogues, dye) scales of motion and the <span class="hlt">Eulerian</span> (current meters) scales, however, a preliminary experiment, consisting of a 6 mooring current meter array and a short (approx. 3 hours) drogue experiment, was conducted during March 1980. Results of this preliminary experiment and their implications to the experimental program are discussed. The principal results were an improved design of our current meter array, and a wider variety of drogue experiments, i.e., multi-level, multi-scale, and continuous source simulation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22408277','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22408277"><span>Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, <span class="hlt">Eulerian</span>, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Andreussi, T.; Morrison, P. J.; Pegoraro, F.</p>
<p>2015-03-15</p>
<p>An algebraic mistake in the rendering of the Energy Casimir stability condition for a symmetric magnetohydrodynamics plasma configuration with flows made in the article Andreussi et al. “Hamiltonian magnetohydrodynamics: Lagrangian, <span class="hlt">Eulerian</span>, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFMDI11A4249S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFMDI11A4249S"><span>Brittle <span class="hlt">Solvers</span>: Lessons and insights into effective <span class="hlt">solvers</span> for visco-plasticity in geodynamics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Spiegelman, M. W.; May, D.; Wilson, C. R.</p>
<p>2014-12-01</p>
<p>Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear <span class="hlt">solvers</span>. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23496620','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23496620"><span>Lagrangian-<span class="hlt">Eulerian</span> dynamics of breaking shallow water waves through tracer tracking of fluid elements.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Pen, Ue-Yu; Chang, Mei-Chu; I, Lin</p>
<p>2013-02-01</p>
<p>We experimentally investigate the Lagrangian-<span class="hlt">Eulerian</span> dynamics of fluid motion and wave-form evolution for a breaking shallow water wave approaching a slope by tracking tracer motions. It is found that, before breaking, the surface element can climb over the crest and exhibits cyclic oscillation with small forward drift. The increasing asymmetric tangential compression (accumulation) and rarefaction (depletion) in the crest front and the crest are the keys for the crest front steepening with the increasing particle cyclic excursion and forward Stoke drift. Eventually, the surface layer cannot climb over the crest with the vertical front. It curls up and forms an overhanging plunging jet leading the crest, while the lower flow still can reach the crest rear. This process leads to wave breaking with the rapid drop of crest height and the transition from slow divergence to rapid divergence of the adjacent fluid trajectories.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AtmRe.100..357S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AtmRe.100..357S"><span>Introduction of an atmospheric moment combining <span class="hlt">Eulerian</span> and Lagrangian aspects of vortices: Application to tornadoes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Schielicke, Lisa; Névir, Peter</p>
<p>2011-06-01</p>
<p>Various definitions of the intensity of atmospheric vortices exist. These definitions are often based on local parameters in a field. Otherwise, atmospheric vortices are analyzed concerning their geometric properties. A combination of both is rarely used. The aim of this publication is an expansion from a local, mass-specific view to a mass-related strength parameter, called atmospheric moment. The atmospheric moment is characterized by a combination of <span class="hlt">Eulerian</span> parameters of intensity and Lagrangian aspects like track length and area of atmospheric vortices. The atmospheric moment is designed analogous to the seismic moment that describes the strength of earthquakes. Probability density distributions of tornadoes concerning their atmospheric moment show power law behavior. Compared with earthquakes, the scaling exponent is slightly smaller but of comparable order. In principle, this theoretical concept can also be applied to other atmospheric vortices like cyclones and hurricanes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6103503','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6103503"><span>Recent developments of the arbitrary Lagrangian-<span class="hlt">Eulerian</span> containment code ALICE-II. [LMFBR</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wang, C.Y.; Zeuch, W.R.</p>
<p>1983-01-01</p>
<p>The ANL arbitrary Lagrangian <span class="hlt">Eulerian</span> containment code ALICE was developed for use in fast reactor containment studies and is particularly suited for problems involving complex fluid-structure interactions. Many improvements have been made which has resulted in a second version of the code, ALICE-II. A selection of some important improvements are given in this paper. To realistically analyze the above-core hydrodynamics containing a movable upper internal structure (UIS), a 3-D pipe element has been adopted to calculate the response of the UIS columns that connect the UIS to the vessel head. A corotational coordinate scheme for large displacement, small strain, elastic-plastic structural-dynamic analysis is utilized in the formulation. Both geometric and material nonlinearities are considered. The governing equations are integrated explicitly using a central difference procedure. Many sample problems are presented, including comparisons of ALICE-II and ICECO-CEL results on the APRICOT Phase 3 problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JCoPh.231.2092S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JCoPh.231.2092S"><span>Semi-implicit surface tension formulation with a Lagrangian surface mesh on an <span class="hlt">Eulerian</span> simulation grid</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Schroeder, Craig; Zheng, Wen; Fedkiw, Ronald</p>
<p>2012-02-01</p>
<p>We present a method for applying semi-implicit forces on a Lagrangian mesh to an <span class="hlt">Eulerian</span> discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013HMT....49.1089K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013HMT....49.1089K"><span>Axi-symmetric simulation of a two phase vertical thermosyphon using <span class="hlt">Eulerian</span> two-fluid methodology</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kafeel, Khurram; Turan, Ali</p>
<p>2013-08-01</p>
<p>Numerical simulation of steady state operation of a vertical two phase closed thermosyphon is performed using the two-fluid methodology within <span class="hlt">Eulerian</span> multiphase domain. A full scale axi-symmetric model is developed for computational fluid dynamics simulation of thermosyphon using ANSYS/FLUENT 13.0. The effects of evaporation, condensation and interfacial heat and mass transfer are taken into account within the whole domain. Cooling water jacket is also modelled along with the wall of thermosyphon to simulate the effect of conjugate heat transfer between the wall and fluid phase. The results obtained are presented and compared with available experimental investigations for a similar thermosyphon. It is established that two-fluid methodology can be used effectively for the purpose of simulation of two phase system like a typical thermosyphon.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JPhA...48J5005P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JPhA...48J5005P"><span>BEST statistics of Markovian fluxes: a tale of <span class="hlt">Eulerian</span> tours and Fermionic ghosts</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Polettini, Matteo</p>
<p>2015-09-01</p>
<p>We provide an exact expression for the statistics of the fluxes of Markov jump processes at all times, improving on asymptotic results from large deviation theory. The main ingredient is a generalization of the BEST theorem in enumeratoric graph theory to <span class="hlt">Eulerian</span> tours with open ends. In the long-time limit we reobtain Sanov’s theorem for Markov processes, which expresses the exponential suppression of fluctuations in terms of relative entropy. The finite-time power-law term, increasingly important with the system size, is a spanning-tree determinant that, by introducing Grassmann variables, can be absorbed into the effective Lagrangian of a Fermionic ghost field on a metric space, coupled to a gauge potential. With reference to concepts in nonequilibrium stochastic thermodynamics, the metric is related to the dynamical activity that measures net communication between states, and the connection is made to a previous gauge theory for diffusion processes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1988ampm.agar.....H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1988ampm.agar.....H"><span>A mixed <span class="hlt">Eulerian</span>-Lagrangian finite element method for simulation of thermo-mechanical forming processes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Huetink, J.; Vanderlugt, J.</p>
<p>1988-08-01</p>
<p>A mixed <span class="hlt">Eulerian</span>-Lagrangian finite element method is developed by which nodal point locations can be adapted independently from the actual material displacements. Numerical difficulties due to large element distortions, as many occur when the updated Lagrange method is applied, can be avoided by this method. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities. The method has been applied to simulations of an upsetting process, a wire drawing process and a cold rolling process. In the simulation of the rolling process, both workpiece and roll are simultaneously analyzed in order to predict the flattening of the roll. Special contact-slip elements are developed for the tool-workpiece interface.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014GeoRL..41.1343H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014GeoRL..41.1343H"><span>Determination of the source regions for surface to stratosphere transport: An <span class="hlt">Eulerian</span> backtracking approach</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.</p>
<p>2014-02-01</p>
<p>A wide range of inverse problems in atmospheric transport and chemistry can be solved within the <span class="hlt">Eulerian</span> backtracking framework. Here it is shown how a new and accurate numerical implementation can be used as an alternative to Lagrangian back trajectory methods in a wide class of process studies. As a key example, the question of how the (time-averaged) stratospheric flux of a finite lifetime chemical species depends upon the location(s) of its surface source(s) is addressed. The resulting sensitivity maps are demonstrated to be robust features of the global atmospheric circulation, with relatively low interannual variability. The maps serve as an at-a-glance resource for policymakers wishing to compare the likely impact of proposed emission locations for very short lived halogenated species on the total loading of stratospheric chlorine and bromine.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15013474','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15013474"><span>Arbitrary Lagrangian-<span class="hlt">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 Lagrangian-<span class="hlt">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 Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.291..238R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.291..238R"><span>Direct numerical simulation of rigid bodies in multiphase flow within 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>Rauschenberger, P.; Weigand, B.</p>
<p>2015-06-01</p>
<p>A new method is presented to simulate rigid body motion in the Volume-of-Fluid based multiphase code Free Surface 3D. The specific feature of the new method is that it works within an <span class="hlt">Eulerian</span> framework without the need for a Lagrangian representation of rigid bodies. Several test cases are shown to prove the validity of the numerical scheme. The technique is able to conserve the shape of arbitrarily shaped rigid bodies and predict terminal velocities of rigid spheres. The instability of a falling ellipsoid is captured. Multiple rigid bodies including collisions may be considered using only one Volume-of-Fluid variable which allows to simulate the drafting, kissing and tumbling phenomena of two rigid spheres. The method can easily be extended to rigid bodies undergoing phase change processes.</p>
</li>
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<ol class="result-class" start="321">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15003343','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15003343"><span>A Dynamically Adaptive Arbitrary Lagrangian-<span class="hlt">Eulerian</span> Method for Solution of the Euler Equations</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Anderson, R W; Elliott, N S; Pember, R B</p>
<p>2003-02-14</p>
<p>A new method that combines staggered grid arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006AGUSM.A44E..05M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006AGUSM.A44E..05M"><span>Convective weather events in high-frequency <span class="hlt">Eulerian</span> observations and model column outputs</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mapes, B.</p>
<p>2006-05-01</p>
<p>Convective cloud systems produce large fractions of the Earth's rainfall. High-frequency <span class="hlt">Eulerian</span> time-height datasets containing such convective storm passages permit clean, objective comparisons between observations and model output. Lagged regressions of these datasets vs. surface rainfall are used to depict the characteristic structure of precipitating disturbances, mainly in the wet tropics. Both observations and models have organized convective rain events with time scales of many hours, even though convection parameterizations (and arguably cumulus cells in nature) operate column by column and typically have no long-time memory. However, different models have very different characteristic structures: very different from observations (which are fairly similar from place to place), and very different from other models. Experiments with single-column versions suggest that this characteristic structure stems largely from the physical parameterizations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930015894','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930015894"><span>A contribution to the great Riemann <span class="hlt">solver</span> debate</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Quirk, James J.</p>
<p>1992-01-01</p>
<p>The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann <span class="hlt">solvers</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016A%26A...586A..82Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016A%26A...586A..82Z"><span>A chemical reaction network <span class="hlt">solver</span> for the astrophysics code NIRVANA</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ziegler, U.</p>
<p>2016-02-01</p>
<p>Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network <span class="hlt">solver</span> into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the <span class="hlt">solver</span> used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920000029&hterms=Linear+Programming&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DLinear%2BProgramming','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920000029&hterms=Linear+Programming&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DLinear%2BProgramming"><span>Menu-Driven <span class="hlt">Solver</span> Of Linear-Programming Problems</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Viterna, L. A.; Ferencz, D.</p>
<p>1992-01-01</p>
<p>Program assists inexperienced user in formulating linear-programming problems. A Linear Program <span class="hlt">Solver</span> (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1994CoStr..52..511D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1994CoStr..52..511D"><span>Direct linear programming <span class="hlt">solver</span> in C for structural applications</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Damkilde, L.; Hoyer, O.; Krenk, S.</p>
<p>1994-08-01</p>
<p>An optimization problem can be characterized by an object-function, which is maximized, and restrictions, which limit the variation of the variables. A subclass of optimization is Linear Programming (LP), where both the object-function and the restrictions are linear functions of the variables. The traditional solution methods for LP problems are based on the simplex method, and it is customary to allow only non-negative variables. Compared to other optimization routines the LP <span class="hlt">solvers</span> are more robust and the optimum is reached in a finite number of steps and is not sensitive to the starting point. For structural applications many optimization problems can be linearized and solved by LP routines. However, the structural variables are not always non-negative, and this requires a reformation, where a variable x is substituted by the difference of two non-negative variables, x(sup + ) and x(sup - ). The transformation causes a doubling of the number of variables, and in a computer implementation the memory allocation doubles and for a typical problem the execution time at least doubles. This paper describes a LP <span class="hlt">solver</span> written in C, which can handle a combination of non-negative variables and unlimited variables. The LP <span class="hlt">solver</span> also allows restart, and this may reduce the computational costs if the solution to a similar LP problem is known a priori. The algorithm is based on the simplex method, and differs only in the logical choices. Application of the new LP <span class="hlt">solver</span> will at the same time give both a more direct problem formulation and a more efficient program.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21511599','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21511599"><span>Boltzmann <span class="hlt">Solver</span> with Adaptive Mesh in Velocity Space</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.</p>
<p>2011-05-20</p>
<p>We describe the implementation of direct Boltzmann <span class="hlt">solver</span> with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1018825','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1018825"><span>Scaling Algebraic Multigrid <span class="hlt">Solvers</span>: On the Road to Exascale</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M</p>
<p>2010-12-12</p>
<p>Algebraic Multigrid (AMG) <span class="hlt">solvers</span> are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1993cfda.work..437D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1993cfda.work..437D"><span>A generalized <span class="hlt">Eulerian</span>-Lagrangian analysis, with application to liquid flows with vapor bubbles</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Dejong, Frederik J.; Meyyappan, Meyya</p>
<p>1993-07-01</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</span>-Lagrangian technique, in which <span class="hlt">Eulerian</span> conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian 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://hdl.handle.net/2060/19950017213','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950017213"><span>A Generalized <span class="hlt">Eulerian</span>-Lagrangian 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</span>-Lagrangian technique, in which <span class="hlt">Eulerian</span> conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian 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/2010AIPC.1301..476G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AIPC.1301..476G"><span>Studying an <span class="hlt">Eulerian</span> Computer Model on Different High-performance Computer Platforms and Some Applications</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Georgiev, K.; Zlatev, Z.</p>
<p>2010-11-01</p>
<p>The Danish <span class="hlt">Eulerian</span> Model (DEM) is an <span class="hlt">Eulerian</span> model for studying the transport of air pollutants on large scale. Originally, the model was developed at the National Environmental Research Institute of Denmark. The model computational domain covers Europe and some neighbour parts belong to the Atlantic Ocean, Asia and Africa. If DEM model is to be applied by using fine grids, then its discretization leads to a huge computational problem. This implies that such a model as DEM must be run only on high-performance computer architectures. The implementation and tuning of such a complex large-scale model on each different computer is a non-trivial task. Here, some comparison results of running of this model on different kind of vector (CRAY C92A, Fujitsu, etc.), parallel computers with distributed memory (IBM SP, CRAY T3E, Beowulf clusters, Macintosh G4 clusters, etc.), parallel computers with shared memory (SGI Origin, SUN, etc.) and parallel computers with two levels of parallelism (IBM SMP, IBM BlueGene/P, clusters of multiprocessor nodes, etc.) will be presented. The main idea in the parallel version of DEM is domain partitioning approach. Discussions according to the effective use of the cache and hierarchical memories of the modern computers as well as the performance, speed-ups and efficiency achieved will be done. The parallel code of DEM, created by using MPI standard library, appears to be highly portable and shows good efficiency and scalability on different kind of vector and parallel computers. Some important applications of the computer model output are presented in short.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020019227','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020019227"><span>Transonic Drag Prediction Using an Unstructured Multigrid <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Mavriplis, D. J.; Levy, David W.</p>
<p>2001-01-01</p>
<p>This paper summarizes the results obtained with the NSU-3D unstructured multigrid <span class="hlt">solver</span> for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid <span class="hlt">solver</span> for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured <span class="hlt">solver</span> on inexpensive clusters of commodity computers is also demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDA31006M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDA31006M"><span>An immersed interface vortex particle-mesh <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Marichal, Yves; Chatelain, Philippe; Winckelmans, Gregoire</p>
<p>2014-11-01</p>
<p>An immersed interface-enabled vortex particle-mesh (VPM) <span class="hlt">solver</span> is presented for the simulation of 2-D incompressible viscous flows, in the framework of external aerodynamics. Considering the simulation of free vortical flows, such as wakes and jets, vortex particle-mesh methods already provide a valuable alternative to standard CFD methods, thanks to the interesting numerical properties arising from its Lagrangian nature. Yet, accounting for solid bodies remains challenging, despite the extensive research efforts that have been made for several decades. The present immersed interface approach aims at improving the consistency and the accuracy of one very common technique (based on Lighthill's model) for the enforcement of the no-slip condition at the wall in vortex methods. Targeting a sharp treatment of the wall calls for substantial modifications at all computational levels of the VPM <span class="hlt">solver</span>. More specifically, the solution of the underlying Poisson equation, the computation of the diffusion term and the particle-mesh interpolation are adapted accordingly and the spatial accuracy is assessed. The immersed interface VPM <span class="hlt">solver</span> is subsequently validated on the simulation of some challenging impulsively started flows, such as the flow past a cylinder and that past an airfoil. Research Fellow (PhD student) of the F.R.S.-FNRS of Belgium.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160008883','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160008883"><span>A Survey of <span class="hlt">Solver</span>-Related Geometry and Meshing Issues</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris</p>
<p>2016-01-01</p>
<p>There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of <span class="hlt">solver</span> or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the <span class="hlt">solver</span> is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the <span class="hlt">solver</span> or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1237574','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1237574"><span>NONLINEAR MULTIGRID <span class="hlt">SOLVER</span> EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.</p>
<p>2016-01-22</p>
<p>The paper introduces a nonlinear multigrid <span class="hlt">solver</span> for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear <span class="hlt">solver</span> is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a <span class="hlt">solver</span> with the potential for mesh-independent convergence on general unstructured meshes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21275983','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21275983"><span>Error control of iterative linear <span class="hlt">solvers</span> for integrated groundwater models.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Dixon, Matthew F; Bai, Zhaojun; Brush, Charles F; Chung, Francis I; Dogrul, Emin C; Kadir, Tariq N</p>
<p>2011-01-01</p>
<p>An open problem that arises when using modern iterative linear <span class="hlt">solvers</span>, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear <span class="hlt">solver</span> to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of "forward error bound estimation" to explain the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed by the US Geological Survey and the California State Department of Water Resources, we observe that this error bound guides the choice of a practical measure for controlling the error in linear systems. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive Over-Relaxation (SOR) method, the most widely known iterative <span class="hlt">solver</span> for nonsymmetric coefficient matrices. With forward error control, GMRES can easily replace the SOR method in legacy groundwater modeling packages, resulting in the overall simulation speedups as large as 7.74×. This research is expected to broadly impact groundwater modelers through the demonstration of a practical and general approach for setting the residual tolerance in line with the solution error tolerance and presentation of GMRES performance benchmarking results.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DPPUP2084C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DPPUP2084C"><span>QED multi-dimensional vacuum polarization finite-difference <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo</p>
<p>2015-11-01</p>
<p>The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference <span class="hlt">solver</span> with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic <span class="hlt">solver</span>. As an illustration of the properties of the <span class="hlt">solver</span>, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/433349','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433349"><span>NITSOL: A Newton iterative <span class="hlt">solver</span> for nonlinear systems</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pernice, M.; Walker, H.F.</p>
<p>1996-12-31</p>
<p>Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear <span class="hlt">solver</span> until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear <span class="hlt">solver</span> from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov <span class="hlt">solver</span> can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18966265','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18966265"><span>Non-linear curve fitting using Microsoft Excel <span class="hlt">solver</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Walsh, S; Diamond, D</p>
<p>1995-04-01</p>
<p><span class="hlt">Solver</span>, an analysis tool incorporated into Microsoft Excel V 5.0 for Windows, has been evaluated for solving non-linear equations. Test and experimental data sets have been processed, and the results suggest that <span class="hlt">solver</span> can be successfully used for modelling data obtained in many analytical situations (e.g. chromatography and FIA peaks, fluorescence decays and ISE response characteristics). The relatively simple user interface, and the fact that Excel is commonly bundled free with new PCs makes it an ideal tool for those wishing to experiment with solving non-linear equations without having to purchase and learn a completely new package. The dynamic display of the iterative search process enables the user to monitor location of the optimum solution by the search algorithm. This, together with the almost universal availability of Excel, makes <span class="hlt">solver</span> an ideal vehicle for teaching the principles of iterative non-linear curve fitting techniques. In addition, complete control of the modelling process lies with the user, who must present the raw data and enter the equation of the model, in contrast to many commercial packages bundled with instruments which perform these operations with a 'black-box' approach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CoPhC.217...99L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CoPhC.217...99L"><span>IGA-ADS: Isogeometric analysis FEM using ADS <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav</p>
<p>2017-08-01</p>
<p>In this paper we present a fast explicit <span class="hlt">solver</span> for solution of non-stationary problems using L2 projections with isogeometric finite element method. The <span class="hlt">solver</span> has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the <span class="hlt">solver</span> framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).</p>
</li>
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<ol class="result-class" start="341">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014ACP....14.6605W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014ACP....14.6605W"><span>Comparison of <span class="hlt">Eulerian</span> and Lagrangian moisture source diagnostics - the flood event in eastern Europe in May 2010</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Winschall, A.; Pfahl, S.; Sodemann, H.; Wernli, H.</p>
<p>2014-07-01</p>
<p>Moisture convergence from different sources is an important prerequisite for a heavy-precipitation event. The contributions from different source regions can, however, hardly be quantified from observations, and their assessment based on model results is complex. Two conceptually different numerical methods are widely used for the quantification of moisture sources: Lagrangian approaches based on the analysis of humidity variations along backward trajectories and <span class="hlt">Eulerian</span> methods based on the implementation of moisture tracers into a numerical model. In this study the moisture sources for a high-impact, heavy-precipitation event that affected eastern Europe in May 2010 are studied with both <span class="hlt">Eulerian</span> and Lagrangian moisture source diagnostics. The precipitation event was connected to a cyclone that developed over northern Africa, moved over the Mediterranean towards eastern Europe and induced transport of moist air towards the Carpathian Mountains. Heavy precipitation and major flooding occurred in Poland, the Czech Republic and Slovakia between 16 and 18 May 2010. The Lagrangian and <span class="hlt">Eulerian</span> diagnostics consistently indicate a wide spatial and temporal range of moisture sources contributing to the event. The source with the largest share is local evapotranspiration from the European land surface, followed by moisture from the North Atlantic. Further contributions come from tropical western Africa (10-20° N) and the Mediterranean Sea. Contrary to what could be expected, the Mediterranean contribution of about 10% is relatively small. A detailed analysis of exemplary trajectories corroborates the general consistency of the two approaches, and underlines their complementarity. The Lagrangian method allows for mapping out moisture source regions with computational efficiency, whereas the more elaborate <span class="hlt">Eulerian</span> model requires predefined moisture sources, but includes also processes such as precipitation, evaporation and turbulent mixing. However, in the <span class="hlt">Eulerian</span> model</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1226207','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1226207"><span>An AMR capable finite element diffusion <span class="hlt">solver</span> for ALE hydrocodes [An AMR capable diffusion <span class="hlt">solver</span> for ALE-AMR</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.; Eder, D. C.; Gunney, B. T. N.; Masters, N. D.; Koniges, A. E.; Anderson, R. W.</p>
<p>2015-02-01</p>
<p>Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion <span class="hlt">solver</span> and associated physics packages yield 2nd order convergence in the L<sub>2</sub> norm.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..GECMW6080T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..GECMW6080T"><span>A Robust Compressible Flow <span class="hlt">Solver</span> for Studies on Solar Fuel Production in Microwave Plasma</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Tadayon Mousavi, Samaneh; Koelman, Peter; Groen, Pieter Willem; van Dijk, Jan; Epg/ Applied Physics/ Eindhoven University Of Technology Team; Dutch InstituteFundamental Energy Research (Differ) Team</p>
<p>2016-09-01</p>
<p>n order to simulate the dissociation of CO2 with H2O admixture by microwave plasma for the production of solar fuels, we need a multicomponent <span class="hlt">solver</span> that is able to capture the complex nature of the plasma by combining the chemistry, flow, and electromagnetic field. To achieve this goal, first we developed a robust finite volume compressible flow <span class="hlt">solver</span> in C++. The <span class="hlt">solver</span> is implemented in the framework of the PLASIMO software and will be used in complete plasma simulations later on. Due to the compressible nature of the <span class="hlt">solver</span>, it can be used for simulation of dissociation of CO2 with H2O admixture by supersonic expansion in microwave plasmas. A spatially second order version of this <span class="hlt">solver</span> is able to reveal the vortex flow structure of the plasmas. Capabilities of this <span class="hlt">solver</span> are presented by benchmarking against well-established analytical and numerical test cases.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1040022','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1040022"><span>Code Verification of the HIGRAD Computational Fluid Dynamics <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.; Sauer, Jeremy A.</p>
<p>2012-05-04</p>
<p>The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) <span class="hlt">solver</span> of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the <span class="hlt">solver</span>. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the <span class="hlt">solver</span> performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AGUFM.H43D1386B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AGUFM.H43D1386B"><span>A New Robust <span class="hlt">Solver</span> for Saturated-Unsaturated Richards' Equation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Barajas-Solano, D. A.; Tartakovsky, D. M.</p>
<p>2012-12-01</p>
<p>We present a novel approach for the numerical integration of the saturated-unsaturated Richards' equation, a degenerate parabolic partial differential equation that models flow in porous media. The method is based on the mixed (pore pressure-water content) form of RE, written as a set of differential algebraic equations (DAEs) of index-1 for the fully saturated case and index-2 for the partially saturated case. A DAE-based approach allows us to overcome the numerical challenges posed by the degenerate nature of the Richards' equation. The resulting set of DAEs is solved using the stiffly-accurate, single-step, 3-stage implicit Runge-Kutta method Radau IIA, chosen for its favorable accuracy and stability properties, and its ease of implementation. For each time step a nonlinear system of equations on the intermediate Runge-Kutta states of the pore pressure is solved, written so to ensure that the next step pore pressure and water content correspond to one another correctly. The implementation of our approach compares favorably to state-of-the-art DAE-based <span class="hlt">solvers</span> in both one- and two-dimensional simulations. These <span class="hlt">solvers</span> use multi-step backward difference formulas together with a pressure-based form of Richards' equation. To the best of our knowledge, our method is the first instance of a successful DAE-based <span class="hlt">solver</span> that uses the mixed form of Richards' equation. We consider this a promising line of research, with future work to be done on the use of globally convergent methods for the solution of the occurring nonlinear systems of equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010038236','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010038236"><span>Application of Aeroelastic <span class="hlt">Solvers</span> Based on Navier Stokes Equations</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Keith, Theo G., Jr.; Srivastava, Rakesh</p>
<p>2001-01-01</p>
<p>The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes <span class="hlt">solver</span> is required. A finite volume based Navier-Stokes <span class="hlt">solver</span> has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes <span class="hlt">solver</span> developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940033043','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940033043"><span>Hierarchically Parallelized Constrained Nonlinear <span class="hlt">Solvers</span> with Automated Substructuring</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Padovan, Joe; Kwang, Abel</p>
<p>1994-01-01</p>
<p>This paper develops a parallelizable multilevel multiple constrained nonlinear equation <span class="hlt">solver</span>. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/219588','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/219588"><span>Preconditioned CG-<span class="hlt">solvers</span> and finite element grids</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bauer, R.; Selberherr, S.</p>
<p>1994-12-31</p>
<p>To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG <span class="hlt">solver</span>. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA488117','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA488117"><span>Evaluating Sparse Linear System <span class="hlt">Solvers</span> on Scalable Parallel Architectures</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2008-10-01</p>
<p>iterations will be necessary to assure sufficient accuracy whenever we do not use a direct method to solve (1.3) or (1.5). The overall SPIKE algorithm...boosting is activated, SPIKE is not used as a direct <span class="hlt">solver</span> but rather as a preconditioner. In this case outer iterations via a Krylov subspace method ...robustness. Preconditioning aims to improve the robustness of iterative methods by transforming the system into M−1Ax = M−1f, or AM−1(Mx) = f. (3.2</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950020168','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950020168"><span>Algorithms for parallel flow <span class="hlt">solvers</span> on message passing architectures</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Vanderwijngaart, Rob F.</p>
<p>1995-01-01</p>
<p>The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow <span class="hlt">solvers</span> -- possibly coupled with structures and heat equation <span class="hlt">solvers</span> -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow <span class="hlt">solver</span> kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow <span class="hlt">solvers</span> that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920002474','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920002474"><span>Some fast elliptic <span class="hlt">solvers</span> on parallel architectures and their complexities</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Gallopoulos, E.; Saad, Youcef</p>
<p>1989-01-01</p>
<p>The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel <span class="hlt">solver</span> is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900031624&hterms=Computational+Complexity&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DComputational%2BComplexity','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900031624&hterms=Computational+Complexity&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DComputational%2BComplexity"><span>Some fast elliptic <span class="hlt">solvers</span> on parallel architectures and their complexities</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Gallopoulos, E.; Saad, Y.</p>
<p>1989-01-01</p>
<p>The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel <span class="hlt">solver</span> is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013MSAIS..24...26F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013MSAIS..24...26F"><span>Advances in the hydrodynamics <span class="hlt">solver</span> of CO5BOLD</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Freytag, Bernd</p>
<p></p>
<p>Many features of the Roe <span class="hlt">solver</span> used in the hydrodynamics module of CO5BOLD have recently been added or overhauled, including the reconstruction methods (by adding the new second-order ``Frankenstein's method''), the treatment of transversal velocities, energy-flux averaging and entropy-wave treatment at small Mach numbers, the CTU scheme to combine the one-dimensional fluxes, and additional safety measures. All this results in a significantly better behavior at low Mach number flows, and an improved stability at larger Mach numbers requiring less (or no) additional tensor viscosity, which then leads to a noticeable increase in effective resolution.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CoPhC.196..569A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CoPhC.196..569A"><span>A Simple Quantum Integro-Differential <span class="hlt">Solver</span> (SQuIDS)</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Argüelles Delgado, Carlos A.; Salvado, Jordi; Weaver, Christopher N.</p>
<p>2015-11-01</p>
<p>Simple Quantum Integro-Differential <span class="hlt">Solver</span> (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040066085','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040066085"><span>High Energy Boundary Conditions for a Cartesian Mesh Euler <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.</p>
<p>2004-01-01</p>
<p>Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow <span class="hlt">solver</span> is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880016472','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880016472"><span>A Navier-Stokes <span class="hlt">solver</span> for cascade flows</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Arnone, A.; Swanson, R. C.</p>
<p>1988-01-01</p>
<p>A computer code for solving the Reynolds averaged full Navier-Stokes equations has been developed and applied using sheared H-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady state calculations. Comparisons with experimental data show that the code is an accurate viscous <span class="hlt">solver</span> and can give very good blade-to-blade predictions for engineering applications in less than 100 multigrid cycles on the finest mesh.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016OptCo.375...63G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016OptCo.375...63G"><span>Reformulation of the Fourier-Bessel steady state mode <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Gauthier, Robert C.</p>
<p>2016-09-01</p>
<p>The Fourier-Bessel resonator state mode <span class="hlt">solver</span> is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950017794','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950017794"><span>Performance issues for iterative <span class="hlt">solvers</span> in device simulation</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai</p>
<p>1994-01-01</p>
<p>Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix <span class="hlt">solver</span> on a variety of problems.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CG.....96..208K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CG.....96..208K"><span>Novel accurate and scalable 3-D MT forward <span class="hlt">solver</span> based on a contracting integral equation method</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kruglyakov, M.; Geraskin, A.; Kuvshinov, A.</p>
<p>2016-11-01</p>
<p>We present a novel, open source 3-D MT forward <span class="hlt">solver</span> based on a method of integral equations (IE) with contracting kernel. Special attention in the <span class="hlt">solver</span> is paid to accurate calculations of Green's functions and their integrals which are cornerstones of any IE solution. The <span class="hlt">solver</span> supports massive parallelization and is able to deal with highly detailed and contrasting models. We report results of a 3-D numerical experiment aimed at analyzing the accuracy and scalability of the code.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19870044132&hterms=lala&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dlala','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19870044132&hterms=lala&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dlala"><span>Multiply scaled constrained nonlinear equation <span class="hlt">solvers</span>. [for nonlinear heat conduction problems</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Padovan, Joe; Krishna, Lala</p>
<p>1986-01-01</p>
<p>To improve the numerical stability of nonlinear equation <span class="hlt">solvers</span>, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation <span class="hlt">solvers</span>. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original <span class="hlt">solvers</span>. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled <span class="hlt">solvers</span>, results are presented for several benchmark examples.</p>
</li>
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<ol class="result-class" start="361">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EPJWC.14302027F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EPJWC.14302027F"><span>On the implicit density based OpenFOAM <span class="hlt">solver</span> for turbulent 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>Fürst, Jiří</p>
<p></p>
<p>The contribution deals with the development of coupled implicit density based <span class="hlt">solver</span> for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated <span class="hlt">solvers</span> for compressible flows, the performance of those <span class="hlt">solvers</span> is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled <span class="hlt">solver</span>. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS) whereas the turbulence model variables are updated using implicit Euler method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21499760','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21499760"><span>A Riemann <span class="hlt">solver</span> for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pelanti, Marica; Bouchut, Francois; Mangeney, Anne</p>
<p>2011-02-01</p>
<p>We present a Riemann <span class="hlt">solver</span> derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing <span class="hlt">solvers</span>. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed <span class="hlt">solver</span> is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation <span class="hlt">solver</span> is related to Roe <span class="hlt">solver</span> in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation <span class="hlt">solver</span> has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow <span class="hlt">solver</span> efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation <span class="hlt">solver</span> is formally equivalent to the VFRoe <span class="hlt">solver</span> with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPS...323..201J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPS...323..201J"><span>Numerical study of droplet dynamics in a polymer electrolyte fuel cell gas channel using an embedded <span class="hlt">Eulerian</span>-Lagrangian approach</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Jarauta, Alex; Ryzhakov, Pavel; Secanell, Marc; Waghmare, Prashant R.; Pons-Prats, Jordi</p>
<p>2016-08-01</p>
<p>An embedded <span class="hlt">Eulerian</span>-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an <span class="hlt">Eulerian</span> formulation, whereas water is described with a Lagrangian framework. Using this framework, the gas-liquid interface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. The method naturally accounts for material property changes across the interface and accurately represents the pressure discontinuity. A sessile drop in a horizontal surface, a sessile drop in an inclined plane and droplets in a PEFC channel are solved for as numerical examples and compared to experimental data. Numerical results are in excellent agreement with experimental data. Numerical results are also compared to results obtained with the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach.</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('http://adsabs.harvard.edu/abs/2007APS..SHK.V2005H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007APS..SHK.V2005H"><span>Implementation of the TEPLA Damage Model in a 3D <span class="hlt">Eulerian</span> Hydrocode</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Holian, Kathleen S.; Clancy, Sean P.; Maudlin, Paul J.</p>
<p>2007-06-01</p>
<p>A sophisticated damage model (TEPLA) has been implemented into a three-dimensional (Cartesian) computer code (Pagosa) used here at Los Alamos National Laboratory. TEPLA was originally an isotropic damage model based upon the Gurson flow surface (a potential function used in conjunction with the associated flow law) that models damage due to both porosity growth and plastic strain. It has since been modified to model anisotropic elastoplastic material strength as well. Pagosa is an <span class="hlt">Eulerian</span> hydrodynamics code that has the following special features: a predictor-corrector Lagrangian step that advances the state variables in time, a high-order advection algorithm that remaps the problem back to the original mesh every time step, and a material interface tracking scheme with van Leer monotonic advection. It also includes a variety of equation of state, strength, fracture, and high explosive burn models. We will describe the physics of the TEPLA model (that models both strength and damage) and will show preliminary results of test problems that are used to validate the model. The four test problems (simple shear, stretching rod, Taylor anvil, and plate impact) can be compared with either analytic solutions or with experimental data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004AIPC..706..529B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004AIPC..706..529B"><span>Coupled Plasticity and Damage Modeling and Their Applications in a Three-Dimensional <span class="hlt">Eulerian</span> Hydrocode</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Burkett, Michael W.; Clancy, Sean P.; Maudlin, Paul J.; Holian, Kathleen S.</p>
<p>2004-07-01</p>
<p>Previously developed constitutive models and solution algorithms for continuum-level anisotropic elastoplastic material strength and an isotropic damage model TEPLA have been implemented in the three-dimensional <span class="hlt">Eulerian</span> hydrodynamics code known as CONEJO. The anisotropic constitutive modeling is posed in an unrotated material frame of reference using the theorem of polar decomposition to compute rigid-body rotation. TEPLA is based upon the Gurson flow surface (a potential function used in conjunction with the associated flow law). The original TEPLA equation set has been extended to include anisotropic elastoplasticity and has been recast into a new implicit solution algorithm based upon an eigenvalue scheme to accommodate the anisotropy. This algorithm solves a two-by-two system of nonlinear equations using a Newton-Raphson iteration scheme. Simulations of a shaped-charge jet formation, a Taylor cylinder impact, and an explosively loaded hemishell were selected to demonstrate the utility of this modeling capability. The predicted deformation topology, plastic strain, and porosity distributions are shown for the three simulations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015AGUFM.P23A2102L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.P23A2102L"><span>A cyclostrophic transformed <span class="hlt">Eulerian</span> zonal mean model for the middle atmosphere of slowly rotating planets</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Li, K. F.; Yao, K.; Taketa, C.; Zhang, X.; Liang, M. C.; Jiang, X.; Newman, C. E.; Tung, K. K.; Yung, Y. L.</p>
<p>2015-12-01</p>
<p>With the advance of modern computers, studies of planetary atmospheres have heavily relied on general circulation models (GCMs). Because these GCMs are usually very complicated, the simulations are sometimes difficult to understand. Here we develop a semi-analytic zonally averaged, cyclostrophic residual <span class="hlt">Eulerian</span> model to illustrate how some of the large-scale structures of the middle atmospheric circulation can be explained qualitatively in terms of simple thermal (e.g. solar heating) and mechanical (the Eliassen-Palm flux divergence) forcings. This model is a generalization of that for fast rotating planets such as the Earth, where geostrophy dominates (Andrews and McIntyre 1987). The solution to this semi-analytic model consists of a set of modified Hough functions of the generalized Laplace's tidal equation with the cyclostrohpic terms. As examples, we apply this model to Titan and Venus. We show that the seasonal variations of the temperature and the circulation of these slowly-rotating planets can be well reproduced by adjusting only three parameters in the model: the Brunt-Väisälä bouyancy frequency, the Newtonian radiative cooling rate, and the Rayleigh friction damping rate. We will also discuss the application of this model to study the meridional transport of photochemically produced tracers that can be observed by space instruments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.3662L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.3662L"><span>A cyclostrophic transformed <span class="hlt">Eulerian</span> zonal mean model for the middle atmosphere of slowly rotating planets</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Li, King-Fai; Yao, Kaixuan; Taketa, Cameron; Zhang, Xi; Liang, Mao-Chang; Jiang, Xun; Newman, Claire; Tung, Ka-Kit; Yung, Yuk L.</p>
<p>2016-04-01</p>
<p>With the advance of modern computers, studies of planetary atmospheres have heavily relied on general circulation models (GCMs). Because these GCMs are usually very complicated, the simulations are sometimes difficult to understand. Here we develop a semi-analytic zonally averaged, cyclostrophic residual <span class="hlt">Eulerian</span> model to illustrate how some of the large-scale structures of the middle atmospheric circulation can be explained qualitatively in terms of simple thermal (e.g. solar heating) and mechanical (the Eliassen-Palm flux divergence) forcings. This model is a generalization of that for fast rotating planets such as the Earth, where geostrophy dominates (Andrews and McIntyre 1987). The solution to this semi-analytic model consists of a set of modified Hough functions of the generalized Laplace's tidal equation with the cyclostrohpic terms. As an example, we apply this model to Titan. We show that the seasonal variations of the temperature and the circulation of these slowly-rotating planets can be well reproduced by adjusting only three parameters in the model: the Brunt-Väisälä bouyancy frequency, the Newtonian radiative cooling rate, and the Rayleigh friction damping rate. We will also discuss an application of this model to study the meridional transport of photochemically produced tracers that can be observed by space instruments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26738020','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26738020"><span>The detection of breathing behavior using <span class="hlt">Eulerian</span>-enhanced thermal video.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Bennett, Stephanie L; Goubran, Rafik; Knoefel, Frank</p>
<p>2015-01-01</p>
<p>The current gold standard for detecting and distinguishing between types of sleep apnea is expensive and invasive. This paper aims to examine the potential of inexpensive and unobtrusive thermal cameras in the identification and distinction between types of sleep apnea. A thermal camera was used to gather video of a subject performing regular nasal breathing, nasal hyperventilation and an additional trial simulating one type of sleep apnea. Simultaneously, a respiratory inductance plethysmography (RIP) band gathered respiratory data. Thermal video of all three trials were subjected to <span class="hlt">Eulerian</span> Video Magnification; a procedure developed at MIT for enhancing subtle color variations in video data. Post magnification, nasal regions of interest were defined and mean region intensities were found for each frame of each trial. These signals were compared to determine the best performing region and compared to RIP data to validate breathing behavior. While some regions performed better, all region intensity signals depicted correct breathing behavior. The mean intensity signals for normal breathing and hyperventilation were correct and correlated well with RIP data. Furthermore, the RIP data resulting from the sleep apnea simulation clearly depicted chest movement while the corresponding mean intensity signal depicted lack of cyclical air flow. These results indicate that a subject's breathing behavior can be captured using thermal video and suggest that, with further development and additional equipment, thermal video can be used to detect and distinguish between types of sleep apnea.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27380322','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27380322"><span>CFD transient simulation of the cough clearance process using an <span class="hlt">Eulerian</span> wall film model.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Paz, Concepción; Suárez, Eduardo; Vence, Jesús</p>
<p>2017-02-01</p>
<p>In this study, a cough cycle is reproduced using a computational methodology. The <span class="hlt">Eulerian</span> wall film approach is proposed to simulate airway mucus flow during a cough. The reproduced airway domain is based on realistic geometry from the literature and captures the deformation of flexible tissue. To quantify the overall performance of this complex phenomenon, cough efficiency (CE) was calculated, which provided an easily reproducible measurement parameter for the cough clearance process. Moreover, the effect of mucus layer thickness was examined. The relationship between the CE and the mucus viscosity was quantified using reductions from 20 to 80%. Finally, predictions of CE values based on healthy person inputs were compared with values obtained from patients with different respiratory diseases, including chronic obstructive pulmonary disease (COPD) and respiratory muscle weakness (RMW). It was observed that CE was reduced by 50% in patients with COPD compared with that of a healthy person. On average, CE was reduced in patients with RMW to 10% of the average value of a healthy person.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16600492','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16600492"><span>Simulation of a spray scrubber performance with <span class="hlt">Eulerian</span>/Lagrangian approach in the aerosol removing process.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Bozorgi, Y; Keshavarz, P; Taheri, M; Fathikaljahi, J</p>
<p>2006-09-01</p>
<p>In this study, a mathematical model has been developed to simulate the performance of a spray scrubber in an industrial ammonium nitrate plant. The model is based on the Lagrangian approach for the droplets movement and particle source in cell (PSI-CELL) model for calculating the droplet concentration distribution. Consequently, unlike former research, the emphasis is on the droplet dynamic behavior. In the current study, for approaching a realistic model, a droplet size distribution rather than average diameter, and also liquid film formation rather than uniform and constant droplet flow rate has been applied. Also, the <span class="hlt">Eulerian</span> method has been used for the calculation of the particles removal efficiency and energy balance has been applied on the gas to estimate the droplet size distribution. In the experimental section, the concentration of particles and their size distribution in both inlet and outlet gas of the studied scrubber has been measured for the validation of the predicted particles collection efficiency. In addition, the temperature of the gas at inlet, outlet and in the middle of the tower has been measured for the confirmation of the predicted droplet size distribution in the tower. A good consistency between the model and data has been observed. After the model is validated, it is used to investigate the various variable profiles such as liquid film, total projected surface area of the droplets, velocity profile of the droplets and some of the other parameters in the spray scrubbers.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFD.A4008D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFD.A4008D"><span>Numerical flow Simulation around a flat plate during heavy rainfall using Lagrangian <span class="hlt">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>Dhir, Gaurav; Suman, Sawan</p>
<p>2015-11-01</p>
<p>Experimental evidence shows that aircrafts operating under heavy rainfall conditions face deterioration of lift and increase in drag. This scenario can be a critical design challenge especially for slow moving vehicles such as airships. Effective roughening of airfoil surface caused by an uneven water film, loss of flow momentum and the loss of vehicle momentum due to its collision with the raindrops are the primary reasons causing the drag to increase. Our work focuses primarily on the numerical quantification of boundary layer momentum loss caused due to raindrops. The collision of raindrops with a solid surface leads to formation of an ejecta fog of splashed back droplets with their sizes being of the order of micrometers and their acceleration leads to boundary layer momentum loss. We model the airflow within a flat plate boundary layer using a Lagrangian-<span class="hlt">Eulerian</span> approach with the raindrops being considered as non-deformable, non-spinning and non-interacting droplets. We employ an inter-phase coupling term to account for the interaction between the boundary layer flow and the droplets. Our presentation will focus on several comparisons (velocity field, lift and drag at various angles of attack) with the results of the standard (rain-free) Prandtl boundary layer flow. Indian Institute of Technology, Delhi.</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</span>-Lagrangian 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 Lagrangian 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 Lagrangian 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>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPSJ...86f4402Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPSJ...86f4402Z"><span>Fine-Grid <span class="hlt">Eulerian</span> Simulation of Sedimenting Particles: Liquid-Solid and Gas-Solid Systems</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Zaheer, Muhammad; Hamid, Adnan; Ullah, Atta</p>
<p>2017-06-01</p>
<p>A computational study of mono-dispersed spherical sedimenting particles was performed with <span class="hlt">Eulerian</span> two-fluid model (TFM). The aim was to investigate the applicability and accuracy of TFM with proper closure laws from kinetic theory of granular flow (KTGF) for sedimentation studies. A three-dimensional cubical box with full periodic boundaries was employed. The volume fraction of particles (ϕs) was varied from very low (ϕs = 0.01) to dense regimes (ϕs = 0.4), for two different types of fluids, i.e., gas and liquid. It is observed that the results for liquid-solid sedimentation are in good agreement with simulation studies and experimental correlation of Richardson and Zaki. However, for gas-solid system, results show different behavior at low volume fractions, which is more pronounced with increasing Stokes number. This can be attributed to inhomogeneous distribution of solid particles in gas phase at dilute concentrations, which causes meso-scale clusters and streamers formation. It is concluded that the ratio of density of particles to density of fluid which appears in Stokes number plays critical role in settling behavior of particles.</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 Lagrangian <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 Lagrangian <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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..SHK.L3004B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..SHK.L3004B"><span>Modeling Anisotropic Plasticity: 3D <span class="hlt">Eulerian</span> Hydrocode Simulations of High Strain Rate Deformation Processes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Burkett, Michael; Clancy, Sean; Maudlin, Paul; Holian, Kathleen</p>
<p>2001-06-01</p>
<p>: Previously developed constitutive models and solution algorithms for anisotropic elastoplastic material strength has been implemented in the three-dimensional CONEJO hydrodynamics code. CONEJO is an explicit, <span class="hlt">Eulerian</span> continuum mechanics code that is utilized to predict formation processes associated with material deformation at elevated strain-rates and is a code development project under the Accelerated Strategic Computing Initiative (ASCI) program. Some special features of CONEJO include a high-order advection algorithm, a material interface tracking scheme, and van Leer monotonic advection-limiting. The anisotropic constitutive modeling is posed in an unrotated material frame using the theorem of polar decomposition to describe rigid body rotation. An Euler-Rodrigues description is used to quantify the rigid body rotations. Continuous quadratic yield functions fitted from polycrystal simulations for a metallic hexagonal-close-packed structure were utilized. Associative flow formulations incorporating these yield functions were solved using a geometric normal return method. Simple rectangular shear problems, "R-value" problems, and Taylor cylinder impact test data were utilized to verify and validate the implementation of the anisotropic model. A "stretching rod" problem (involving large strain and strain-rate deformation) was selected to investigate the effects of material anisotropy for this deformation process. The rod necking rate and topology was compared for CONEJO simulations using several isotropic and anisotropic descriptions that utilized the Mechanical Threshold Stress (MTS) model.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..SHK.F3001M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..SHK.F3001M"><span>Coupled <span class="hlt">Eulerian</span>-Lagrangian simulations of detonation induced shock response in Tantalum</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Meiron, Daniel</p>
<p>2001-06-01</p>
<p>The ASCI Alliance Center at Caltech is constructing a virtual shock physics facility with the aim of facilitating fully three dimensional simulations of the interaction of strong shock waves initiated by the detonation of high explosives (HE) with solid targets. In this talk we will present an overview of the current capabilities of the software environment under development at the center. A parallel implementation of an algorithm to dynamically couple <span class="hlt">Eulerian</span> CFD (used for simulation of HE detonation) with Lagrangian solid mechanics will be presented along with computations on the ASCI terascale platforms utilizing this approach. We will also present results from a multi-scale modeling effort being pursued at the center to provide improved sub-grid scale models for those physical length and time scales that cannot be captured directly by simulation. We discuss the application of this approach to the development of a reduced reaction network for nitramine explosives and the development of models for plastic response of metals such as Tantalum.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MMTA...48.2618Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MMTA...48.2618Y"><span>Microstructural Modeling of Pitting Corrosion in Steels Using an Arbitrary Lagrangian-<span class="hlt">Eulerian</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>Yu, Qifeng; Pan, Tongyan</p>
<p>2017-05-01</p>
<p>Two microscale numerical models are developed in this work using a moving-mesh approach to investigate the growth process of pitting in different iron phases and the corrosion prevention capability of polyaniline (PANi) on steels. The distributions of corrosion potential and current in the electrolyte-coating-steel system are computed to evaluate the anti-corrosion ability of PANi. The arbitrary Lagrangian-<span class="hlt">Eulerian</span> approach was used to accomplish the continuous remesh process as was needed to simulate the dynamic growing forefront of the modeled pitting domain. Experimental validation of the numerical models was conducted using the technique of scanning kelvin probe force microscopy (SKPFM). The SKPFM-scanned surface topography and Volta potential difference exhibit comparable results to and thereby prove the numerical results. The potential distribution in the electrolyte phase of the validated models shows that the corrosion pit grows faster in the epoxy-only-coated steel than that in the PANi-primer-coated steel over the simulation time; also, the corrosion pit grows faster in the ferrite phase than in the cementite phase. The simulation results indicate that the epoxy-only coating lost its anti-corrosion capability as the coating was penetrated by electrolyte, while the PANi-based coating can still protect the steel from corrosion after the electrolyte penetration. The models developed in this work can be used to study the mechanisms of pitting corrosion as well as develop more effective corrosion prevention strategies for general metallic materials.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JPhCS.656a2160M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JPhCS.656a2160M"><span>Modelling Cavitating Flows using an <span class="hlt">Eulerian</span>-Lagrangian Approach and a Nucleation Model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Ma, Jingsen; Hsiao, Chao-Tsung; Chahine, Georges L.</p>
<p>2015-12-01</p>
<p>An <span class="hlt">Eulerian</span>/Lagrangian multi-scale two-phase flow model is developed to simulate the various types of cavitation including bubble, sheet, and tip vortex cavitation. Sheet cavitation inception, unsteady breakup, and cloud shedding on a hydrofoil are used as an example here. No assumptions are needed on mass transfer between phases; instead, the method tracks bubble nuclei, which are in the bulk of the liquid and those generated by nucleation from solid boundaries and this is- sufficient to accurately capture the sheet dynamics. The multi-scale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics and a transition scheme to bridge the micro and macro scales. Nuclei are treated as flow singularities until they grow into large bubbles, which eventually merge to form a large scale discretised sheet cavity. The sheet performs large scale oscillations with a periodic reentrant jet forming under the sheet cavity, traveling upstream, and breaking the cavity. This results in bubble cloud formation and in high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The results for a NACA0015 foil are in good agreement with the experimental data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1008123','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1008123"><span>Parallel octree-based hexahedral mesh generation for <span class="hlt">eulerian</span> to lagrangian conversion.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Staten, Matthew L.; Owen, Steven James</p>
<p>2010-09-01</p>
<p>Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from <span class="hlt">Eulerian</span>-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.</p>
</li>
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<ol class="result-class" start="381">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DPPJP8075B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DPPJP8075B"><span>Efficient simulation of pitch angle collisions in a 2+2-D <span class="hlt">Eulerian</span> Vlasov code</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.</p>
<p>2014-10-01</p>
<p>Here we discuss pitch angle scattering collisions in the context of the <span class="hlt">Eulerian</span>-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 12-ERD-061.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/12186025','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/12186025"><span>A linearized <span class="hlt">Eulerian</span> sound propagation model for studies of complex meteorological effects.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Blumrich, Reinhard; Heimann, Dietrich</p>
<p>2002-08-01</p>
<p>Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized <span class="hlt">Eulerian</span> (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MMTA..tmp..122Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MMTA..tmp..122Y"><span>Microstructural Modeling of Pitting Corrosion in Steels Using an Arbitrary Lagrangian-<span class="hlt">Eulerian</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>Yu, Qifeng; Pan, Tongyan</p>
<p>2017-03-01</p>
<p><Heading>Abstracts</Heading> Two microscale numerical models are developed in this work using a moving-mesh approach to investigate the growth process of pitting in different iron phases and the corrosion prevention capability of polyaniline (PANi) on steels. The distributions of corrosion potential and current in the electrolyte-coating-steel system are computed to evaluate the anti-corrosion ability of PANi. The arbitrary Lagrangian-<span class="hlt">Eulerian</span> approach was used to accomplish the continuous remesh process as was needed to simulate the dynamic growing forefront of the modeled pitting domain. Experimental validation of the numerical models was conducted using the technique of scanning kelvin probe force microscopy (SKPFM). The SKPFM-scanned surface topography and Volta potential difference exhibit comparable results to and thereby prove the numerical results. The potential distribution in the electrolyte phase of the validated models shows that the corrosion pit grows faster in the epoxy-only-coated steel than that in the PANi-primer-coated steel over the simulation time; also, the corrosion pit grows faster in the ferrite phase than in the cementite phase. The simulation results indicate that the epoxy-only coating lost its anti-corrosion capability as the coating was penetrated by electrolyte, while the PANi-based coating can still protect the steel from corrosion after the electrolyte penetration. The models developed in this work can be used to study the mechanisms of pitting corrosion as well as develop more effective corrosion prevention strategies for general metallic materials.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1194068','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1194068"><span>A point-centered arbitrary Lagrangian <span class="hlt">Eulerian</span> hydrodynamic approach for tetrahedral meshes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.</p>
<p>2015-02-24</p>
<p>We present a three dimensional (3D) arbitrary Lagrangian <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 at 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.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JMS...160...81A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JMS...160...81A"><span>Validation of an <span class="hlt">Eulerian</span> population model for the marine copepod Calanus finmarchicus in the Norwegian Sea</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Alver, Morten Omholt; Broch, Ole Jacob; Melle, Webjørn; Bagøien, Espen; Slagstad, Dag</p>
<p>2016-08-01</p>
<p>Calanus finmarchicus is an important zooplankton species in the Norwegian Sea, as a dominant food organism for pelagic fish larvae, and a potentially large source of marine lipids and proteins. Its position in the marine food web also makes it an important model species in assessing the risk posed by oil spills in the Norwegian and Arctic Seas. In this study, an <span class="hlt">Eulerian</span> population model for C.finmarchicus, coupled to the physical and ecological model SINMOD, is presented. The model includes the full life cycle of C. finmarchicus with a representation of all developmental stages. The model has been validated against field measurements made in different areas of the Norwegian Sea in 1997 and 1998. The model displays geographical and temporal distributions of development stages that is in line with observed patterns. When comparing time series for selected regions, we see a high degree of variability both in the field samples and model output. On average, the model deviations are near half of the summed variability of the field data and model estimates. The model has applications within assessment of ecological production, and the potential for harvesting in the Norwegian and Arctic Seas, but in combination with other models, also for the assessment of ecological effects of oil spills and other types of pollution.</p>
</li>
<li>
<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 Lagrangian 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 Lagrangian Coherent Structures (LCS) analysis is a Lagrangian 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>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010MS%26E...10a2074N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010MS%26E...10a2074N"><span>Arbitrary Lagrangian-<span class="hlt">Eulerian</span> method for non-linear problems of geomechanics</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Nazem, M.; Carter, J. P.; Airey, D. W.</p>
<p>2010-06-01</p>
<p>In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-<span class="hlt">Eulerian</span> (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011MNRAS.415..271H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011MNRAS.415..271H"><span>Flow-driven cloud formation and fragmentation: results from <span class="hlt">Eulerian</span> and Lagrangian simulations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Heitsch, Fabian; Naab, Thorsten; Walch, Stefanie</p>
<p>2011-07-01</p>
<p>The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian smoothed particle hydrodynamics (SPH) code VINE and the <span class="hlt">Eulerian</span> grid code PROTEUS. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydrodynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300 K. For clumps more massive than 1 M⊙ pc-1, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of magnitude smaller than their relative motion, rendering it subsonic with respect to the internal sound speed of the clumps but supersonic as seen by an external observer. For the SPH simulations most of the cold gas resides at temperatures below 100 K, while the grid-based models show an additional, substantial component between 100 and 300 K. Independent of the numerical method, our models confirm that converging flows of warm neutral gas fragment rapidly and form high-density, low-temperature clumps as possible seeds for star formation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..DFD.R3005L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..DFD.R3005L"><span><span class="hlt">Eulerian</span>-Lagrangian Simulations of Bubbly Flows in A Vertical Square Duct</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Liu, Rui; Vanka, Surya P.; Thomas, Brian G.</p>
<p>2013-11-01</p>
<p>We report results of <span class="hlt">Eulerian</span>-Lagrangian simulations of developing upward and downward bubbly flows in a vertical square duct with a bulk Reynolds number of 5000. The continuous fluid is simulated with DNS, solving the Navier-Stokes equations by a second-order accurate finite volume fractional step method. Bubbles of sizes comparable to the Kolmogorov scale are injected at the duct entrance with a mean bulk volume fraction below 10-2. A two-way coupling approach is adopted for the interaction between the continuous fluid phase and dispersed bubble phase. The bubbles are tracked by a Lagrangian method including drag and lift forces due to buoyancy and Saffman lift. A in-house code, CU-FLOW, implemented on Graphic Processing Unit (GPU) is used for simulations in this work. The preferential distributions of bubbles and their impact on local turbulence structures and their effects on turbulent kinetic energy budgets are studied. Results between an upward flow and a downward flow with the bubbles are compared. Work Supported by Continuous Casting Consortium at UIUC.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CTM....20..221C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CTM....20..221C"><span>Simulations of sooting turbulent jet flames 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; Nmira, Fatiha; Burot, Daria</p>
<p>2016-03-01</p>
<p>The stochastic <span class="hlt">Eulerian</span> field method is applied to simulate 12 turbulent C1-C3 hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22410329','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22410329"><span>Relativistic <span class="hlt">Eulerian</span> Vlasov simulations of the amplification of seed pulses by Brillouin backscattering in plasmas</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Shoucri, M.; Matte, J.-P.; Vidal, F.</p>
<p>2015-05-15</p>
<p>We apply an <span class="hlt">Eulerian</span> Vlasov code to study the amplification by Brillouin scattering of a short seed laser pulse by a long pump laser pulse in an underdense plasma. The stimulated Brillouin backscattering interaction is the coupling of the pump and seed electromagnetic waves propagating in opposite directions, and the ion plasma wave. The code solves the one-dimensional relativistic Vlasov-Maxwell set of equations. Large amplitude ion waves are generated. In the simulations we present, the density plateau of the plasma is n{sub e}=0.3 n{sub c} (n{sub c} is the critical density), which excludes spurious stimulated Raman scattering amplification (which can occur only if n{sub e}<n{sub c}/4). We also varied the duration and/or amplitude of the short input seed pulse to study how these influence its subsequent behaviour. An initially broad pulse grows more rapidly than an initially narrow pulse. Furthermore, for an initially broader seed pulse, towards the end of the simulation, it is seen to become narrower and to gradually detach from the trailing signal. On the contrary, initially very narrow seed pulses are seen to broaden. The absence of noise in the Vlasov simulations allows to simulate long plasma amplifier lengths, and to follow the evolution of the system with a fully kinetic description and with an accurate representation of the phase-space structures of distribution function.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ComAC...3....5P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ComAC...3....5P"><span>Riemann <span class="hlt">solvers</span> and Alfven waves in black hole magnetospheres</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip</p>
<p>2016-09-01</p>
<p>In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann <span class="hlt">solver</span>, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann <span class="hlt">solver</span>, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21308111','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21308111"><span>A massively parallel fractional step <span class="hlt">solver</span> for incompressible flows</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Houzeaux, G. Vazquez, M. Aubry, R. Cela, J.M.</p>
<p>2009-09-20</p>
<p>This paper presents a parallel implementation of fractional <span class="hlt">solvers</span> for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified 'continuity' equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler <span class="hlt">solvers</span> and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CG, Deflated CG). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040008285','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040008285"><span>Agglomeration Multigrid for an Unstructured-Grid Flow <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Frink, Neal; Pandya, Mohagna J.</p>
<p>2004-01-01</p>
<p>An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow <span class="hlt">solver</span>. Efficiency and robustness of the multigrid-enhanced flow <span class="hlt">solver</span> have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JEI....21d3007L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JEI....21d3007L"><span>Matrix decomposition graphics processing unit <span class="hlt">solver</span> for Poisson image editing</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lei, Zhao; Wei, Li</p>
<p>2012-10-01</p>
<p>In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) <span class="hlt">solver</span> (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid <span class="hlt">solver</span> (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..CAL.C1001A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..CAL.C1001A"><span>A Hybrid Stiff <span class="hlt">Solver</span> for the Rayleigh-Plesset Equation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Alsayegh, Mutaz; Lee, Chung-Min</p>
<p>2011-11-01</p>
<p>We seek to apply efficient computational algorithms to investigate the locations of bubble concentrations in liquid flow. In flows with large velocities, bubbles tend to form in concentrated areas. Moreover, experiments show that bubbles formed at high velocities release large amount of energy once they collapse causing damage to equipment and objects that are in the path of the flow. To gain more insight on the formation of these bubbles, we will first study the dynamics of a single bubble and assume the bubble is a sphere. The dynamics of the bubble in terms of its radius and the driven pressure is modeled by the Rayleigh-Plesset (RP) equation. The RP equation is a second order nonlinear stiff ordinary differential equation (ode) and theoretically, its solution can be obtained numerically using Finite Difference (FD) methods. However, under large pressure variations, the rate of change of the bubble's radius approaches infinity when the bubble is collapsing. Explicit numerical integration methods require time steps of magnitude of (10-12 s) to achieve stable solutions. Iterations under this time scale are highly impractical and require immense CPU time. Therefore, a stiff ode <span class="hlt">solver</span> is needed to alleviate the computation cost. Therefore, we would like to devise a hybrid algorithm that automatically selects between an explicit method and the stiff ode <span class="hlt">solver</span>. Once we have a robust implementation, we will use it to process the data and analyze the relations between bubble locations and flow structures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014SPIE.9118E..10P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014SPIE.9118E..10P"><span>Using computer algebra and SMT <span class="hlt">solvers</span> in algebraic biology</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pineda Osorio, Mateo</p>
<p>2014-05-01</p>
<p>Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT <span class="hlt">Solvers</span> and the use of computer algebra. Software such as Maple and Z3 was used in this case. The number of stationary states for each network was calculated. The network studied here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and the number of stationary states of the immune network. Results obtained show Z3's great potential as a SMT <span class="hlt">Solver</span>. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important in biology systems and are expected to help in the design of immune therapies. As a future line of research, more complex Boolean network representations of the immune system as well as the whole psychological apparatus are suggested.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.321..874F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.321..874F"><span>Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully <span class="hlt">Eulerian</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>Frei, S.; Richter, T.; Wick, T.</p>
<p>2016-09-01</p>
<p>In this work, we develop numerical schemes for mechano-chemical fluid-structure interactions with long-term effects. We investigate a model of a growing solid interacting with an incompressible fluid. A typical example for such a situation is the formation and growth of plaque in blood vessels. This application includes two particular difficulties: First, growth may lead to very large deformations, up to full clogging of the fluid domain. We derive a simplified set of equations including a fluid-structure interaction system coupled to an ODE model for plaque growth in Arbitrary Lagrangian <span class="hlt">Eulerian</span> (ALE) coordinates and in <span class="hlt">Eulerian</span> coordinates. The latter novel technique is capable of handling very large deformations up to contact. The second difficulty stems from the different time scales: while the dynamics of the fluid demand to resolve a scale of seconds, growth typically takes place in a range of months. We propose a temporal two-scale approach using local small-scale problems to compute an effective wall stress that will enter a long-scale problem. Our proposed techniques are substantiated with several numerical tests that include comparisons of the <span class="hlt">Eulerian</span> and ALE approaches as well as convergence studies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6806484','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6806484"><span>ICECO-CEL: a coupled <span class="hlt">Eulerian</span>-Lagrangian code for analyzing primary system response in fast reactors</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wang, C.Y.</p>
<p>1981-02-01</p>
<p>This report describes a coupled <span class="hlt">Eulerian</span>-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit <span class="hlt">Eulerian</span> method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the <span class="hlt">Eulerian</span> hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005JGRA..110.9310K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005JGRA..110.9310K"><span>E × B drift simulation in an <span class="hlt">Eulerian</span> ionospheric model using the total variation diminishing numerical scheme</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kulchitsky, Anton; Maurits, Sergei; Watkins, Brenton; McAllister, Jeffrey</p>
<p>2005-09-01</p>
<p>The University of Alaska Fairbanks <span class="hlt">Eulerian</span> Polar Parallel Ionospheric Model is a high-resolution model of the polar ionosphere that incorporates multiple ion species. This paper briefly describes this model and the implementation of the total variation diminishing (TVD) advection scheme. The model is based on an <span class="hlt">Eulerian</span> framework. It is demonstrated that the minimal numerical diffusion of the TVD advection scheme is critical for maintaining ion density gradients with high-resolution <span class="hlt">Eulerian</span> ionospheric models. The performance of this method is discussed and compared with an upwind numerical scheme. A sample model run for 24 October 2003 that simulates the formation of polar cap ionospheric structures is presented. The results using the TVD advection scheme are compared with the corner transport upwind advection scheme to demonstrate the advantage of the TVD method for simulating steep density gradients and small-scale density structures. These small-scale density features result from time-varying electric fields and are commonly observed using experimental techniques (e.g., incoherent scatter radar) in polar regions.</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/310920','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/310920"><span>User documentation for PVODE, an ODE <span class="hlt">solver</span> for parallel computers</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Hindmarsh, A.C., LLNL</p>
<p>1998-05-01</p>
<p>PVODE is a general purpose ordinary differential equation (ODE) <span class="hlt">solver</span> for stiff and nonstiff ODES It is based on CVODE [5] [6], which is written in ANSI- standard C PVODE uses MPI (Message-Passing Interface) [8] and a revised version of the vector module in CVODE to achieve parallelism and portability PVODE is intended for the SPMD (Single Program Multiple Data) environment with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation The idea is for each processor to solve a certain fixed subset of the ODES To better understand PVODE, we first need to understand CVODE and its historical background The ODE <span class="hlt">solver</span> CVODE, which was written by Cohen and Hindmarsh, combines features of two earlier Fortran codes, VODE [l] and VODPK [3] Those two codes were written by Brown, Byrne, and Hindmarsh. Both use variable-coefficient multi-step integration methods, and address both stiff and nonstiff systems (Stiffness is defined as the presence of one or more very small damping time constants ) VODE uses direct linear algebraic techniques to solve the underlying banded or dense linear systems of equations in conjunction with a modified Newton method in the stiff ODE case On the other hand, VODPK uses a preconditioned Krylov iterative method [2] to solve the underlying linear system User-supplied preconditioners directly address the dominant source of stiffness Consequently, CVODE implements both the direct and iterative methods Currently, with regard to the nonlinear and linear system solution, PVODE has three method options available. functional iteration, Newton iteration with a diagonal approximate Jacobian, and Newton iteration with the iterative method SPGMR (Scaled Preconditioned Generalized Minimal Residual method) Both CVODE and PVODE are written in such a way that other linear</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/786924','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/786924"><span>A fast <span class="hlt">solver</span> for systems of reaction-diffusion equations.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Garbey, M.; Kaper, H. G.; Romanyukha, N.</p>
<p>2001-04-20</p>
<p>In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, {partial_derivative}{sub t} u + a {center_dot} {del}u = {Delta}u + f(x,t,u), and x element of {Omega} contained in R{sup 3}, t > 0. Here, u is a vector-valued function, u triple bond u(x,t) element of R{sup m} is large, and the corresponding system of ODEs, {partial_derivative}{sub t}u = F(x,t,u), is stiff. Typical examples arise in air pollution studies, where a is the given wind field and the nonlinear function F models the atmospheric chemistry. The time integration of Eq. (1) is best handled by the method of characteristics. The problem is thus reduced to designing for the reaction-diffusion part a fast <span class="hlt">solver</span> that has good stability properties for the given time step and does not require the computation of the full Jacobi matrix. An operator-splitting technique, even a high-order one, combining a fast nonlinear ODE <span class="hlt">solver</span> with an efficient <span class="hlt">solver</span> for the diffusion operator is less effective when the reaction term is stiff. In fact, the classical Strang splitting method may underperform a first-order source splitting method. The algorithm we propose in this paper uses an a posteriori filtering technique to stabilize the computation of the diffusion term. The algorithm parallelizes well, because the solution of the large system of ODEs is done pointwise; however, the integration of the chemistry may lead to load-balancing problems. The Tchebycheff acceleration technique proposed in offers an alternative that complements the approach presented here. To facilitate the presentation, we limit the discussion to domains {Omega} that either admit a regular discretization grid or decompose into subdomains that admit regular discretization grids. We describe the algorithm for one-dimensional domains in Section 2 and for multidimensional domains in Section 3. Section 4 briefly outlines future work.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/555364','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/555364"><span>Evaluation of linear <span class="hlt">solvers</span> for oil reservoir simulation problems. Part 2: The fully implicit case</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Joubert, W.; Janardhan, R.</p>
<p>1997-12-01</p>
<p>A previous paper [Joubert/Biswas 1997] contained investigations of linear <span class="hlt">solver</span> performance for matrices arising from Amoco`s Falcon parallel oil reservoir simulation code using the IMPES formulation (implicit pressure, explicit saturation). In this companion paper, similar issues are explored for linear <span class="hlt">solvers</span> applied to matrices arising from more difficult fully implicit problems. The results of numerical experiments are given.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/145291','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/145291"><span>T2CG1, a package of preconditioned conjugate gradient <span class="hlt">solvers</span> for TOUGH2</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Moridis, G.; Pruess, K.; Antunez, E.</p>
<p>1994-03-01</p>
<p>Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient <span class="hlt">solvers</span>, has been added to TOUGH2 to complement its direct <span class="hlt">solver</span> and significantly increase the size of problems tractable on PCs. T2CG1 includes three different <span class="hlt">solvers</span>: a Bi-Conjugate Gradient (BCG) <span class="hlt">solver</span>, a Bi-Conjugate Gradient Squared (BCGS) <span class="hlt">solver</span>, and a Generalized Minimum Residual (GMRES) <span class="hlt">solver</span>. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct <span class="hlt">solver</span>, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS <span class="hlt">solver</span> is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUOSPO31C..08P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSPO31C..08P"><span>Horizontal distribution of near-inertial waves in the western Gulf of Mexico: <span class="hlt">Eulerian</span> vs Lagrangian.</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Pallas Sanz, E.; García-Carrillo, P.; Garcia Gomez, B. I.; Lilly, J. M.; Perez-Brunius, P.</p>
<p>2016-02-01</p>
<p>The time-average horizontal distribution of the near-inertial waves (NIWs) on the western Gulf of Mexico (GoM) is investigated using horizontal velocity data obtained from Lagrangian trajectories of 200 surface drifters drogued at 50m and deployed between September 2008 and September 2012. Preliminary results suggest maximum time-averaged near-inertial circle radius of 2.6km located in the southern Campeche bay near [22N,95W]; implying an inertial velocity of about 0.14m/s. Similar conclusions are delineated using horizontal velocity data obtained from 21 moorings deployed in the western GoM during the same time period. Maximum near-inertial kinetic energy and clockwise spectral energy is found in the mooring LNK3500 located at 21.850N and 94.028W. Maximum inertial circles measured with mooring data, however, are of about 1.6km leading to inertial currents of 0.087m/s, approximately a 40% smaller. This discrepancy seems to be due to the different depth level of the measurements and the bandwidth used to extract the near-inertial oscillations from the total flow. The time-average horizontal distributions of wind work computed from Lagrangian and <span class="hlt">Eulerian</span> data are compared and they are not consistent with the time-averaged NIW field. The differences are not well understood but we speculate they may be due to the different time scales of wind fluctuations in the northwestern GoM compared to those observed in the Bay of Campeche, together with the change of sign of the background vorticity in the region; being negative (anticyclonic) in the northern GoM and positive (cyclonic) in the Bay of Campeche.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ACP....17.2543E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ACP....17.2543E"><span>Limits on the ability of global <span class="hlt">Eulerian</span> models to resolve intercontinental transport of chemical plumes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Eastham, Sebastian D.; Jacob, Daniel J.</p>
<p>2017-02-01</p>
<p>Quasi-horizontal chemical plumes in the free troposphere can preserve their concentrated structure for over a week, enabling transport on intercontinental scales with important environmental impacts. Global <span class="hlt">Eulerian</span> chemical transport models (CTMs) fail to preserve these plumes due to fast numerical dissipation. We examine the causes of this dissipation and how it can be cured. Goddard Earth Observing System (GEOS-5) meteorological data at 0.25° × 0.3125° horizontal resolution and ˜ 0.5 km vertical resolution in the free troposphere are used to drive a worldwide ensemble of GEOS-Chem CTM plumes at resolutions from 0.25° × 0.3125° to 4° × 5°, in both 2-D (horizontal) and 3-D. Two-dimensional simulations enable examination of the sensitivity of numerical dissipation to grid resolution. We show that plume decay is driven by flow divergence and shear, filamenting the plumes until GEOS-Chem's high-order advection scheme cannot resolve gradients and fast numerical diffusion ensues. This divergence can be measured by the Lyapunov exponent (λ) of the flow. Dissipation of plumes is much faster at extratropical latitudes than in the tropics and this can be explained by stronger divergence. The plume decay constant (α) is linearly related to λ, and increasing grid resolution provides only modest benefits toward plume preservation. Three-dimensional simulations show near-complete dissipation of plumes within a few days, independent of horizontal grid resolution and even in the tropics. This is because vertical grid resolution is inadequate in all cases to properly resolve plume gradients. We suggest that finer vertical grid resolution in the free troposphere is essential for models to resolve intercontinental plumes, while current horizontal resolution in these models (˜ 1°) is sufficient.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JGRD..12114414V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JGRD..12114414V"><span>Multiple subtropical stratospheric intrusions over Reunion Island: Observational, Lagrangian, and <span class="hlt">Eulerian</span> numerical modeling approaches</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Vérèmes, H.; Cammas, J.-P.; Baray, J.-L.; Keckhut, P.; Barthe, C.; Posny, F.; Tulet, P.; Dionisi, D.; Bielli, S.</p>
<p>2016-12-01</p>
<p>Signatures of multiple stratospheric intrusions were observed on simultaneous and collocated ozone and water vapor profiles retrieved by lidars and radiosondes at the Maïdo Observatory, Reunion Island (21°S, 55°E, 2160 m above sea level), during MAïdo LIdar Calibration CAmpaign in April 2013. A singular structure of the ozone vertical profile with three peaks (in excess of 90 ppbv, at 8, 10, and 13 km altitude) embedded in a thick dry layer of air suggested stratospheric intrusions with multiple origins. The hypothesis is corroborated by a synoptic analysis based on re-analyses. European Centre for Medium-Range Weather Forecasts ERA-Interim temporal series associated with 5 days Lagrangian back trajectories initialized on each ozone peak allows to capture their stratospheric origin. The ozone peak at the lowest altitude is associated with an irreversible tropopause folding process along the polar jet stream during an extratropical cutoff low formation. Simultaneous lidar water vapor profiles of this peak show that the anticorrelation with ozone has been removed, due to mixing processes. Back trajectories indicate that the two other ozone peaks observed at higher altitudes are associated with the dynamics of the subtropical jet stream and the lower stratosphere. The observations confirm the recent stratospheric origins. The highest ozone peak is explained by the horizontal distribution of the intrusion. Use of a Lagrangian Reverse Domain Filling model and of the Meso-NH <span class="hlt">Eulerian</span> mesoscale model with a passive stratospheric tracer allow to further document the stratosphere-troposphere transport processes and to describe the detailed potential vorticity and ozone structures in which are embedded in the observed multiple stratospheric intrusions.</p>
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<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</span>-Lagrangian 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</span>-Lagrangian 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>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFMOS51C0993M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFMOS51C0993M"><span>Observed sea ice thickness changes in the Beaufort Gyre through synthesis of <span class="hlt">Eulerian</span> and Lagrangian data</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mahoney, A. R.; Hutchings, J. K.; Haas, C.; Eicken, H.</p>
<p>2014-12-01</p>
<p>In-situ and satellite observations have shown significant reductions in the extent and thickness of Arctic sea ice, which are considered by many to be evidence of major cryospheric changes amplifying global climate change. Multiyear (MY) sea ice thinning and retreat of the oldest and thickest ice, will accelerate further ice loss. MY sea ice also represents the greatest impediment to navigation in the Arctic and greatest hazard to marine infrastructure. Recirculation of sea ice within the Beaufort Gyre is critical to the replenishment of MY ice lost from the Arctic through either melt or export. Here we analyze thickness changes of sea ice as it drifts in different regions of the Gyre. Using a combined <span class="hlt">Eulerian</span>-Lagrangian approach we identify satellite-tracked buoys that made repeat overpasses within 30 km of four moored ice profiling sonars (IPSs), which comprise part of the Beaufort Gyre Exploration Program (BGEP). Using the IPS data, we derive ice draft distributions corresponding to each of these overpasses, which allows tracking of changes in the ice thickness in vicinity of each buoy. Changes in modal values of ice thickness during winter agree with simple models of thermodynamic growth.In the case of one buoy that made a total of four overpasses (see figure below), a dramatic shift in a secondary modal thickness during the summer of 2007 agrees well the magnitude of melt recorded by a nearby ice mass balance buoy (IMB). To extend the number of repeat passes, we generate pseudo-Langrangian ice drift tracks using daily gridded fields of satellite-derived ice velocity. This allows us to deploy "numerical buoys" every day anywhere in the Arctic. Using this approach we identify numerous cases where sea ice observed over one mooring persistently drifts over another. Such inter-mooring ice advection events allow us to examine how sea ice thickness distribution in the Beaufort Gyre is influenced by dynamic and thermodynamic processes processes.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFMEP11A3483S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFMEP11A3483S"><span><span class="hlt">Eulerian</span> and Lagrangian Measurements of Water Flow and Residence Time in a Fringing Coral Reef Embayment</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Storlazzi, C. D.; Messina, A. M.; Cheriton, O. M.; Biggs, T. W.</p>
<p>2014-12-01</p>
<p>Hydrodynamic processes on coral reefs are important for nutrient cycling, larval dispersal, temperature variability, and understanding the impacts of terrestrial sediment, nutrients, and contaminants from adjacent impaired watersheds on coral reef ecosystems. Our goal was to understand the spatial and temporal variability in flow velocities and the associated residence time of water in the fringing coral reef flat-lined embayment of Faga'alu, on the island of Tutuila in American Samoa. To accomplish this, data from three bottom-mounted acoustic current profilers and 102 individual Lagrangian ocean surface current drifter deployments (5 drifters x 21 deployments) were combined with meteorologic data and numerical wave model results. These data and model results, collected over nine days, made it possible to evaluate the relative contribution of tidal, wind, and wave forcing on the flow patterns. The high number of drifter deployments made it possible for the velocity data to be binned into 100 m x 100 m grid cells and the resulting residence times computed for the different sets of forcing conditions. Cumulative progressive vectors calculated from the acoustic current profilers closely matched the tracks from concurrently deployed surface current drifters, showing the applicability of this hybrid Lagrangian-<span class="hlt">Eulerian</span> measurement scheme to understand flow patterns in this geomorphically complex embayment. The bay-wide man current speeds (residence times) varied from 1-37 cm/s (2.78-0.08 hr), 1-36 cm/s (2.78-0.08 hr), and 5-64 cm/s (0.56-0.04 hr) under tidal, wind, and wave forcing, respectively; the highest speeds (shortest residence times) were measured on the outer reef flat closest to where waves were breaking on the reef crest and were slowest (longest) over the inner reef flat close to shore and deep in the embayment.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15015130','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15015130"><span>SIMULATION OF GEOMATERIALS USING CONTINUUM DAMAGE MODELS ON AN <span class="hlt">EULERIAN</span> GRID</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Lomov, I; Antoun, T H</p>
<p>2004-09-17</p>
<p>A new continuum model for directional tensile failure has been developed that can simulate weakening and void formation due to directional tensile failure. The model is developed within the context of a properly invariant nonlinear thermomechanical theory. A second order damage tensor is introduced which allows simulation of weakening to tension applied in one direction, without weakening to subsequent tension applied in perpendicular directions. This damage tensor can be advected using standard methods in computer codes. Porosity is used as an isotropic measure of volumetric void strain and its evolution is influenced by tensile failure. The rate of dissipation due to directional tensile failure takes a particularly simple form, which can be analyzed easily. Specifically, the model can be combined with general constitutive equations for porous compaction and dilation, as well as viscoplasticity. A robust non-iterative numerical scheme for integrating these evolution equations is proposed. This constitutive model has been implemented into an <span class="hlt">Eulerian</span> shock wave code with adaptive mesh refinement. A comparison of experimental results and computational simulations of spherical wave propagation in Danby marble was made. The experiment consisted of a 2-cm-diameter explosive charge detonated in the center of a cylindrical rock sample. Radial particle velocity histories were recorded at several concentric locations in the sample. An extensively damaged region near the charge cavity and two networks of cracks were evident in the specimen after the test. The first network consists of radial cracks emanating form the cavity and extending about halfway through the specimen. The second network consists of circumferential cracks occurring in a relatively narrow band that extends from the outer boundary of the radially cracked region toward the free surface. The calculations indicated load-induced anisotropy such as was observed in the experiment.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.109...33L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.109...33L"><span>A Newton-Krylov <span class="hlt">solver</span> for fast spin-up of online ocean tracers</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Lindsay, Keith</p>
<p>2017-01-01</p>
<p>We present a Newton-Krylov based <span class="hlt">solver</span> to efficiently spin up tracers in an online ocean model. We demonstrate that the <span class="hlt">solver</span> converges, that tracer simulations initialized with the solution from the <span class="hlt">solver</span> have small drift, and that the <span class="hlt">solver</span> takes orders of magnitude less computational time than the brute force spin-up approach. To demonstrate the application of the <span class="hlt">solver</span>, we use it to efficiently spin up the tracer ideal age with respect to the circulation from different time intervals in a long physics run. We then evaluate how the spun-up ideal age tracer depends on the duration of the physics run, i.e., on how equilibrated the circulation is.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910001939','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910001939"><span>High-performance equation <span class="hlt">solvers</span> and their impact on finite element analysis</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.</p>
<p>1990-01-01</p>
<p>The role of equation <span class="hlt">solvers</span> in modern structural analysis software is described. Direct and iterative equation <span class="hlt">solvers</span> which exploit vectorization on modern high-performance computer systems are described and compared. The direct <span class="hlt">solvers</span> are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative <span class="hlt">solvers</span> are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation <span class="hlt">solvers</span> in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.</p>
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<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011NIMPA.652..537M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011NIMPA.652..537M"><span>Experimental validation of a coupled neutron-photon inverse radiation transport <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mattingly, John; Mitchell, Dean J.; Harding, Lee T.</p>
<p>2011-10-01</p>
<p>Sandia National Laboratories has developed an inverse radiation transport <span class="hlt">solver</span> that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse <span class="hlt">solver</span> uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that <span class="hlt">solver</span>. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport <span class="hlt">solver</span> to evaluate the <span class="hlt">solver</span>'s ability to correctly infer the configuration of the source from its measured radiation signatures.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20767047','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20767047"><span>A finite element Poisson <span class="hlt">solver</span> for gyrokinetic particle simulations in a global field aligned mesh</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Nishimura, Y. . E-mail: nishimuy@uci.edu; Lin, Z.; Lewandowski, J.L.V.; Ethier, S.</p>
<p>2006-05-20</p>
<p>A new finite element Poisson <span class="hlt">solver</span> is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element <span class="hlt">solver</span> has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element <span class="hlt">solver</span> has been compared to the solution from the original GTC's iterative <span class="hlt">solver</span> which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element <span class="hlt">solver</span> enables the implementation of advanced kinetic electron models for global electromagnetic simulations.</p>
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<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1024472','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1024472"><span>Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport <span class="hlt">solver</span>.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.</p>
<p>2010-08-01</p>
<p>Sandia National Laboratories has developed an inverse radiation transport <span class="hlt">solver</span> that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse <span class="hlt">solver</span> uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that <span class="hlt">solver</span>. This paper describes a series of experiments conducted with a 4.5 kg sphere of {alpha}-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport <span class="hlt">solver</span> to evaluate the <span class="hlt">solver</span>'s ability to correctly infer the configuration of the source from its measured radiation signatures.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970015318','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970015318"><span>A High-Order Direct <span class="hlt">Solver</span> for Helmholtz Equations with Neumann Boundary Conditions</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Sun, Xian-He; Zhuang, Yu</p>
<p>1997-01-01</p>
<p>In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct <span class="hlt">solver</span>. Analytical and experimental results show this newly proposed <span class="hlt">solver</span> is comparable to the conventional second-order elliptic <span class="hlt">solver</span> when accuracy is not a primary concern, and is significantly faster than that of the conventional <span class="hlt">solver</span> if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz <span class="hlt">solver</span> is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23893938','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23893938"><span>Polyurethanes: versatile materials and sustainable problem <span class="hlt">solvers</span> for today's challenges.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Engels, Hans-Wilhelm; Pirkl, Hans-Georg; Albers, Reinhard; Albach, Rolf W; Krause, Jens; Hoffmann, Andreas; Casselmann, Holger; Dormish, Jeff</p>
<p>2013-09-02</p>
<p>Polyurethanes are the only class of polymers that display thermoplastic, elastomeric, and thermoset behavior depending on their chemical and morphological makeup. In addition to compact polyurethanes, foamed variations in particular are very widespread, and they achieve their targeted properties at very low weights. The simple production of sandwich structures and material composites in a single processing step is a key advantage of polyurethane technology. The requirement of energy and resource efficiency increasingly demands lightweight structures. Polyurethanes can serve this requirement by acting as matrix materials or as flexible adhesives for composites. Polyurethanes are indispensable when it comes to high-quality decorative coatings or maintaining the value of numerous objects. They are extremely adaptable and sustainable problem <span class="hlt">solvers</span> for today's challenges facing our society, all of which impose special demands on materials.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3816640','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3816640"><span>Progress in developing Poisson-Boltzmann equation <span class="hlt">solvers</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>Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil</p>
<p>2013-01-01</p>
<p>This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing <span class="hlt">solvers</span> to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20020039039&hterms=UPS&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DUPS','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20020039039&hterms=UPS&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DUPS"><span>Status Of The UPS Space-Marching Flow <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Lawerence, Scott L.; VanDalsem, William (Technical Monitor)</p>
<p>1995-01-01</p>
<p>The status of the three-dimensional parabolized Navier-Stokes <span class="hlt">solver</span> UPS is described. The UPS code, initiated at NASA Ames Research Center in 1986, continues to develop and evolve through application to supersonic and hypersonic flow fields. Hypersonic applications have motivated enhancement of the physical modeling capabilities of the code, specifically real gas modeling, boundary conditions, and turbulence and transition modeling. The UPS code has also been modified to enhance robustness and efficiency in order to be practically used in concert with an optimization code for supersonic transport design. These developments are briefly described along with some relevant results for generic test problems obtained during verification of the enhancements. Included developments and results have previously been published and widely disseminated domestically.</p>
</li>
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<ol class="result-class" start="421">
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20020051884&hterms=Ebm&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DEbm','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20020051884&hterms=Ebm&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DEbm"><span>Workload Characterization of CFD Applications Using Partial Differential Equation <span class="hlt">Solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)</p>
<p>1998-01-01</p>
<p>Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE <span class="hlt">solver</span> workloads and high performance computing platforms and is useful for tuning these applications.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20020051884&hterms=differential+equation&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Ddifferential%2Bequation','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20020051884&hterms=differential+equation&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Ddifferential%2Bequation"><span>Workload Characterization of CFD Applications Using Partial Differential Equation <span class="hlt">Solvers</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)</p>
<p>1998-01-01</p>
<p>Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE <span class="hlt">solver</span> workloads and high performance computing platforms and is useful for tuning these applications.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21159380','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21159380"><span>Performance evaluation of a parallel sparse lattice Boltzmann <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Axner, L. Bernsdorf, J. Zeiser, T. Lammers, P. Linxweiler, J. Hoekstra, A.G.</p>
<p>2008-05-01</p>
<p>We develop a performance prediction model for a parallelized sparse lattice Boltzmann <span class="hlt">solver</span> and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and/or complex topology such as porous media, fissured rocks and geometries from medical applications. The topology of the lattice nodes representing the fluid fraction of the computational domain is mapped on a graph. Graph decomposition is performed with both multilevel recursive-bisection and multilevel k-way schemes based on modified Kernighan-Lin and Fiduccia-Mattheyses partitioning algorithms. Performance results and optimization strategies are presented for a variety of platforms, showing a parallel efficiency of almost 80% for the largest problem size. A good agreement between the performance model and experimental results is demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21096818','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21096818"><span>GPU accelerated FDTD <span class="hlt">solver</span> and its application in MRI.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S</p>
<p>2010-01-01</p>
<p>The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD <span class="hlt">solver</span> and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24317341','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24317341"><span>Large-scale linear nonparallel support vector machine <span class="hlt">solver</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Tian, Yingjie; Ping, Yuan</p>
<p>2014-02-01</p>
<p>Twin support vector machines (TWSVMs), as the representative nonparallel hyperplane classifiers, have shown the effectiveness over standard SVMs from some aspects. However, they still have some serious defects restricting their further study and real applications: (1) They have to compute and store the inverse matrices before training, it is intractable for many applications where data appear with a huge number of instances as well as features; (2) TWSVMs lost the sparseness by using a quadratic loss function making the proximal hyperplane close enough to the class itself. This paper proposes a Sparse Linear Nonparallel Support Vector Machine, termed as L1-NPSVM, to deal with large-scale data based on an efficient <span class="hlt">solver</span>-dual coordinate descent (DCD) method. Both theoretical analysis and experiments indicate that our method is not only suitable for large scale problems, but also performs as good as TWSVMs and SVMs.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008AIPC.1048..715M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008AIPC.1048..715M"><span>A Coupled Finite Volume <span class="hlt">Solver</span> for Incompressible Flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Moukalled, F.; Darwish, M.</p>
<p>2008-09-01</p>
<p>This paper reports on a pressure-based coupled algorithm for the solution of laminar incompressible flow problems. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. The superiority of the coupled approach over the segregated approach is demonstrated by solving the lid-driven flow in a square cavity problem using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled <span class="hlt">solver</span> is grid independent. Moreover, recorded CPU time values reveal that the coupled approach substantially reduces the computational cost with the reduction rate for the problem solved increasing as the grid size increases and reaching a value as high as 115.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1251177','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1251177"><span>Extending the QUDA Library with the eigCG <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Strelchenko, Alexei; Stathopoulos, Andreas</p>
<p>2014-12-12</p>
<p>While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear <span class="hlt">solvers</span>, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24199185','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24199185"><span>Progress in developing Poisson-Boltzmann equation <span class="hlt">solvers</span>.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil</p>
<p>2013-03-01</p>
<p>This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing <span class="hlt">solvers</span> to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008JCoPh.227.4895A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JCoPh.227.4895A"><span>Performance evaluation of a parallel sparse lattice Boltzmann <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A. G.</p>
<p>2008-05-01</p>
<p>We develop a performance prediction model for a parallelized sparse lattice Boltzmann <span class="hlt">solver</span> and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and/or complex topology such as porous media, fissured rocks and geometries from medical applications. The topology of the lattice nodes representing the fluid fraction of the computational domain is mapped on a graph. Graph decomposition is performed with both multilevel recursive-bisection and multilevel k-way schemes based on modified Kernighan-Lin and Fiduccia-Mattheyses partitioning algorithms. Performance results and optimization strategies are presented for a variety of platforms, showing a parallel efficiency of almost 80% for the largest problem size. A good agreement between the performance model and experimental results is demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22340105','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22340105"><span>AN ADAPTIVE PARTICLE-MESH GRAVITY <span class="hlt">SOLVER</span> FOR ENZO</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Passy, Jean-Claude; Bryan, Greg L.</p>
<p>2014-11-01</p>
<p>We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid <span class="hlt">solver</span> available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940017111','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940017111"><span>Using parallel banded linear system <span class="hlt">solvers</span> in generalized eigenvalue problems</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Zhang, Hong; Moss, William F.</p>
<p>1993-01-01</p>
<p>Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded <span class="hlt">solvers</span> in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920004734','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920004734"><span>Blade design and analysis using a modified Euler <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Leonard, O.; Vandenbraembussche, R. A.</p>
<p>1991-01-01</p>
<p>An iterative method for blade design based on Euler <span class="hlt">solver</span> and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22570217','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22570217"><span>Accurate derivative evaluation for any Grad–Shafranov <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Ricketson, L.F.; Cerfon, A.J.; Rachh, M.; Freidberg, J.P.</p>
<p>2016-01-15</p>
<p>We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov <span class="hlt">solver</span> to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6514557','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6514557"><span>A fast <span class="hlt">solver</span> for systems of axisymmetric ring vortices</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Strickland, J.H.; Amos, D.E.</p>
<p>1990-09-01</p>
<p>A method which is capable of efficient calculation of the axisymmetric flow field produced by a large system of ring vortices is presented in this report. The system of ring vortices can, in turn, be used to model body surfaces and wakes in incompressible unsteady axisymmetric flow fields. This method takes advantage of source point and field point series expansions which enables one to make calculations for interactions between groups of vortices which are in well separated spatial domains rather than having to consider interactions between every pair of vortices. In this work, series expansions for the stream function of the ring vortex system are obtained. Such expansions explicitly contain the radial and axial velocity components. A Fortran computer code RSOLV has been written to execute the fast solution technique to calculate the stream function and the axial and radial velocity components at points in the flow field. Test cases have been run to optimize the code and to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the stream function and total velocity field are on the order of 5 {times} 10{sup {minus}5} and 3 {times} 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities up to about 1 {times} 10{sup {minus}5}. For 100 vortices in the field, there is virtually no CPU time savings with the fast <span class="hlt">solver</span>. For 10,000 vortices in the flow, the fast <span class="hlt">solver</span> obtains solutions in about 1% to 3% of the time required for the direct solution technique. Simulations of vortices with square and circular cores were run in order to obtain expressions for the self-induced velocities of such vortices. 8 refs., 26 figs.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AGUFMDI14A..02M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AGUFMDI14A..02M"><span>Tightly Coupled Geodynamic Systems: Software, Implicit <span class="hlt">Solvers</span> & Applications</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>May, D.; Le Pourhiet, L.; Brown, J.</p>
<p>2011-12-01</p>
<p>The generic term "multi-physics" is used to define physical processes which are described by a collection of partial differential equations, or "physics". Numerous processes in geodynamics fall into this category. For example, the evolution of viscous fluid flow and heat transport within the mantle (Stokes flow + energy conservation), the dynamics of melt migration (Stokes flow + Darcy flow + porosity evolution) and landscape evolution (Stokes + diffusion/advection over a surface). The development of software to numerically investigate processes that are described through the composition of different physics components are typically (a) designed for one particular set of physics and are never intended to be extended, or coupled to other processes (b) enforce that certain non-linearity's (or coupling) are explicitly removed from the system for reasons of computational efficiency, or due the lack of a robust non-linear <span class="hlt">solver</span> (e.g. most models in the mantle convection community). We describe a software infrastructure which enables us to easily introduce new physics with minimal code modifications; tightly couple all physics without introducing splitting errors; exploit modern linear/non-linear <span class="hlt">solvers</span> and permit the re-use of monolithic preconditioners for individual physics blocks (e.g. saddle point preconditioners for Stokes). Here we present a number of examples to illustrate the flexibility and importance of using this software infra-structure. Using the Stokes system as a prototype, we show results illustrating (i) visco-plastic shear banding experiments, (ii) how coupling Stokes flow with the evolution of the material coordinates can yield temporal stability in the free surface evolution and (iii) the discretisation error associated with decoupling Stokes equation from the heat transport equation in models of mantle convection with various rheologies.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/223829','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/223829"><span>Domain decomposed preconditioners with Krylov subspace methods as subdomain <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Pernice, M.</p>
<p>1994-12-31</p>
<p>Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact <span class="hlt">solvers</span> to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative <span class="hlt">solver</span> on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030066122','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030066122"><span>High Energy Boundary Conditions for a Cartesian Mesh Euler <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Pandya, Shishir; Murman, Scott; Aftosmis, Michael</p>
<p>2003-01-01</p>
<p>Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow <span class="hlt">solver</span> is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow <span class="hlt">solver</span> uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/10154027','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/10154027"><span>A three-dimensional fast <span class="hlt">solver</span> for arbitrary vorton distributions</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Strickland, J.H.; Baty, R.S.</p>
<p>1994-05-01</p>
<p>A method which is capable of an efficient calculation of the three-dimensional flow field produced by a large system of vortons (discretized regions of vorticity) is presented in this report. The system of vortons can, in turn, be used to model body surfaces, container boundaries, free-surfaces, plumes, jets, and wakes in unsteady three-dimensional flow fields. This method takes advantage of multipole and local series expansions which enables one to make calculations for interactions between groups of vortons which are in well-separated spatial domains rather than having to consider interactions between every pair of vortons. In this work, series expansions for the vector potential of the vorton system are obtained. From such expansions, the three components of velocity can be obtained explicitly. A Fortran computer code FAST3D has been written to calculate the vector potential and the velocity components at selected points in the flow field. In this code, the evaluation points do not have to coincide with the location of the vortons themselves. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the magnitudes of the vector potential and velocity fields are on the order of 10{sup {minus}4}and 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities of up to 10{sup {minus}5}. For less than 1,000 to 2,000 vortons in the field, there is virtually no CPU time savings with the fast <span class="hlt">solver</span>. For 100,000 vortons in the flow, the fast <span class="hlt">solver</span> obtains solutions in 1 % to 10% of the time required for the direct solution technique depending upon the configuration.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhDT.......169R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhDT.......169R"><span>A Fast Poisson <span class="hlt">Solver</span> with Periodic Boundary Conditions for GPU Clusters in Various Configurations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Rattermann, Dale Nicholas</p>
<p></p>
<p>Fast Poisson <span class="hlt">solvers</span> using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson <span class="hlt">solver</span> for periodic boundary conditions for use on a variety of GPU configurations. The <span class="hlt">solver</span> used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these <span class="hlt">solvers</span> are still computationally costly to employ, and the total <span class="hlt">solver</span> time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid <span class="hlt">solvers</span> by integrating a parallel FFT <span class="hlt">solver</span> on a uniform grid during a coarse level. This hybrid <span class="hlt">solver</span> could then be theoretically improved by replacing the highly-parallelizable FFT <span class="hlt">solver</span> with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT <span class="hlt">solver</span> (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson <span class="hlt">solver</span> that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007AGUFM.T11C0736F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007AGUFM.T11C0736F"><span>Development of three dimensional <span class="hlt">Eulerian</span> numerical procedure toward plate-mantle simulation: accuracy test by the fluid rope coiling</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Furuichi, M.; Kameyama, M.; Kageyama, A.</p>
<p>2007-12-01</p>
<p>Reproducing a realistic plate tectonics with mantle convection simulation is one of the greatest challenges in computational geophysics. We have developed a three dimensional <span class="hlt">Eulerian</span> numerical procedure toward plate-mantle simulation, which includes a finite deformation of the plate in the mantle convection. Our method, combined with CIP-CSLR (Constrained Interpolation Profile method-Conservative Semi-Lagrangian advection scheme with Rational function) and ACuTE method, enables us to solve advection and force balance equations even with a large and sharp viscosity jump, which marks the interface between the plates and surrounding upper mantle materials. One of the typical phenomena represented by our method is a fluid rope coiling event, where a stream of viscous fluid is poured onto the bottom plane from a certain height. This coiling motion is due to delicate balances between bending, twisting and stretching motions of fluid rope. In the framework of the <span class="hlt">Eulerian</span> scheme, the fluid rope and surrounding air are treated as a viscosity profile which differs by several orders of magnitude. Our method solves the complex force balances of the fluid rope and air, by a multigrid iteration technique of ACuTE algorithm. In addition, the CIP-CSLR advection scheme allows us to obtain a deforming shape of the fluid rope, as a low diffusive solution in the <span class="hlt">Eulerian</span> frame of reference. In this presentation, we will show the simulation result of the fluid rope coiling as an accuracy test for our simulation scheme, by comparing with the simplified numerical solution for thin viscous jet.</p>
</li>
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<ol class="result-class" start="441">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/440725','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/440725"><span>The impact of improved sparse linear <span class="hlt">solvers</span> on industrial engineering applications</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu</p>
<p>1996-12-31</p>
<p>There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear <span class="hlt">solver</span> are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved <span class="hlt">solver</span> often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct <span class="hlt">solvers</span> in several key industrial CFD and structures codes, and show the impact that recent advances in linear <span class="hlt">solvers</span> have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these <span class="hlt">solvers</span>. Finally, we discuss future requirements for sparse linear <span class="hlt">solvers</span> on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear <span class="hlt">solver</span> capabilities.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CoPhC.188..177M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CoPhC.188..177M"><span>Oasis: A high-level/high-performance open source Navier-Stokes <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mortensen, Mikael; Valen-Sendstad, Kristian</p>
<p>2015-03-01</p>
<p>Oasis is a high-level/high-performance finite element Navier-Stokes <span class="hlt">solver</span> written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The <span class="hlt">solver</span> is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the <span class="hlt">solver</span>. A version of the <span class="hlt">solver</span>, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative <span class="hlt">solvers</span> provided by the linear algebra backend, which is arguably the best performance any similar implicit <span class="hlt">solver</span> using PETSc may hope for. Higher order accuracy is also demonstrated and new <span class="hlt">solvers</span> may be easily added within the same framework.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20588502','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20588502"><span>Acceleration of FDTD mode <span class="hlt">solver</span> by high-performance computing techniques.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Han, Lin; Xi, Yanping; Huang, Wei-Ping</p>
<p>2010-06-21</p>
<p>A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode <span class="hlt">solver</span> is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode <span class="hlt">solver</span>. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode <span class="hlt">solver</span> is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode <span class="hlt">solver</span> with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode <span class="hlt">solver</span> running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode <span class="hlt">solver</span> and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode <span class="hlt">solvers</span> are no longer applicable due to memory limitation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/967024','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/967024"><span>A parallel 3D poisson <span class="hlt">solver</span> for space charge simulation in cylindrical coordinates.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Xu, J.; Ostroumov, P. N.; Nolen, J.; Physics</p>
<p>2008-02-01</p>
<p>This paper presents the development of a parallel three-dimensional Poisson <span class="hlt">solver</span> in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson <span class="hlt">solver</span> uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the (r,{theta}) plane. This <span class="hlt">solver</span> was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel <span class="hlt">solver</span> and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson <span class="hlt">solver</span> in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson <span class="hlt">solver</span> in Cartesian coordinate system is not accurate because different boundary condition used. While using the new <span class="hlt">solver</span>, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JQSRT.176...50B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JQSRT.176...50B"><span>GORRAM: Introducing accurate operational-speed radiative transfer Monte Carlo <span class="hlt">solvers</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Buras-Schnell, Robert; Schnell, Franziska; Buras, Allan</p>
<p>2016-06-01</p>
<p>We present a new approach for solving the radiative transfer equation in horizontally homogeneous atmospheres. The motivation was to develop a fast yet accurate radiative transfer <span class="hlt">solver</span> to be used in operational retrieval algorithms for next generation meteorological satellites. The core component is the program GORRAM (Generator Of Really Rapid Accurate Monte-Carlo) which generates <span class="hlt">solvers</span> individually optimized for the intended task. These <span class="hlt">solvers</span> consist of a Monte Carlo model capable of path recycling and a representative set of photon paths. Latter is generated using the simulated annealing technique. GORRAM automatically takes advantage of limitations on the variability of the atmosphere. Due to this optimization the number of photon paths necessary for accurate results can be reduced by several orders of magnitude. For the shown example of a forward model intended for an aerosol satellite retrieval, comparison with an exact yet slow <span class="hlt">solver</span> shows that a precision of better than 1% can be achieved with only 36 photons. The computational time is at least an order of magnitude faster than any other type of radiative transfer <span class="hlt">solver</span>. Merely the lookup table approach often used in satellite retrieval is faster, but on the other hand suffers from limited accuracy. This makes GORRAM-generated <span class="hlt">solvers</span> an eligible candidate as forward model in operational-speed retrieval algorithms and data assimilation applications. GORRAM also has the potential to create fast <span class="hlt">solvers</span> of other integrable equations.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CoPhC.185.2730S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CoPhC.185.2730S"><span>Implementation of density-based <span class="hlt">solver</span> for all speeds in the framework of OpenFOAM</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Shen, Chun; Sun, Fengxian; Xia, Xinlin</p>
<p>2014-10-01</p>
<p>In the framework of open source CFD code OpenFOAM, a density-based <span class="hlt">solver</span> for all speeds flow field is developed. In this <span class="hlt">solver</span> the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) <span class="hlt">solver</span> for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this <span class="hlt">solver</span> possesses high accuracy and the <span class="hlt">solver</span> developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned <span class="hlt">solvers</span> with and without the dual time scheme. Nonetheless, the <span class="hlt">solvers</span> described in this paper reproduce the main features of this flow, including the evolution of the initial transient.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003PhDT........53M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003PhDT........53M"><span>Extending the functionalities of Cartesian grid <span class="hlt">solvers</span>: Viscous effects modeling and MPI parallelization</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Marshall, David D.</p>
<p></p>
<p>With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid <span class="hlt">solver</span> functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids <span class="hlt">solvers</span> for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian <span class="hlt">solvers</span>. This research presents advances in two areas of interest in Cartesian grid <span class="hlt">solvers</span>, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid <span class="hlt">solver</span>, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian <span class="hlt">solvers</span> on distributed memory parallel environments. This work is performed on an existing Cartesian grid <span class="hlt">solver</span>, CART3D, with modifications to its parallelization methodology.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19760056903&hterms=blast&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dblast','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19760056903&hterms=blast&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dblast"><span>Exit of a blast wave from a conical nozzle. [flow field calculations by <span class="hlt">Eulerian</span> computer code DORF</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Kim, K.; Johnson, W. E.</p>
<p>1976-01-01</p>
<p>The <span class="hlt">Eulerian</span> computer code DORF was used in the analysis of a two-dimensional, unsteady flow field resulting from semi-confined explosions for propulsive applications. Initially, the ambient gas inside the conical shaped nozzle is set into motion due to the expansion of the explosion product gas, forming a shock wave. When this shock front exits the nozzle, it takes almost a spherical form while a complex interaction between the nozzle and compression and rarefaction waves takes place behind the shock. The results show an excellent agreement with experimental data.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009MSSP...23.1634O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009MSSP...23.1634O"><span>Online condition monitoring of axial-flow turbomachinery blades using rotor-axial <span class="hlt">Eulerian</span> laser Doppler vibrometry</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Oberholster, A. J.; Heyns, P. S.</p>
<p>2009-07-01</p>
<p>The ability to monitor the vibration of blades online is of great importance to the structural health of turbomachinery. This paper focuses on the fixed reference frame or <span class="hlt">Eulerian</span> implementation of laser Doppler vibrometry to perform this function. The way in which this measurement technique works is studied analytically and then a numerical simulation approach is proposed. Through experimental testing and finite element modeling, it is shown that this measurement approach is in principle viable for online blade condition monitoring when phase angles at reference frequencies are monitored, using non-harmonic Fourier analysis.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010EGUGA..1210300M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010EGUGA..1210300M"><span>Long-term simulations of European air quality using the Danish <span class="hlt">Eulerian</span> Hemispheric Model</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Mantzius Hansen, Kaj</p>
<p>2010-05-01</p>
<p>Effects of air quality on nature and human health have been on the agenda for several decades. Air quality monitoring sites have been established throughout Europe and several of the sites have been operating for more than two decades. Long term evaluation of air quality from specific monitoring sites or smaller regions has been performed in several studies. For studies of larger regions, models with comprehensive chemistry schemes have been developed and applied to study atmospheric transport, transformation and deposition of various air pollutants. With faster and faster computers, the development over the years has been towards more complex chemistry schemes and higher spatial and temporal resolution of model output. This often limits the studied period to single or a few years. We will present a study of European air quality covering 18 years, simulated with a state-of-the-art atmospheric chemistry transport model. The Danish <span class="hlt">Eulerian</span> Hemispheric Model (DEHM) covers the majority of the Northern Hemisphere with a horizontal grid resolution of 150 km X 150 km. DEHM has 29 vertical layers in terrain-following sigma-coordinates extending up to a height of 100 hPa. Two-way nesting options with a nesting factor of three can be applied with higher resolution over a limited area of the model. At present the model can be run without nests or with one, two or three nests, each with grid resolutions of 50 km X 50 km, 16.7 km X 16.7 km, and 5.6 km X 5.6 km, respectively. The model includes a comprehensive chemistry scheme with more than 100 reactions and 67 atmospheric constituents, of which 4 relate to primary particulates (PM2.5, PM10, TSP and sea salt); other species are SOx, NOx, NHx, VOCs, and secondary inorganic particulates. DEHM is driven by meteorological data from the numerical weather prediction model MM5v3. One long-term simulation was performed with DEHM covering the period from 1989 to 2006. The predicted concentrations were evaluated against measurements</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.292...56B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.292...56B"><span>Direct Arbitrary-Lagrangian-<span class="hlt">Eulerian</span> ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws</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; Loubère, Raphaël; Dumbser, Michael</p>
<p>2015-07-01</p>
<p>In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-<span class="hlt">Eulerian</span> (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multi-dimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/876345','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/876345"><span>Robust large-scale parallel nonlinear <span class="hlt">solvers</span> for simulations.</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson</p>
<p>2005-11-01</p>
<p>This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based <span class="hlt">solvers</span> (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear <span class="hlt">solver</span>, which makes it simple to write</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/72891','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/72891"><span>A new set of direct and iterative <span class="hlt">solvers</span> for the TOUGH2 family of codes</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Moridis, G.J.</p>
<p>1995-04-01</p>
<p>Two new <span class="hlt">solvers</span> are discussed. LUBAND, the first routine is a direct <span class="hlt">solver</span> for banded systems and is based on a LU decomposition with partial pivoting and row interchange. BCGSTB, the second routine, is a Preconditioned Conjugate Gradient (PCG) <span class="hlt">solver</span> with improved speed and convergence characteristics. Bandwidth minimization and gridblock ordering schemes are also introduced into TOUGH2 to improve speed and accuracy. TOUGH2 simulates fluid and heat flows in permeable media and is used for the evaluation of WIPP and TEVES (Thermal Enhanced Vapor Extraction System) that will be used to extract solvents from the Chemical Waste Landfill at Sandia National Laboratories.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1376302','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1376302"><span>Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Zhang, Bo; Lu, Benzhuo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai; McCammon, J. Andrew</p>
<p>2013-01-01</p>
<p>This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) <span class="hlt">solver</span>. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB <span class="hlt">solver</span> to large-scale long-time molecular dynamics simulations. Lastly, the potential of the <span class="hlt">solver</span> is demonstrated with preliminary numerical results.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930040952&hterms=automobile&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dautomobile','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930040952&hterms=automobile&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dautomobile"><span>Application of an unstructured grid flow <span class="hlt">solver</span> to planes, trains and automobiles</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram</p>
<p>1993-01-01</p>
<p>Rampant, an unstructured flow <span class="hlt">solver</span> developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow <span class="hlt">solver</span> capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow <span class="hlt">solver</span> and presents flow field solutions about a plane, train, and automobile.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992pcfd.conf....1A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992pcfd.conf....1A"><span>A parallel explicit <span class="hlt">solver</span> for unsteady 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>Akay, H. U.; Ecer, A.; Kemle, W. B.</p>
<p></p>
<p>A previously developed sequential <span class="hlt">solver</span> for unsteady compressible Euler equations is implemented on INTEL iPSC/860 parallel computer. An explicit finite element formulation using Clebsch variable form of the Euler equations is presented. A streamwise upwinding technique is employed for introducing artificial diffusion to convective terms. Applications are presented for the solution of transonic potential equations. For parallel implementation of the method, the three-dimensional solution domain is partitioned into a number of subdomains requiring each subdomain to reside on a separate processor for parallel computations. The exchange of information between the solution blocks is due to overlapped boundaries at the block interfaces. The same algorithm can also be applied to steady flows by continuing the time integrations until the steady flow conditions are reached. It has been observed that the convergence rate to steady state is affected little with increased number of solution blocks. Efficiency curves for nearly-balanced loads are obtained for different partitioning algorithms. The partition efficiency is shown to affect the central processing unit (CPU) efficiency of the algorithm directly.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MNRAS.462.4517K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MNRAS.462.4517K"><span>Approximate Riemann <span class="hlt">solvers</span> for the cosmic ray magnetohydrodynamical equations</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Kudoh, Yuki; Hanawa, Tomoyuki</p>
<p>2016-11-01</p>
<p>We analyse the cosmic ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR `number' conservation, where the CR number density is defined as the three-fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann <span class="hlt">solver</span> is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second-order accuracy in space and time. Our numerical examples include an expansion of high-pressure sphere in a magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005PhDT........23H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005PhDT........23H"><span>An implicit-explicit flow <span class="hlt">solver</span> for complex unsteady flows</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Hsu, John Ming-Jey</p>
<p>2005-12-01</p>
<p>Current calculations of complex unsteady flows are prohibitively expensive for use in real engineering applications. Typical flow <span class="hlt">solvers</span> for unsteady integration employ a fully implicit time stepping scheme, in which the equations are solved by an inner iteration. In order to achieve convergence within each physical time step, a substantial number of pseudo-time steps (typically between 30--100, depending on the case) are required. Another unfavorable characteristic of the dual time stepping method is that there are no available error estimates for time accuracy available unless the inner iterations are fully converged, although numerical experiments have demonstrated second order accuracy in time. The approach in this thesis is to construct hybrid type schemes by combining implicit and explicit schemes in a manner that guarantees second order accuracy in time. An initial time accurate ADI step is introduced, followed by a small number of cycles of the dual-time stepping scheme augmented by multigrid. The formal second order accuracy in time should be retained without the need for large numbers of inner iterations. The number of inner iterations required for convergence can thus be reduced while maintaining the same overall error levels. To investigate the effectiveness of the proposed scheme, several pitching airfoil test cases were examined, offering a close look at possible reductions in computational cost by adopting the present approach.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhPl...22c2511H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhPl...22c2511H"><span>Verification of continuum drift kinetic equation <span class="hlt">solvers</span> in NIMROD</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Held, E. D.; Kruger, S. E.; Ji, J.-Y.; Belli, E. A.; Lyons, B. C.</p>
<p>2015-03-01</p>
<p>Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra <span class="hlt">solver</span> provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22408212','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22408212"><span>Verification of continuum drift kinetic equation <span class="hlt">solvers</span> in NIMROD</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Held, E. D.; Ji, J.-Y.; Kruger, S. E.; Belli, E. A.; Lyons, B. C.</p>
<p>2015-03-15</p>
<p>Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra <span class="hlt">solver</span> provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.</p>
</li>
</ol>
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<ol class="result-class" start="461">
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/219617','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/219617"><span>An optimal iterative <span class="hlt">solver</span> for the Stokes problem</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Wathen, A.; Silvester, D.</p>
<p>1994-12-31</p>
<p>Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal <span class="hlt">solver</span> for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910012482','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910012482"><span>A multiblock multigrid three-dimensional Euler equation <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.</p>
<p>1990-01-01</p>
<p>Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit <span class="hlt">solvers</span> (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950022340','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950022340"><span>Cooperative solutions coupling a geometry engine and adaptive <span class="hlt">solver</span> codes</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Dickens, Thomas P.</p>
<p>1995-01-01</p>
<p>Follow-on work has progressed in using Aero Grid and Paneling System (AGPS), a geometry and visualization system, as a dynamic real time geometry monitor, manipulator, and interrogator for other codes. In particular, AGPS has been successfully coupled with adaptive flow <span class="hlt">solvers</span> which iterate, refining the grid in areas of interest, and continuing on to a solution. With the coupling to the geometry engine, the new grids represent the actual geometry much more accurately since they are derived directly from the geometry and do not use refits to the first-cut grids. Additional work has been done with design runs where the geometric shape is modified to achieve a desired result. Various constraints are used to point the solution in a reasonable direction which also more closely satisfies the desired results. Concepts and techniques are presented, as well as examples of sample case studies. Issues such as distributed operation of the cooperative codes versus running all codes locally and pre-calculation for performance are discussed. Future directions are considered which will build on these techniques in light of changing computer environments.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890017179','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890017179"><span>Incremental planning to control a blackboard-based problem <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Durfee, E. H.; Lesser, V. R.</p>
<p>1987-01-01</p>
<p>To control problem solving activity, a planner must resolve uncertainty about which specific long-term goals (solutions) to pursue and about which sequences of actions will best achieve those goals. A planner is described that abstracts the problem solving state to recognize possible competing and compatible solutions and to roughly predict the importance and expense of developing these solutions. With this information, the planner plans sequences of problem solving activities that most efficiently resolve its uncertainty about which of the possible solutions to work toward. The planner only details actions for the near future because the results of these actions will influence how (and whether) a plan should be pursued. As problem solving proceeds, the planner adds new details to the plan incrementally, and monitors and repairs the plan to insure it achieves its goals whenever possible. Through experiments, researchers illustrate how these new mechanisms significantly improve problem solving decisions and reduce overall computation. They briefly discuss current research directions, including how these mechanisms can improve a problem <span class="hlt">solver</span>'s real-time response and can enhance cooperation in a distributed problem solving network.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22493686','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22493686"><span>A generalized Poisson <span class="hlt">solver</span> for first-principles device simulations</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost; Brück, Sascha; Luisier, Mathieu</p>
<p>2016-01-28</p>
<p>Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The <span class="hlt">solver</span> can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/433353','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/433353"><span>Parallelizable approximate <span class="hlt">solvers</span> for recursions arising in preconditioning</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Shapira, Y.</p>
<p>1996-12-31</p>
<p>For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate <span class="hlt">solver</span> is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27587603','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27587603"><span>Solute <span class="hlt">solver</span> 'what if' module for modeling urea kinetics.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Daugirdas, John T</p>
<p>2016-11-01</p>
<p>The publicly available Solute <span class="hlt">Solver</span> module allows calculation of a variety of two-pool urea kinetic measures of dialysis adequacy using pre- and postdialysis plasma urea and estimated dialyzer clearance or estimated urea distribution volumes as inputs. However, the existing program does not have a 'what if' module, which would estimate the plasma urea values as well as commonly used measures of hemodialysis adequacy for a patient with a given urea distribution volume and urea nitrogen generation rate dialyzed according to a particular dialysis schedule. Conventional variable extracellular volume 2-pool urea kinetic equations were used. A javascript-HTML Web form was created that can be used on any personal computer equipped with internet browsing software, to compute commonly used Kt/V-based measures of hemodialysis adequacy for patients with differing amounts of residual kidney function and following a variety of treatment schedules. The completed Web form calculator may be particularly useful in computing equivalent continuous clearances for incremental hemodialysis strategies. © The Author 2016. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EUCAS...9..387E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EUCAS...9..387E"><span>Development and acceleration of unstructured mesh-based cfd <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Emelyanov, V.; Karpenko, A.; Volkov, K.</p>
<p>2017-06-01</p>
<p>The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD <span class="hlt">solver</span> works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040001429','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040001429"><span>Algorithmic Enhancements to the VULCAN Navier-Stokes <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Litton, D. K.; Edwards, J. R.; White, J. A.</p>
<p>2003-01-01</p>
<p>VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes <span class="hlt">solver</span> implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014snam.conf04105M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014snam.conf04105M"><span>Shared Memory Parallelism for 3D Cartesian Discrete Ordinates <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre</p>
<p>2014-06-01</p>
<p>This paper describes the design and the performance of DOMINO, a 3D Cartesian SN <span class="hlt">solver</span> that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPlPh..83c7002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPlPh..83c7002C"><span>A `metric' semi-Lagrangian Vlasov-Poisson <span class="hlt">solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Colombi, Stéphane; Alard, Christophe</p>
<p>2017-06-01</p>
<p>We propose a new semi-Lagrangian Vlasov-Poisson <span class="hlt">solver</span>. It employs metric elements to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position of any test particle , by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time and position by proper interpolation of initial conditions, following Liouville theorem. When distortion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third-order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four- or six-dimensional phase space. It can also be trivially generalised to plasmas.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1995ApJS...98..355X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1995ApJS...98..355X"><span>A New Parallel N-Body Gravity <span class="hlt">Solver</span>: TPM</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Xu, Guohong</p>
<p>1995-05-01</p>
<p>We have developed a gravity <span class="hlt">solver</span> based on combining the particle-mesh (PM) method and TREE methods. It is designed for and has been implemented on parallel computer architectures. The new code can deal with tens of millions of particles on current computers, with the calculation done on a parallel super- computer or a group of workstations. Typically, the spatial resolution is enhanced by more than a factor of 20 over the pure PM code with mass resolution retained at nearly the PM level. This code runs much faster than a pure TREE code with the same number of particles and maintains almost the same resolution in high-density regions. Multiple time step integration has also been implemented with the code, with second-order time accuracy. The performance of the code has been checked in several kinds of parallel computer configurations, including IBM SP1, SGI Challenge, and a group of workstations, with the speedup of the parallel code on a 32 processor IBM SP2 supercomputer nearly linear (efficiency ≍ 80%) in the number of processors. The computation/communication ratio is also very high (˜50), which means the code spends 95% of its CPU time in computation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015A%26A...576A..50M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015A%26A...576A..50M"><span>New numerical <span class="hlt">solver</span> for flows at various Mach numbers</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Miczek, F.; Röpke, F. K.; Edelmann, P. V. F.</p>
<p>2015-04-01</p>
<p>Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims: While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods: Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe <span class="hlt">solver</span>. Results: Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions: Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110016396','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110016396"><span>Two-Dimensional Ffowcs Williams/Hawkings Equation <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Lockard, David P.</p>
<p>2005-01-01</p>
<p>FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings <span class="hlt">solver</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1261494','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1261494"><span>Towards Batched Linear <span class="hlt">Solvers</span> on Accelerated Hardware Platforms</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Haidar, Azzam; Dong, Tingzing Tim; Tomov, Stanimire; Dongarra, Jack J</p>
<p>2015-01-01</p>
<p>As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance <span class="hlt">solvers</span>, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs for every floating-point operation. In this paper, we describe the development of the main one-sided factorizations: LU, QR, and Cholesky; that are needed for a set of small dense matrices to work in parallel. We refer to such algorithms as batched factorizations. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-contained execution. Note that this is similar in functionality to the LAPACK and the hybrid MAGMA algorithms for large-matrix factorizations. But it is different from a straightforward approach, whereby each of GPU's symmetric multiprocessors factorizes a single problem at a time. We illustrate how our performance analysis together with the profiling and tracing tools guided the development of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library on a two-sockets, Intel Sandy Bridge server. Compared to a batched LU factorization featured in the NVIDIA's CUBLAS library for GPUs, we achieves up to 2.5-fold speedup on the K40 GPU.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDA12001T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDA12001T"><span>Intrusive Method for Uncertainty Quantification in a Multiphase Flow <span class="hlt">Solver</span></span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Turnquist, Brian; Owkes, Mark</p>
<p>2016-11-01</p>
<p>Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow <span class="hlt">solver</span> is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120013786','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120013786"><span>Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar PDF 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>2012-01-01</p>
<p>This paper presents the numerical simulations of the 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 probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JOM....68h2160L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JOM....68h2160L"><span>Investigation of Bubble-Slag Layer Behaviors with Hybrid <span class="hlt">Eulerian</span>-Lagrangian Modeling and Large Eddy Simulation</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Li, Linmin; Li, Baokuan</p>
<p>2016-08-01</p>
<p>In ladle metallurgy, bubble-liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The <span class="hlt">Eulerian</span> volume of fluid model is adopted to track the liquid steel-slag-air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O'Rourke's algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air-liquid interface. The turbulent liquid flow that is induced by bubble-liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open-close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid <span class="hlt">Eulerian</span>-Lagrangian-LES model provides a valid modeling framework to predict the unsteady gas bubble-slag layer coupled behaviors.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JCoPh.229.5518B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JCoPh.229.5518B"><span>An <span class="hlt">Eulerian</span> method for multi-component problems in non-linear elasticity with sliding interfaces</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Barton, Philip T.; Drikakis, Dimitris</p>
<p>2010-08-01</p>
<p>This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann <span class="hlt">solver</span> and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GMD.....9..749B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GMD.....9..749B"><span>Adjoint of the global <span class="hlt">Eulerian</span>-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation</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 A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander</p>
<p>2016-02-01</p>
<p>We present the development of the Adjoint of the Global <span class="hlt">Eulerian</span>-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an <span class="hlt">Eulerian</span> three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the <span class="hlt">Eulerian</span> model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed <span class="hlt">Eulerian</span> adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the <span class="hlt">Eulerian</span> model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an <span class="hlt">Eulerian</span> discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated</p>
</li>
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<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1208899','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1208899"><span>A 3D approximate maximum likelihood <span class="hlt">solver</span> for localization of fish implanted with acoustic transmitters</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; Sun, Yannan; USA, Richland Washington; Martinez, Jayson J.; USA, Richland Washington; Fu, Tao; USA, Richland Washington; McMichael, Geoffrey A.; USA, Richland Washington; Carlson, Thomas J.; USA, Richland Washington</p>
<p>2014-11-27</p>
<p>Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood <span class="hlt">solver</span> was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1208899-approximate-maximum-likelihood-solver-localization-fish-implanted-acoustic-transmitters','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1208899-approximate-maximum-likelihood-solver-localization-fish-implanted-acoustic-transmitters"><span>A 3D approximate maximum likelihood <span class="hlt">solver</span> for localization of fish implanted with acoustic transmitters</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; ...</p>
<p>2014-11-27</p>
<p>Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood <span class="hlt">solver</span> was developedmore » using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1237365','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1237365"><span>Fault tolerance in an inner-outer <span class="hlt">solver</span>: A GVR-enabled case study</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita</p>
<p>2015-04-18</p>
<p>Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear <span class="hlt">solvers</span>, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear <span class="hlt">solver</span> can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer <span class="hlt">solvers</span> appropriate across a range of error rates. We implement them, extending Trilinos’ <span class="hlt">solver</span> library with the Global View Resilience (GVR) programming model, which provides multi-stream snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1237365-fault-tolerance-inner-outer-solver-gvr-enabled-case-study','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1237365-fault-tolerance-inner-outer-solver-gvr-enabled-case-study"><span>Fault tolerance in an inner-outer <span class="hlt">solver</span>: A GVR-enabled case study</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p>
<p>Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita</p>
<p>2015-04-18</p>
<p>Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear <span class="hlt">solvers</span>, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear <span class="hlt">solver</span> can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer <span class="hlt">solvers</span> appropriate across a range of error rates. We implement them, extending Trilinos’ <span class="hlt">solver</span> library with the Global View Resilience (GVR) programming model, which provides multi-streammore » snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.« less</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000108734','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000108734"><span>User's Manual for PCSMS (Parallel Complex Sparse Matrix <span class="hlt">Solver</span>). Version 1.</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Reddy, C. J.</p>
<p>2000-01-01</p>
<p>PCSMS (Parallel Complex Sparse Matrix <span class="hlt">Solver</span>) is a computer code written to make use of the existing real sparse direct <span class="hlt">solvers</span> to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix <span class="hlt">solvers</span> to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix <span class="hlt">solver</span>. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002TJSAI..17....1Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002TJSAI..17....1Y"><span>Cognitive Distance Learning Problem <span class="hlt">Solver</span> Reduces Search Cost through Learning Processes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Yamakawa, Hiroshi; Miyamoto, Yuji; Baba, Takayuki; Okada, Hiroyuki</p>
<p></p>
<p>Our proposed cognitive distance learning problem <span class="hlt">solver</span> generates sequence of actions from initial state to goal states in problem state space. This problem <span class="hlt">solver</span> learns cognitive distance (path cost) of arbitrary combination of two states. Action generation at each state is selection of next state that has minimum cognitive distance to the goal, like Q-learning agent. In this paper, first, we show that our proposed method reduces search cost than conventional search method by analytical simulation in spherical state space. Second, we show that an average search cost is more reduced more the prior learning term is long and our problem <span class="hlt">solver</span> is familiar to the environment, by a computer simulation in a tile world state space. Third, we showed that proposed problem <span class="hlt">solver</span> is superior to the reinforcement learning techniques when goal is changed by a computer simulation. Forth, we found that our simulation result consist with psychological experimental results.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.317..223D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.317..223D"><span>A novel high-order, entropy stable, 3D AMR MHD <span class="hlt">solver</span> with guaranteed positive pressure</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie</p>
<p>2016-07-01</p>
<p>We describe a high-order numerical magnetohydrodynamics (MHD) <span class="hlt">solver</span> built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the <span class="hlt">solver</span> conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The <span class="hlt">solver</span> described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new <span class="hlt">solver</span> into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu).</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25427517','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25427517"><span>A 3D approximate maximum likelihood <span class="hlt">solver</span> for localization of fish implanted with acoustic transmitters.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J</p>
<p>2014-11-27</p>
<p>Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood <span class="hlt">solver</span> was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014NatSR...4E7215L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014NatSR...4E7215L"><span>A 3D approximate maximum likelihood <span class="hlt">solver</span> for localization of fish implanted with acoustic transmitters</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.</p>
<p>2014-11-01</p>
<p>Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood <span class="hlt">solver</span> was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4245526','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4245526"><span>A 3D approximate maximum likelihood <span class="hlt">solver</span> for localization of fish implanted with acoustic transmitters</span></a></p>
<p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p>
<p>Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.</p>
<p>2014-01-01</p>
<p>Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional <span class="hlt">solver</span> was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood <span class="hlt">solver</span> was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed <span class="hlt">solver</span> performed significantly better in tracking efficiency and accuracy than other <span class="hlt">solvers</span> described in the literature. PMID:25427517</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.712a2004G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.712a2004G"><span>Finite difference method accelerated with sparse <span class="hlt">solvers</span> for structural analysis of the metal-organic complexes</span></a></p>
<p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p>
<p>Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.</p>
<p>2016-05-01</p>
<p>Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse <span class="hlt">solver</span> would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse <span class="hlt">solvers</span> and the direct one MUMPS <span class="hlt">solver</span> with METIS ordering turned out to be the best. Compared to the Gaussian <span class="hlt">solver</span> present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA554888','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA554888"><span>Development of a Flow <span class="hlt">Solver</span> with Complex Kinetics on the Graphic Processing Units</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2011-09-22</p>
<p>Physics 109, 11 (2011), 113308. [9] Klockner, A., Warburton, T., Bridge, J., and Hesthaven, J. Nodal Discontinuous Galerkin Methods on Graphics...Graphic Processing Units ( GPU ) to model reactive gas mixture with detailed chemical kinetics. The <span class="hlt">solver</span> incorporates high-order finite volume methods...method. We explored different approaches in implementing a fast kinetics <span class="hlt">solver</span> on the GPU . The detail of the implementation is discussed in the</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920034805&hterms=earl+dowell&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dearl%2Bdowell','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920034805&hterms=earl+dowell&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dearl%2Bdowell"><span>Eigenvalue calculation procedure for an Euler/Navier-Stokes <span class="hlt">solver</span> with application to flows over airfoils</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Mahajan, Aparajit J.; Dowell, Earl H.; Bliss, Donald B.</p>
<p>1991-01-01</p>
<p>A Lanczos procedure is presently applied to a Navier-Stokes (N-S) <span class="hlt">solver</span> for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S <span class="hlt">solvers</span>.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880016743','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880016743"><span>The development of an intelligent interface to a computational fluid dynamics flow-<span class="hlt">solver</span> code</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Williams, Anthony D.</p>
<p>1988-01-01</p>
<p>Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-<span class="hlt">solver</span> codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow <span class="hlt">solver</span>. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950018686','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950018686"><span>Implementation of a parallel unstructured Euler <span class="hlt">solver</span> on the CM-5</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Morano, Eric; Mavriplis, D. J.</p>
<p>1995-01-01</p>
<p>An efficient unstructured 3D Euler <span class="hlt">solver</span> is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow <span class="hlt">solver</span> is discussed.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA190590','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA190590"><span>A New Block <span class="hlt">Solver</span> for Large, Full, Unsymmetric, Complex Systems of Linear Algebraic Equations.</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>1988-02-01</p>
<p>THE COEFFICIENT C MATRIX IN THAT ORDER. ON OUTPUT, UTI CONTAINS THE SOLUTION C MATRIX. C C THE NASTRAN DMAP INSTRUCTIONS TO INTERFACE WITH ’OCSOLVE...developed. Although OCSOLVE was developed for use with the finite element program NASTRAN , it is designed t,) be easily adapted for other applications...solve such a system of 500 equations with complex- valued coefficients to about 5% of the time required by the equation <span class="hlt">solver</span> in NASTRAN . The <span class="hlt">solver</span></p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19890029592&hterms=fluid+dynamics+fluid+flow&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dfluid%2Bdynamics%2Bfluid%2Bflow','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890029592&hterms=fluid+dynamics+fluid+flow&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dfluid%2Bdynamics%2Bfluid%2Bflow"><span>The development of an intelligent interface to a computational fluid dynamics flow-<span class="hlt">solver</span> code</span></a></p>
<p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p>
<p>Williams, Anthony D.</p>
<p>1988-01-01</p>
<p>Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-<span class="hlt">solver</span> codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow <span class="hlt">solver</span>. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/775574','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/775574"><span>THE USE OF CLASSICAL LAX-FRIEDRICHS RIEMANN <span class="hlt">SOLVERS</span> WITH DISCONTINUOUS GALERKIN METHODS</span></a></p>
<p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p>
<p>W. J. RIDER; R. B. LOWRIE</p>
<p>2001-03-01</p>
<p>While conducting a von Neumann stability analysis of discontinuous Galerkin methods we found that the standard Lax-Friedrichs (LxF) Riemann <span class="hlt">solver</span> is unstable for all time-step sizes. A simple modification of the Riemann <span class="hlt">solver</span>'s dissipation returns the method to stability. Furthermore, the method has a smaller truncation error than the corresponding method with an upwind flux for the RK2-DG(1) method. These results are confirmed upon testing.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/15980304','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/15980304"><span>Wavelet-based Poisson <span class="hlt">solver</span> for use in particle-in-cell simulations.</span></a></p>
<p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p>
<p>Terzić, Balsa; Pogorelov, Ilya V</p>
<p>2005-06-01</p>
<p>We report on a successful implementation of a wavelet-based Poisson <span class="hlt">solver</span> for use in three-dimensional particle-in-cell simulations. Our method harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and additional compression of relevant data sets. We present and discuss preliminary results relating to the application of the new <span class="hlt">solver</span> to test problems in accelerator physics and astrophysics.</p>
</li>
<li>
<p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA562299','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA562299"><span>Dynamic Linear <span class="hlt">Solver</span> Selection for Transient Simulations Using Multi-label Classifiers</span></a></p>
<p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p>
<p></p>
<p>2012-01-01</p>
<p>Conference on Computational Science, ICCS 2012 Dynamic linear <span class="hlt">solver</span> selection for transient simulations using multi-label classifiers Paul R. Eller ...preconditioned linear <span class="hlt">solver</span> as the output. Email addresses: Paul.R.Eller@usace.army.mil (Paul R. Eller ), Ruth.C.Cheng@usace.army.mil (Jing-Ru C...unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 1524 Paul R. Eller et al. / Procedia</p>
</li>
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