A high-accuracy Eulerian gyrokinetic solver for collisional plasmas
NASA Astrophysics Data System (ADS)
Candy, J.; Belli, E. A.; Bravenec, R. V.
2016-11-01
We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker-Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order conservative upwind scheme is used to permit high-accuracy electromagnetic simulation even in the limit of very high plasma β and vanishingly small perpendicular wavenumber, k⊥ → 0. To our knowledge, this is the first pseudospectral implementation of the collision operator in a gyrokinetic code. We show that the new solver agrees closely with GYRO in the limit of weak Lorentz collisions, but gives a significantly more realistic description of collisions at high collision frequency. The numerical methods are also designed to be efficient and scalable for multiscale simulations that treat ion-scale and electron-scale turbulence simultaneously.
EUPDF: An Eulerian-Based Monte Carlo Probability Density Function (PDF) Solver. User's Manual
NASA Technical Reports Server (NTRS)
Raju, M. S.
1998-01-01
EUPDF is an Eulerian-based Monte Carlo PDF solver developed for application with sprays, combustion, parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with the coding required to couple the PDF code to any given flow code and a basic understanding of the EUPDF code structure as well as the models involved in the PDF formulation. The source code of EUPDF will be available with the release of the National Combustion Code (NCC) as a complete package.
Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver
NASA Astrophysics Data System (ADS)
Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind
2016-09-01
Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid Eulerian- Lagrangian approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.
NASA Astrophysics Data System (ADS)
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
NASA Astrophysics Data System (ADS)
Pathak, Ashish; Raessi, Mehdi
2016-04-01
We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented.
NASA Technical Reports Server (NTRS)
Raju, M. S.
1998-01-01
The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. 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 the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic
Objective Eulerian coherent structures.
Serra, Mattia; Haller, George
2016-05-01
We define objective Eulerian Coherent Structures (OECSs) in two-dimensional, non-autonomous dynamical systems as the instantaneously most influential material curves. Specifically, OECSs are stationary curves of the averaged instantaneous material stretching-rate or material shearing-rate functionals. From these objective (frame-invariant) variational principles, we obtain explicit differential equations for hyperbolic, elliptic, and parabolic OECSs. As an illustration, we compute OECSs in an unsteady ocean velocity data set. In comparison to structures suggested by other common Eulerian diagnostic tools, we find OECSs to be the correct short-term cores of observed trajectory deformation patterns. PMID:27249950
A compressible real gas eulerian model for LES of fuel sprays
NASA Astrophysics Data System (ADS)
Knudsen, Edward; Doran, Eric
2015-11-01
A compressible solver for eulerian multiphase spray simulations is presented. This large eddy simulation solver employs a Peng-Robinson (PR) equation of state to describe mixtures of two species such as liquid dodecane and gaseous nitrogen. Modeling challenges associated with the use of PR are discussed, as are the resource requirements associated with using a compressible formulation to describe liquids when full fuel injector applications are considered. The solver is analyzed using canonical cases and the Spray A experiment from the Engine Combustion Network.
Stanley, Vendall S.; Heroux, Michael A.; Hoekstra, Robert J.; Sala, Marzio
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. where A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. wheremore » A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.« less
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
NASA Astrophysics Data System (ADS)
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Comparison of Joint Modeling Approaches Including Eulerian Sliding Interfaces
Lomov, I; Antoun, T; Vorobiev, O
2009-12-16
Accurate representation of discontinuities such as joints and faults is a key ingredient for high fidelity modeling of shock propagation in geologic media. The following study was done to improve treatment of discontinuities (joints) in the Eulerian hydrocode GEODYN (Lomov and Liu 2005). Lagrangian methods with conforming meshes and explicit inclusion of joints in the geologic model are well suited for such an analysis. Unfortunately, current meshing tools are unable to automatically generate adequate hexahedral meshes for large numbers of irregular polyhedra. Another concern is that joint stiffness in such explicit computations requires significantly reduced time steps, with negative implications for both the efficiency and quality of the numerical solution. An alternative approach is to use non-conforming meshes and embed joint information into regular computational elements. However, once slip displacement on the joints become comparable to the zone size, Lagrangian (even non-conforming) meshes could suffer from tangling and decreased time step problems. The use of non-conforming meshes in an Eulerian solver may alleviate these difficulties and provide a viable numerical approach for modeling the effects of faults on the dynamic response of geologic materials. We studied shock propagation in jointed/faulted media using a Lagrangian and two Eulerian approaches. To investigate the accuracy of this joint treatment the GEODYN calculations have been compared with results from the Lagrangian code GEODYN-L which uses an explicit treatment of joints via common plane contact. We explore two approaches to joint treatment in the code, one for joints with finite thickness and the other for tight joints. In all cases the sliding interfaces are tracked explicitly without homogenization or blending the joint and block response into an average response. In general, rock joints will introduce an increase in normal compliance in addition to a reduction in shear strength. In the
Gaston, L.; Glut, B.; Bellet, M.; Chenot, J.L.
1995-12-31
This paper presents a two-dimensional lagrangian-eulerian finite element approach of non-steady state Navier-Stokes fluid flows with free surfaces, like those occurring during the mould filling stage in casting processes. The proposed model is based on a mixed velocity-pressure finite element formulation, including an augmented Lagrangian technique and an iterative solver of Uzawa type. Mesh updating is carried out through an arbitrary lagrangian-eulerian method in order to describe properly the free surface evolution. Heat transfer through the fluid flow is solved by a convection-diffusion splitting technique. The efficiency of the method is illustrated on an example of gravity casting.
Direct Eulerian MUSCL scheme for gas dynamics
Colella, P.
1985-01-01
The authors present a second order extension of Godunov's method for gas dynamics in Eulerian coordinates patterned after van Leer's MUSCL scheme for gas dynamics in Lagrangian coordinates. The present method performs the Eulerian calculation in a single step by solving Riemann problems and characteristic equations for the fluxes in the Eulerian frame. The authors also make several modifications in the formulation of MUSCL, applicable to both this scheme and to the original Lagrangian scheme, all aimed at making a more robust and accurate scheme. The authors present the results of test calculations in one and two space variables. 12 references, 5 figures.
Eulerian formulation of elastic rods
NASA Astrophysics Data System (ADS)
Huynen, Alexandre; Detournay, Emmanuel; Denoël, Vincent
2016-06-01
In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface. This reformulation hinges on describing the rod-deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this re-parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two-points boundary-value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment.
Improvements to SOIL: An Eulerian hydrodynamics code
Davis, C.G.
1988-04-01
Possible improvements to SOIL, an Eulerian hydrodynamics code that can do coupled radiation diffusion and strength of materials, are presented in this report. Our research is based on the inspection of other Eulerian codes and theoretical reports on hydrodynamics. Several conclusions from the present study suggest that some improvements are in order, such as second-order advection, adaptive meshes, and speedup of the code by vectorization and/or multitasking. 29 refs., 2 figs.
A Lagrangian-Eulerian approach to modeling homogeneous condensation in high density gas expansions.
Jansen, Ryan; Gimelshein, Natalia; Gimelshein, Sergey; Wysong, Ingrid
2011-03-14
A computational approach to homogeneous nucleation is proposed based on Eulerian description of the gas phase expansion coupled with a Lagrangian approach to the cluster formation. A continuum, Euler/Navier-Stokes solver versatile advection code is used to model the gas transport, and a kinetic particle solver is developed in this work to simulate cluster nucleation and growth. Parameters in the new model were adjusted so as to match the known theoretical dimer formation equilibrium constants for the two gases under consideration, argon and water. Reasonable agreement between computed and available experimental data was found in terminal cluster size distributions for nozzle water expansions in a wide range of stagnation pressures. The proposed approach was found to be orders of magnitude faster than a comparable approach based on the direct simulation Monte Carlo method.
Majorczyk, Vincent; Cotin, Stéphane; Duriez, Christian; Allard, Jeremie
2013-01-01
We present a method to simulate the outcome of reconstructive facial surgery based on fat-filling. Facial anatomy is complex: the fat is constrained between layers of tissues which behave as walls along the face; in addition, connective tissues that are present between these different layers also influence the fat-filling procedure. To simulate the end result, we propose a method which couples a 2.5D Eulerian fluid model for the fat and a finite element model for the soft tissues. The two models are coupled using the computation of the mechanical compliance matrix. Two contributions are presented in this paper: a solver for fluids which couples properties of solid tissues and fluid pressure, and an application of this solver to fat-filling surgery procedure simulation. PMID:24505774
Performance Analysis of GYRO: A Tool Evaluation
Worley, P.; Roth, P.; Candy, J.; Shan, Hongzhang; Mahinthakumar,G.; Sreepathi, S.; Carrington, L.; Kaiser, T.; Snavely, A.; Reed, D.; Zhang, Y.; Huck, K.; Malony, A.; Shende, S.; Moore, S.; Wolf, F.
2005-06-26
The performance of the Eulerian gyrokinetic-Maxwell solver code GYRO is analyzed on five high performance computing systems. First, a manual approach is taken, using custom scripts to analyze the output of embedded wall clock timers, floating point operation counts collected using hardware performance counters, and traces of user and communication events collected using the profiling interface to Message Passing Interface (MPI) libraries. Parts of the analysis are then repeated or extended using a number of sophisticated performance analysis tools: IPM, KOJAK, SvPablo, TAU, and the PMaC modeling tool suite. The paper briefly discusses what has been discovered via this manual analysis process, what performance analyses are inconvenient or infeasible to attempt manually, and to what extent the tools show promise in accelerating or significantly extending the manual performance analyses.
Parallel processing of Eulerian-Lagrangian, cell-based adaptive method for moving boundary problems
NASA Astrophysics Data System (ADS)
Kuan, Chih-Kuang
In this study, issues and techniques related to the parallel processing of the Eulerian-Lagrangian method for multi-scale moving boundary computation are investigated. The scope of the study consists of the Eulerian approach for field equations, explicit interface-tracking, Lagrangian interface modification and reconstruction algorithms, and a cell-based unstructured adaptive mesh refinement (AMR) in a distributed-memory computation framework. We decomposed the Eulerian domain spatially along with AMR to balance the computational load of solving field equations, which is a primary cost of the entire solver. The Lagrangian domain is partitioned based on marker vicinities with respect to the Eulerian partitions to minimize inter-processor communication. Overall, the performance of an Eulerian task peaks at 10,000-20,000 cells per processor, and it is the upper bound of the performance of the Eulerian- Lagrangian method. Moreover, the load imbalance of the Lagrangian task is not as influential as the communication overhead of the Eulerian-Lagrangian tasks on the overall performance. To assess the parallel processing capabilities, a high Weber number drop collision is simulated. The high convective to viscous length scale ratios result in disparate length scale distributions; together with the moving and topologically irregular interfaces, the computational tasks require temporally and spatially resolved treatment adaptively. The techniques presented enable us to perform original studies to meet such computational requirements. Coalescence, stretch, and break-up of satellite droplets due to the interfacial instability are observed in current study, and the history of interface evolution is in good agreement with the experimental data. The competing mechanisms of the primary and secondary droplet break up, along with the gas-liquid interfacial dynamics are systematically investigated. This study shows that Rayleigh-Taylor instability on the edge of an extruding sheet
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-10-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
The Case for Including Eulerian Kinematics in Undergraduate Dynamics.
ERIC Educational Resources Information Center
Uram, Earl M.
A Eulerian framework is proposed as an alternative to the Lagrangian framework usually used in undergraduate dynamics courses. An attempt to introduce Eulerian kinematics into a dynamics course is discussed. (LMH)
Parallel Multigrid Equation Solver
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
2004-03-01
PLIRIS is an object-oriented solver built on top of a previous matrix solver used in a number of application codes. Puns solves a linear system directly via LU factorization with partial pivoting. The user provides the linear system in terms of Epetra Objects including a matrix and right-hand-sides. The user can then factor the matrix and perform the forward and back solve at a later time or solve for multiple right-hand-sides at once. This packagemore » is used when dense matrices are obtained in the problem formulation. These dense matrices occur whenever boundary element techniques are chosen for the solution procedure. This has been used in electromagnetics for both static and frequency domain problems.« less
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Koniges, A.; Eder, D.; Masters, N.; Fisher, A.; Anderson, R.; Gunney, B.; Wang, P.; Benson, D.; Dixit, P.
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being applied to slurry flow (landslides).
NASA Technical Reports Server (NTRS)
Dang, A. L.; Navaz, H. K.; Rangel, R. H.
1992-01-01
The liquid thrust chambers performance (LTCP) code is used for parametric studies of flow and combustion in liquid rocket engines. Multiphase flow equations are solved in an Eulerian-Eulerian framework, and multistep finite rate chemistry is incorporated. The discretization scheme is fully implicit and is based on the total variation diminishing (TVD) scheme, which is accurate, robust, very efficient and capable of handling steep gradients and stiff chemistry. Effects of injection velocity and chamber size have been considered, and the effect of group combustion on the evaporation rate has been studied for a dense spray.
Heroux, Michael A.
2007-03-01
HPCCG is a simple PDE application and preconditioned conjugate gradient solver that solves a linear system on a beam-shaped domain. Although it does not address many performance issues present in real engineering applications, such as load imbalance and preconditioner scalability, it can serve as a first "sanity test" of new processor design choices, inter-connect network design choices and the scalability of a new computer system. Because it is self-contained, easy to compile and easily scaled to 100s or 1000s of porcessors, it can be an attractive study code for computer system designers.
Scalable solvers and applications
Ribbens, C J
2000-10-27
The purpose of this report is to summarize research activities carried out under Lawrence Livermore National Laboratory (LLNL) research subcontract B501073. This contract supported the principal investigator (P1), Dr. Calvin Ribbens, during his sabbatical visit to LLNL from August 1999 through June 2000. Results and conclusions from the work are summarized below in two major sections. The first section covers contributions to the Scalable Linear Solvers and hypre projects in the Center for Applied Scientific Computing (CASC). The second section describes results from collaboration with Patrice Turchi of LLNL's Chemistry and Materials Science Directorate (CMS). A list of publications supported by this subcontract appears at the end of the report.
2007-03-01
HPCCG is a simple PDE application and preconditioned conjugate gradient solver that solves a linear system on a beam-shaped domain. Although it does not address many performance issues present in real engineering applications, such as load imbalance and preconditioner scalability, it can serve as a first "sanity test" of new processor design choices, inter-connect network design choices and the scalability of a new computer system. Because it is self-contained, easy to compile and easily scaledmore » to 100s or 1000s of porcessors, it can be an attractive study code for computer system designers.« less
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being appliedmore » to slurry flow (landslides).« less
Parameterized Complexity of Eulerian Deletion Problems.
Cygan, Marek; Marx, Dániel; Pilipczuk, Marcin; Pilipczuk, Michał; Schlotter, Ildikó
2014-01-01
We study a family of problems where the goal is to make a graph Eulerian, i.e., connected and with all the vertices having even degrees, by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. The collection of results shows an interesting contrast: while the node-deletion variants remain intractable, i.e., W[1]-hard for all the studied cases, edge-deletion problems are either fixed-parameter tractable or polynomial-time solvable. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the color coding technique. For versions that remain NP-complete but fixed-parameter tractable we consider also possibilities of polynomial kernelization; unfortunately, we prove that this is not possible unless NP⊆coNP/poly. PMID:24415818
Parallel tridiagonal equation solvers
NASA Technical Reports Server (NTRS)
Stone, H. S.
1974-01-01
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
Amesos2 Templated Direct Sparse Solver Package
2011-05-24
Amesos2 is a templated direct sparse solver package. Amesos2 provides interfaces to direct sparse solvers, rather than providing native solver capabilities. Amesos2 is a derivative work of the Trilinos package Amesos.
Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame
NASA Astrophysics Data System (ADS)
Azarnykh, Dmitrii; Litvinov, Sergey; Adams, Nikolaus A.
2016-06-01
A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.
An Eulerian-based Bubble Dynamics Model for Computational Fluid Dynamics
NASA Astrophysics Data System (ADS)
Balu, Asish; Kinzel, Michael
2015-11-01
Cavitation dynamics of nuclei are largely governed by the Rayleigh-Plesset Equation (RPE). This research explores the implementation of a one-way coupling to the solution of the RPE to a computational fluid dynamics (CFD) simulation in an Eulerian-framework. In this work, we used transport equations (i.e., advection) of the bubble radius and bubble growth rate, both of which are governed by advection mechanisms and coupling to the RPE through the CFD pressure field. The method is validated in the context of hypothetical pressure fields by prescribing a temporally varying pressure. Then, it is extended to one-way coupling with cavitation development in three different flow situations: (1) flow over a cylinder, (2) bubble formation during a bottle collapse event, and (3) cavitation in a tip vortex. In the context of these flows, the CFD simulations replicate an equivalent MATLAB-based solution to the RPE, thus validating the model. Additionally, an analytical formulation for appropriate upper and lower bounds for the bubble's physical properties is presented. These boundary values allow the CFD solver to run at larger time steps, therefore increasing the rate of convergence as well as maintaining solution accuracy. The results from this work suggest that Eulerian-based RPE cavitation models are practical and have the potential to simulate large numbers of bubbles that challenge Lagrangian methods.
Fragmentation statistics from Eulerian hydrocode calculations
Trucano, T.G.; Grady, D.E.; McGlaun, J.M.
1989-01-01
In this paper, we discuss a procedure for computing discrete fragmentation information for terminal ballistics events from the continuum data that emerges from two-dimensional Eulerian hydrocode simulations of these events. The present examples deal with the normal impact of lead cylinders on lead plates at velocities below 1600 m/s. In this regime, the resulting debris is almost exclusively solid lead fragments. We have experimental data of sufficient accuracy to evaluate the extraction of such fragmentation information from code simulations. The problem is interesting because the observed distribution of fragment size would require extreme subgrid resolution in the hydrocode if the statistics were computed directly. Our approach is different. We ask whether or not the general continuum description predicted by the code contains enough information to allow coupling of an analytic fragmentation theory that successfully predicts fragmentation statistics. We believe that this approach is valid, and discuss our current success in matching experimental data. 10 refs., 7 figs., 5 tabs.
NASA Technical Reports Server (NTRS)
Ilin, Andrew V.
2006-01-01
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Sherlock Holmes, Master Problem Solver.
ERIC Educational Resources Information Center
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
2D Resistive Magnetohydrodynamics Calculations with an Arbitrary Lagrange Eulerian Code
NASA Astrophysics Data System (ADS)
Rousculp, C. L.; Gianakon, T. A.; Lipnikov, K. N.; Nelson, E. M.
2015-11-01
Single fluid resistive MHD is useful for modeling Z-pinch configurations in cylindrical geometry. One such example is thin walled liners for shock physics or HEDP experiments driven by capacitor banks such as the LANL's PHELIX or Sandia-Z. MHD is also useful for modeling high-explosive-driven flux compression generators (FCGs) and their high-current switches. The resistive MHD in our arbitrary Lagrange Eulerian (ALE) code operates in one and two dimensions in both Cartesian and cylindrical geometry. It is implemented as a time-step split operator, which consists of, ideal MHD connected to the explicit hydro momentum and energy equations and a second order mimetic discretization solver for implicit solution of the magnetic diffusion equation. In a staggered grid scheme, a single-component of cell-centered magnetic flux is conserved in the Lagrangian frame exactly, while magnetic forces are accumulated at the nodes. Total energy is conserved to round off. Total flux is conserved under the ALE relaxation and remap. The diffusion solver consistently computes Ohmic heating. Both Neumann and Dirichlet boundary conditions are available with coupling to external circuit models. Example calculations will be shown.
NASA Astrophysics Data System (ADS)
Jaishree, J.; Haworth, D. C.
2012-06-01
Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-15
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics
NASA Astrophysics Data System (ADS)
Zhang, W.; Howell, L.; Almgren, A.; Burrows, A.; Dolence, J.; Bell, J.
2013-01-01
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
Eulerian Formulation of Spatially Constrained Elastic Rods
NASA Astrophysics Data System (ADS)
Huynen, Alexandre
Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional Lagrangian formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the Eulerian framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed Eulerian reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration
AUTOMATIC DIFFERENTIATION OF AN EULERIAN HYDROCODE
R. HENNINGER; A. CARLE; P. MAUDLIN
2000-11-01
Automatic differentiation (AD) is applied to a two-dimensional Eulerian hydrodynamics computer code (hydrocode) to provide gradients that will be used for design optimization and uncertainty analysis. We examine AD in both the forward and adjoint (reverse) mode using Automatic Differentiation of Fortran (ADIFOR, version 3.0). Setup time, accuracy, and run times are described for three problems. The test set consists of a one-dimensional shock-propagation problem, a two-dimensional metal-jet-formation problem and a two-dimensional shell-collapse problem. Setup time for ADIFOR was approximately one month starting from a simplified, fixed-dimension version of the original code. ADIFOR produced accurate (as compared to finite difference) gradients in both modes for all of the problems. These test problems had 17 independent variables. We find that the forward mode is up to 39% slower and the adjoint mode is at least 11% faster than finding the gradient by means of finite differences. Problems of real interest will certainly have more independent variables. The adjoint mode is thus favored since the computational time increases only slightly for additional independent variables.
Coupled Eulerian/Lagrangian Simulation for Overpressure Structural Response
NASA Astrophysics Data System (ADS)
Lloyd, Andrew; Pan, Hua; Miller, David; Cogar, John
2011-06-01
Accurately modeling blast dynamics is critical in the assessment of structures subjected to blast loading. The current industry standard for modeling blast effects in Lagrangian based Finite Element simulations is CONWEP; tabulated pressure data taken directly from blast events. CONWEP is limited, however, and may not always be physically representative of the blast/structural interaction that occurs in the field. Eulerian hydrocodes provide advantages over CONWEP in that they can capture shock front interaction and model blast surface interfaces with fidelity due to the presence of the working fluid. Eulerian codes, however, break down over larger time scales; whereas, Lagrangian modeling allows for discrete finite elements with definable boundary interfaces that can be tracked out to longer time scales. Hence, a hybrid approach that couples the Eulerian blast modeling with Lagrangian system dynamics is necessary. The objective of this paper is to demonstrate improvements in overpressure structural response modeling using a Coupled Eulerian/Lagrangian algorithm implemented in VelodyneTM. Velodyne results using the Coupled Eulerian/Lagrangian algorithm are compared to results from Eulerian hydrocode simulations and Velodyne simulations using the CONWEP algorithm.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
A lagrangian-eulerian description of debris transport by a tsunami in the Lisbon waterfront
NASA Astrophysics Data System (ADS)
Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.
2013-04-01
Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (eulerian) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (lagrangian) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the eulerian solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P.
2007-10-01
Aims:We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods: Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results: ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a
Lagrangian and Eulerian Acceleration Statistics in Turbulent Stratified Shear Flows
NASA Astrophysics Data System (ADS)
Jacobitz, Frank; Schneider, Kai; Farge, Marie
2014-11-01
The Lagrangian and Eulerian acceleration statistics in homogeneous turbulence with shear and stratification are studied using direct numerical simulations. The Richardson number is varied from Ri = 0 , corresponding to unstratified shear flow, to Ri = 1 , corresponding to strongly stratified shear flow. In addition, the scale dependence of the acceleration statistics is studied using a wavelet-based approach. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar influence on the Richardson number and extreme values for Eulerian acceleration are stronger than those observed for the Lagrangian acceleration. Similarly, the Eulerian time-rate of change of fluctuating density is observed to have larger extreme values than that of the Lagrangian time-rate of change. Hence, the time-rate of change of fluctuating density obtained at a fixed location by an Eulerian observer is mainly due to advection of fluctuating density through this location, while the time-rate of change of fluctuating density following a fluid particle is substantially smaller, and due to production and dissipation of fluctuating density.
Ice Accretion Modeling using an Eulerian Approach for Droplet Impingement
NASA Technical Reports Server (NTRS)
Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.
2012-01-01
A three-dimensional Eulerian analysis has been developed for modeling droplet impingement on lifting bodes. The Eulerian model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the Eulerian approach is more efficient because the Lagrangian approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the Lagrangian approach used in an industry standard analysis called LEWICE.
Time-domain Raman analytical forward solvers.
Martelli, Fabrizio; Binzoni, Tiziano; Sekar, Sanathana Konugolu Venkata; Farina, Andrea; Cavalieri, Stefano; Pifferi, Antonio
2016-09-01
A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffusive media is presented. The time-domain solvers have been developed for two geometries: the parallelepiped and the finite cylinder. The potential presence of a background fluorescence emission, contaminating the Raman signal, has also been taken into account. All the solvers have been obtained as solutions of the time dependent diffusion equation. The validation of the solvers has been performed by means of comparisons with the results of "gold standard" Monte Carlo simulations. These forward solvers provide an accurate tool to explore the information content encoded in the time-resolved Raman measurements. PMID:27607645
Eulerian Time-Domain Filtering for Spatial LES
NASA Technical Reports Server (NTRS)
Pruett, C. David
1997-01-01
Eulerian time-domain filtering seems to be appropriate for LES (large eddy simulation) of flows whose large coherent structures convect approximately at a common characteristic velocity; e.g., mixing layers, jets, and wakes. For these flows, we develop an approach to LES based on an explicit second-order digital Butterworth filter, which is applied in,the time domain in an Eulerian context. The approach is validated through a priori and a posteriori analyses of the simulated flow of a heated, subsonic, axisymmetric jet.
On unstructured grids and solvers
NASA Technical Reports Server (NTRS)
Barth, T. J.
1990-01-01
The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
Numerical Study of Coal Gasification Using Eulerian-Eulerian Multiphase Model
Shi, S.; Guenther, C.; Orsino, S.
2007-09-01
Gasification converts the carbon-containing material into a synthesis gas (syngas) which can be used as a fuel to generate electricity or used as a basic chemical building block for a large number of uses in the petrochemical and refining industries. Based on the mode of conveyance of the fuel and the gasifying medium, gasification can be classified into fixed or moving bed, fluidized bed, and entrained flow reactors. Entrained flow gasifiers normally feature dilute flow with small particle size and can be successfully modeled with the Discrete Phase Method (DPM). For the other types, the Eulerian-Eulerian (E-E) or the so called two-fluid multiphase model is a more appropriate approach. The E-E model treats the solid phase as a distinct interpenetrating granular “fluid” and it is the most general-purposed multi-fluid model. This approach provides transient, three-dimensional, detailed information inside the reactor which would otherwise be unobtainable through experiments due to the large scale, high pressure and/or temperature. In this paper, a transient, three-dimensional model of the Power Systems Development Facility (PSDF) transport gasifier will be presented to illustrate how Computational Fluid Dynamics (CFD) can be used for large-scale complicated geometry with detailed physics and chemistry. In the model, eleven species are included in the gas phase while four pseudo-species are assumed in the solid phase. A total of sixteen reactions, both homogeneous (involving only gas phase species) and heterogeneous (involving species in both gas and solid phases), are used to model the coal gasification chemistry. Computational results have been validated against PSDF experimental data from lignite to bituminous coals under both air and oxygen blown conditions. The PSDF gasifier geometry was meshed with about 70,000, hexahedra-dominated cells. A total of six cases with different coal, feed gas, and/or operation conditions have been performed. The predicted and
A Eulerian-Lagrangian description of cavitating flow
NASA Astrophysics Data System (ADS)
Iben, U.; Ivanov, N. G.; Isaenko, I. I.; Schmidt, A. A.
2015-12-01
We propose a method of cavitating flow calculation that is based on the Eulerian-Lagrangian description of multiphase flows. The formation and growth of cavitation bubbles are described using the model of heterogeneous volume nucleation. Results of test calculations demonstrate the efficiency of the proposed model.
QUANTIFYING SUBGRID POLLUTANT VARIABILITY IN EULERIAN AIR QUALITY MODELS
In order to properly assess human risk due to exposure to hazardous air pollutants or air toxics, detailed information is needed on the location and magnitude of ambient air toxic concentrations. Regional scale Eulerian air quality models are typically limited to relatively coar...
Crystal level simulations using Eulerian finite element methods
Becker, R; Barton, N R; Benson, D J
2004-02-06
Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations.
Eulerian-Lagrangian solution of the convection-dispersion equation in natural co-ordinates.
Cheng, R.T.; Casulli, V.; Milford, S.N.
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system.-from Authors
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Analysis Tools for CFD Multigrid Solvers
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Diskin, Boris
2004-01-01
Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.
Bavo, Alessandra M; Rocatello, Giorgia; Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick
2016-01-01
In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.
Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick
2016-01-01
In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798
Accurate direct Eulerian simulation of dynamic elastic-plastic flow
Kamm, James R; Walter, John W
2009-01-01
The simulation of dynamic, large strain deformation is an important, difficult, and unsolved computational challenge. Existing Eulerian schemes for dynamic material response are plagued by unresolved issues. We present a new scheme for the first-order system of elasto-plasticity equations in the Eulerian frame. This system has an intrinsic constraint on the inverse deformation gradient. Standard Godunov schemes do not satisfy this constraint. The method of Flux Distributions (FD) was devised to discretely enforce such constraints for numerical schemes with cell-centered variables. We describe a Flux Distribution approach that enforces the inverse deformation gradient constraint. As this approach is new and novel, we do not yet have numerical results to validate our claims. This paper is the first installment of our program to develop this new method.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (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.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (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.
An overview of mesoscale material modeling with Eulerian hydrocodes
NASA Astrophysics Data System (ADS)
Olney, K.; Benson, D. J.; Nesterenko, V.
2014-05-01
Eulerian hydrocodes were originally developed for simulating strong shocks in solids and fluids, but their ability to handle arbitrarily large deformations and the formation of new free surfaces makes them attractive for simulating the deformation and failure of materials at the mesoscopic scale. A summary of several numerical techniques that have been developed to address issues that commonly arise for this class of problems is presented.
KLU2 Direct Linear Solver Package
2012-01-04
KLU2 is a direct sparse solver for solving unsymmetric linear systems. It is related to the existing KLU solver, (in Amesos package and also as a stand-alone package from University of Florida) but provides template support for scalar and ordinal types. It uses a left looking LU factorization method.
Improving Resource-Unaware SAT Solvers
NASA Astrophysics Data System (ADS)
Hölldobler, Steffen; Manthey, Norbert; Saptawijaya, Ari
The paper discusses cache utilization in state-of-the-art SAT solvers. The aim of the study is to show how a resource-unaware SAT solver can be improved by utilizing the cache sensibly. The analysis is performed on a CDCL-based SAT solver using a subset of the industrial SAT Competition 2009 benchmark. For the analysis, the total cycles, the resource stall cycles, the L2 cache hits and the L2 cache misses are traced using sample based profiling. Based on the analysis, several techniques - some of which have not been used in SAT solvers so far - are proposed resulting in a combined speedup up to 83% without affecting the search path of the solver. The average speedup on the benchmark is 60%. The new techniques are also applied to MiniSAT2.0 improving its runtime by 20% on average.
Belos Block Linear Solvers Package
2004-03-01
Belos is an extensible and interoperable framework for large-scale, iterative methods for solving systems of linear equations with multiple right-hand sides. The motivation for this framework is to provide a generic interface to a collection of algorithms for solving large-scale linear systems. Belos is interoperable because both the matrix and vectors are considered to be opaque objects--only knowledge of the matrix and vectors via elementary operations is necessary. An implementation of Balos is accomplished viamore » the use of interfaces. One of the goals of Belos is to allow the user flexibility in specifying the data representation for the matrix and vectors and so leverage any existing software investment. The algorithms that will be included in package are Krylov-based linear solvers, like Block GMRES (Generalized Minimal RESidual) and Block CG (Conjugate-Gradient).« less
On two-phase flow solvers in irregular domains with contact line
NASA Astrophysics Data System (ADS)
Lepilliez, Mathieu; Popescu, Elena Roxana; Gibou, Frederic; Tanguy, Sébastien
2016-09-01
We present numerical methods that enable the direct numerical simulation of two-phase flows in irregular domains. A method is presented to account for surface tension effects in a mesh cell containing a triple line between the liquid, gas and solid phases. Our numerical method is based on the level-set method to capture the liquid-gas interface and on the single-phase Navier-Stokes solver in irregular domain proposed in [35] to impose the solid boundary in an Eulerian framework. We also present a strategy for the implicit treatment of the viscous term and how to impose both a Neumann boundary condition and a jump condition when solving for the pressure field. Special care is given on how to take into account the contact angle, the no-slip boundary condition for the velocity field and the volume forces. Finally, we present numerical results in two and three spatial dimensions evaluating our simulations with several benchmarks.
Numerical Analysis of Cold Spray Particles Impacting Behavior by the Eulerian Method: A Review
NASA Astrophysics Data System (ADS)
Li, W. Y.; Yang, K.; Yin, S.; Guo, X. P.
2016-08-01
Numerical simulations have been widely used to study particles impacting behavior in cold spraying. Among the used simulation methods, the Eulerian frame becomes increasingly attractive for its absence of mesh distortion which happens in the Lagrangian frame. It has been proved that particle deformation behaviors upon impacting calculated by the Eulerian method are well comparable to the experimental observations. In this review article, the literature on modeling particle impacting by the Eulerian method was summarized. In the second part, the Eulerian method was detailedly introduced. In the third part, the particle/substrate impacting behavior, and its influencing factors, i.e., mesh resolution, particle impacting velocity, preheating (particle or/and substrate) and oxide film, were summarized. Additionally, the prediction of critical velocity and residual stresses by using the Eulerian method was also discussed in detail. Finally, the current issues, problems and prospects existing in the Eulerian simulations of particle impacting were explored.
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
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 Solver, 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 solvers 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.
GARDNER, P.R.
2006-04-01
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 solver, 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 solver successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
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 solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver 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.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
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 solvers, 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.
Euler solvers for transonic applications
NASA Technical Reports Server (NTRS)
Vanleer, Bram
1989-01-01
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 solvers 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.
An Overview of Mesoscale Material Modeling with Eulerian Hydrocodes
NASA Astrophysics Data System (ADS)
Benson, David
2013-06-01
Eulerian hydrocodes were originally developed for simulating strong shocks in solids and fluids, but their ability to handle arbitrarily large deformations and the formation of new free surfaces makes them attractive for simulating the deformation and failure of materials at the mesoscopic scale. A summary of some of the numerical techniques that have been developed to address common issues for this class of problems is presented with the shock compression of powders used as a model problem. Achieving the correct packing density with the correct statistical distribution of particle sizes and shapes is, in itself, a challenging problem. However, since Eulerian codes permit multiple materials within each element, or cell, the material interfaces do not have to follow the mesh lines. The use of digital image processing to map the pixels of micrographs to the Eulerian mesh has proven to be a popular and useful means of creating accurate models of complex microstructures. Micro CT scans have been used to extend this approach to three dimensions for several classes of materials. The interaction between the particles is of considerable interest. During shock compression, individual particles may melt and form jets, and the voids between them collapse. Dynamic interface ordering has become a necessity, and many codes now have a suite of options for handling multi-material mechanics. True contact algorithms are now replacing multi-material approximations in some cases. At the mesoscale, material properties often vary spatially due to sub-scale effects. Using a large number of material species to represent the variations is usually unattractive. Directly specifying the properties point-wise as history variables has not proven successful because the limiters in the transport algorithms quickly smooth out the variations. Circumventing the limiter problem is shown to be relatively simple with the use of a reference configuration and the transport of the initial coordinates
MESA: A 3-D Eulerian hydrocode for penetration mechanics studies
Mandell, D.A.; Holian, K.S.; Henninger, R.
1991-01-01
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 Eulerian hydrodynamics, a number of material strength and fracture models, and a programmed burn high explosives model. 15 refs., 4 figs.
Parallelizing alternating direction implicit solver on GPUs
Technology Transfer Automated Retrieval System (TEKTRAN)
We present a parallel Alternating Direction Implicit (ADI) solver 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...
Finite Element Interface to Linear Solvers
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on themore » problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.« less
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
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) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, 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 solver 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 solver, 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 solver code needs to be maintained in the MODFLOW source tree. PMID:19563427
Advanced three-dimensional Eulerian hydrodynamic algorithm development
Rider, W.J.; Kothe, D.B.; Mosso, S.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The purpose of this project is to investigate, implement, and evaluate algorithms that have high potential for improving the robustness, fidelity and accuracy of three-dimensional Eulerian hydrodynamic simulations. Eulerian computations are necessary to simulate a number of important physical phenomena ranging from the molding process for metal parts to nuclear weapons safety issues to astrophysical phenomena such as that associated with a Type 2 supernovae. A number of algorithmic issues were explored in the course of this research including interface/volume tracking, surface physics integration, high resolution integration techniques, multilevel iterative methods, multimaterial hydrodynamics and coupling radiation with hydrodynamics. This project combines core strengths of several Laboratory divisions. The project has high institutional benefit given the renewed emphasis on numerical simulations in Science-Based Stockpile Stewardship and the Accelerated Strategic Computing Initiative and LANL`s tactical goals related to high performance computing and simulation.
A cavitation model based on Eulerian stochastic fields
NASA Astrophysics Data System (ADS)
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Eulerian hydrocode modeling of a dynamic tensile extrusion experiment (u)
Burkett, Michael W; Clancy, Sean P
2009-01-01
Eulerian 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 Eulerian 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.
Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities
NASA Technical Reports Server (NTRS)
Bendiksen, Oddvar O.
1994-01-01
This paper presents an overview of recent applications of Eulerian-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 Eulerian 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.
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-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 solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
NASA Technical Reports Server (NTRS)
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian 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 Eulerian 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 Eulerian 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 Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Full Eulerian lattice Boltzmann model for conjugate heat transfer
NASA Astrophysics Data System (ADS)
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian 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.
Noninvasive Free Flap Monitoring Using Eulerian Video Magnification
Liu, Yuan Fang; Vuong, Christopher; Walker, Paul Charles; Peterson, Nathaniel Ray; Inman, Jared Christian; Filho, Pedro Alcantara Andrade; Lee, Steve Choon-Sung
2016-01-01
Eulerian 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
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (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.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (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
A semi-Eulerian method for treating Lagrangian sliding interfaces
Lee, W.H.
1996-07-01
In many two-dimensional Lagrangian radiation hydrodynamic calculations, shear along material boundaries is a serious problem. Since the mesh is tied to the material, this shear will cause distortions in the mesh that make the calculations very difficult. The approach described in this paper adopts a semi-Eulerian calculation that allows material flow through a Lagrangian mesh along an interface. The basic idea is to consider each point along the slip line temporarily as a double point. One would then calculate the motion of each point separately and then pull the points back together using the automatic rezone method. This would allow the materials to shear along the interface. This paper will describe the method as used in a two-dimensional Lagrangian code. The formation of a shaped charge jet is computed using the present method, and the results are discussed with and without the slip treatment.
Full Eulerian lattice Boltzmann model for conjugate heat transfer.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian 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. PMID:26764851
Relativistic perturbations in ΛCDM: Eulerian and Lagrangian approaches
Villa, Eleonora; Rampf, Cornelius E-mail: cornelius.rampf@port.ac.uk
2016-01-01
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 Eulerian 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.
Using SPARK as a Solver for Modelica
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
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 solver 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 solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
New iterative solvers for the NAG Libraries
Salvini, S.; Shaw, G.
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers 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 solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Techniques to derive geometries for image-based Eulerian computations
Dillard, Seth; Buchholz, James; Vigmostad, Sarah; Kim, Hyunggun; Udaykumar, H.S.
2014-01-01
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 Eulerian 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 Eulerian setting. PMID
Development and deployment of constitutive softening routines in Eulerian hydrocodes.
Fuller, Timothy Jesse; Dewers, Thomas A.; Swan, Matthew Scot
2013-03-01
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 Eulerian hydrocode simulations. In this report, recent e orts in coupling a ceramic materials response in the post-failure regime with an Eulerian 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.
ODE System Solver W. Krylov Iteration & Rootfinding
1991-09-09
LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: (a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, (b) Within the corrector iteration,more » LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, (c) LSODKR includes the ability to find roots of given functions of the solution during the integration.« less
Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion
NASA Technical Reports Server (NTRS)
Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.
2012-01-01
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 solvers 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 Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian 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 solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver 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 solver 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 solver 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
Equation solvers for distributed-memory computers
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1994-01-01
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 solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
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/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
Parallel solvers for reservoir simulation on MIMD computers
Piault, E.; Willien, F.; Roux, F.X.
1995-12-01
We have investigated parallel solvers for reservoir simulation. We compare different solvers and preconditioners using T3D and SP1 parallel computers. We use block diagonal domain decomposition preconditioner with non-overlapping sub-domains.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
Wang, C.Y.; Zeuch, W.R.
1982-01-01
This paper describes an arbitrary Lagrangian-Eulerian 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 (Eulerian), or moved in any other prescribed manner (hybrid Lagrangian Eulerian). 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-Eulerian method.
Leung Shingyu; Qian Jianliang
2010-11-20
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian 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 Eulerian 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.
IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN EULERIAN HYDRODYNAMICS INFRASTRUCTURE IN FLASH
Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.
2012-08-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian 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 Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, 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.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian 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 Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, 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.
CASTRO: Multi-dimensional Eulerian AMR Radiation-hydrodynamics Code
NASA Astrophysics Data System (ADS)
CenterComputational Sciences; Engineering (Berkeley); Howell, Louis; Singer, Mike
2011-05-01
CASTRO is a multi-dimensional Eulerian AMR radiation-hydrodynamics code that includes stellar equations of state, nuclear reaction networks, and self-gravity. Initial target applications for CASTRO include Type Ia and Type II supernovae. CASTRO supports calculations in 1-d, 2-d and 3-d Cartesian coordinates, as well as 1-d spherical and 2-d cylindrical (r-z) coordinate systems. Time integration of the hydrodynamics equations is based on an unsplit version of the the piecewise parabolic method (PPM) with new limiters that avoid reducing the accuracy of the scheme at smooth extrema. CASTRO can follow an arbitrary number of isotopes or elements. The atomic weights and amounts of these elements are used to calculate the mean molecular weight of the gas required by the equation of state. CASTRO supports several different approaches to solving for self-gravity. The most general is a full Poisson solve for the gravitational potential. CASTRO also supports a monopole approximation for gravity, and a constant gravity option is also available. The CASTRO software is written in C++ and Fortran, and is based on the BoxLib software framework developed by CCSE.
Lagrangian and Eulerian description of bed-load particle kinematics
NASA Astrophysics Data System (ADS)
Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio
2016-04-01
The motion of bed-load sediment particles transported by a flow can be analyzed within a Lagrangian or an Eulerian 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.
Eulerian simulations of collisional effects on electrostatic plasma waves
Pezzi, Oreste; Valentini, Francesco; Perrone, Denise; Veltri, Pierluigi
2013-09-15
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 Eulerian 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.
Lagrangian, Eulerian, and Dynamically Accessible Stability of MHD flows
NASA Astrophysics Data System (ADS)
Andreussi, Tommaso; Morrison, Philip; Pegoraro, Francesco
2012-10-01
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 energy principle of Ref. [1] is introduced and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD [2] is exploited. For symmetric equilibria, the energy-Casimir principle of Ref. [3] 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 the invariants of the system, are introduced and the respective energy principle is considered. As in Ref. [4], general criteria for stability are obtained. A comparison between the three different approaches is finally presented. [4pt] [1] E.A. Frieman and M. Rotenberg, Rev. Mod. Phys., 32 898 (1960).[0pt] [2] P.J. Morrison, J.M. Greene, Phys. Rev. Lett., 45 790 (1980).[0pt] [3] T. Andreussi, P.J. Morrison, F. Pegoraro, Phys. Plasmas, 19 052102 (2012).[0pt] [4] E. Hameiri, Phys. Plasmas, 10 2643 (2003).
On Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian and Dynamically Accessible Stability
NASA Astrophysics Data System (ADS)
Andreussi, Tommaso; Morrison, Philip J.; Pegoraro, Francesco
2013-10-01
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations 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 Eulerian 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. En route to our results we describe a time-dependent relabeling transformation, which to our knowledge has not heretofore been given, that will be needed in the Lagrangian variable framework in connection with the approach considered in E. A. Frieman, M. Rotenberg, Rev. Mod. Phys. 32, 898 (1960).
Eulerian simulations of collisional effects on electrostatic plasma waves
NASA Astrophysics Data System (ADS)
Pezzi, Oreste; Valentini, Francesco; Perrone, Denise; Veltri, Pierluigi
2013-09-01
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 Eulerian 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.
Ising-like phase transition of an n-component Eulerian face-cubic model.
Ding, Chengxiang; Guo, Wenan; Deng, Youjin
2013-11-01
By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph. PMID:24329232
Ising-like phase transition of an n-component Eulerian face-cubic model
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Guo, Wenan; Deng, Youjin
2013-11-01
By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.
Aleph Field Solver Challenge Problem Results Summary.
Hooper, Russell; Moore, Stan Gerald
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched mod- eling 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 solver 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 challeng- ing problems important to Sandia's mission that Aleph was specifically designed to address.
Domain decomposition for the SPN solver MINOS
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-07-01
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 solver of the APOLLO3 (R) code. (authors)
A perspective on unstructured grid flow solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1995-01-01
This survey paper assesses the status of compressible Euler and Navier-Stokes solvers 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.
A multigrid solver for the semiconductor equations
NASA Technical Reports Server (NTRS)
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver 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 solvers, 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.
Differential geometry based solvation model I: Eulerian formulation
NASA Astrophysics Data System (ADS)
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-11-01
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to
Differential geometry based solvation model I: Eulerian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2010-11-01
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 Eulerian 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
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
NASA Astrophysics Data System (ADS)
Bo, Wurigen; Shashkov, Mikhail
2015-10-01
eW present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35,34,6]. 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. 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. In the current paper we present a new adaptive ReALE method, A-ReALE, that is based on the following design principles. First, a monitor function (or error indicator) based on the Hessian of some flow parameter(s) is utilized. Second, an equi-distribution principle for the monitor function is used as a criterion for adapting the mesh. Third, a centroidal Voronoi tessellation is used to adapt the mesh. Fourth, we scale the monitor function to avoid very small and large cells and then smooth it to permit the use of theoretical results related to weighted centroidal Voronoi tessellation. In the A-ReALE method, both number of cells and their locations are allowed to change at the rezone stage on each time step. The number of generators at each time step is chosen to guarantee the required spatial resolution in regions where monitor function reaches its maximum value. We present all details required for implementation of new adaptive A-ReALE method and demonstrate its performance in comparison with standard ReALE method on series of numerical examples.
Voids in modified gravity reloaded: Eulerian void assignment
NASA Astrophysics Data System (ADS)
Lam, Tsz Yan; Clampitt, Joseph; Cai, Yan-Chuan; Li, Baojiu
2015-07-01
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 Eulerian-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.
MILAMIN 2 - Fast MATLAB FEM solver
NASA Astrophysics Data System (ADS)
Dabrowski, Marcin; Krotkiewski, Marcin; Schmid, Daniel W.
2013-04-01
MILAMIN is a free and efficient MATLAB-based two-dimensional FEM solver utilizing unstructured meshes [Dabrowski et al., G-cubed (2008)]. The code consists of steady-state thermal diffusion and incompressible Stokes flow solvers implemented in approximately 200 lines of native MATLAB code. The brevity makes the code easily customizable. An important quality of MILAMIN is speed - it can handle millions of nodes within minutes on one CPU core of a standard desktop computer, and is faster than many commercial solutions. The new MILAMIN 2 allows three-dimensional modeling. It is designed as a set of functional modules that can be used as building blocks for efficient FEM simulations using MATLAB. The utilities are largely implemented as native MATLAB functions. For performance critical parts we use MUTILS - a suite of compiled MEX functions optimized for shared memory multi-core computers. The most important features of MILAMIN 2 are: 1. Modular approach to defining, tracking, and discretizing the geometry of the model 2. Interfaces to external mesh generators (e.g., Triangle, Fade2d, T3D) and mesh utilities (e.g., element type conversion, fast point location, boundary extraction) 3. Efficient computation of the stiffness matrix for a wide range of element types, anisotropic materials and three-dimensional problems 4. Fast global matrix assembly using a dedicated MEX function 5. Automatic integration rules 6. Flexible prescription (spatial, temporal, and field functions) and efficient application of Dirichlet, Neuman, and periodic boundary conditions 7. Treatment of transient and non-linear problems 8. Various iterative and multi-level solution strategies 9. Post-processing tools (e.g., numerical integration) 10. Visualization primitives using MATLAB, and VTK export functions We provide a large number of examples that show how to implement a custom FEM solver using the MILAMIN 2 framework. The examples are MATLAB scripts of increasing complexity that address a given
Approximate Riemann solvers for the Godunov SPH (GSPH)
NASA Astrophysics Data System (ADS)
Puri, Kunal; Ramachandran, Prabhu
2014-08-01
The Godunov Smoothed Particle Hydrodynamics (GSPH) method is coupled with non-iterative, approximate Riemann solvers for solutions to the compressible Euler equations. The use of approximate solvers 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 solvers. 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 solvers. 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 solvers are found to be suitable replacements for the iterative Riemann solver in the original GSPH scheme.
On Lagrangian and Eulerian Acceleration in Rotating and Sheared Homogeneous Turbulence
NASA Astrophysics Data System (ADS)
Jacobitz, Frank; Schneider, Kai; Bos, Wouter; Farge, Marie
2013-11-01
The Lagrangian and Eulerian acceleration properties of turbulence are of importance for problems ranging from fundamental theoretical considerations to modeling of dispersion processes. The acceleration statistics of rotating and sheared homogeneous turbulence are studied here using direct numerical simulations. The study focusses in particular on the influence of the Coriolis to shear rate ratio and also on the scale dependence of the statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian acceleration show a strong and similar influence on the rotation ratio. The flatness further quantifies this influence and yields values close to three for strong rotation. For moderate and vanishing rotation, the flatness of the Eulerian acceleration is larger than that of the Lagrangian acceleration, contrary to previous results for isotropic turbulence. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian acceleration increases as scale decreases. For strong rotation, the Eulerian acceleration is more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation.
NASA Astrophysics Data System (ADS)
Speetjens, M. F. M.; Lauret, M.; Nijmeijer, H.; Anderson, P. D.
2013-05-01
Transport of passive tracers may be described through the spatio-temporal evolution of Eulerian concentration distributions or via the geometrical composition of the Lagrangian flow structure. The present study seeks to deepen insight into the connection between the Eulerian and Lagrangian perspectives by investigating the role of Lagrangian coherent structures (LCSs) in the Eulerian concentration distributions in time-periodic and spatially-periodic mixing flows. Representation of the Eulerian transport by the mapping method, describing realistic transport problems by distribution matrices, admits a generic analysis based on matrix and graph theory. This reveals that LCSs-and the transport barriers that separate them-leave a distinct “footprint” in the eigenmode spectrum of the distribution matrix and, by proxy, of the underlying Eulerian transport operator. Transport barriers impart a block-diagonal structure upon the mapping matrix, where each block matrix A corresponds with a given LCS. Its kind is reflected in the spectrum of A; higher-order periodicity yields a distinct permutation within A. The composition of the distribution matrix versus the Lagrangian flow structure thus predicted is demonstrated by way of examples. These findings increase fundamental understanding of transport phenomena and have great practical potential for e.g. flow and mixing control.
Updates to the NEQAIR Radiation Solver
NASA Technical Reports Server (NTRS)
Cruden, Brett A.; Brandis, Aaron M.
2014-01-01
The NEQAIR code is one of the original heritage solvers 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.
DPS--a computerised diagnostic problem solver.
Bartos, P; Gyárfas, F; Popper, M
1982-01-01
The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented.
Input-output-controlled nonlinear equation solvers
NASA Technical Reports Server (NTRS)
Padovan, Joseph
1988-01-01
To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.
NASA Astrophysics Data System (ADS)
Ferrer, Esteban; Willden, Richard H. J.
2012-08-01
We present the development of a sliding mesh capability for an unsteady high order (order ⩾ 3) h/p Discontinuous Galerkin solver for the three-dimensional incompressible Navier-Stokes equations. A high order sliding mesh method is developed and implemented for flow simulation with relative rotational motion of an inner mesh with respect to an outer static mesh, through the use of curved boundary elements and mixed triangular-quadrilateral meshes. A second order stiffly stable method is used to discretise in time the Arbitrary Lagrangian-Eulerian form of the incompressible Navier-Stokes equations. Spatial discretisation is provided by the Symmetric Interior Penalty Galerkin formulation with modal basis functions in the x-y plane, allowing hanging nodes and sliding meshes without the requirement to use mortar type techniques. Spatial discretisation in the z-direction is provided by a purely spectral method that uses Fourier series and allows computation of spanwise periodic three-dimensional flows. The developed solver is shown to provide high order solutions, second order in time convergence rates and spectral convergence when solving the incompressible Navier-Stokes equations on meshes where fixed and rotating elements coexist. In addition, an exact implementation of the no-slip boundary condition is included for curved edges; circular arcs and NACA 4-digit airfoils, where analytic expressions for the geometry are used to compute the required metrics. The solver capabilities are tested for a number of two dimensional problems governed by the incompressible Navier-Stokes equations on static and rotating meshes: the Taylor vortex problem, a static and rotating symmetric NACA0015 airfoil and flows through three bladed cross-flow turbines. In addition, three dimensional flow solutions are demonstrated for a three bladed cross-flow turbine and a circular cylinder shadowed by a pitching NACA0012 airfoil.
Eulerian and Lagrangian Analysis of a Simulated unsteady Flow Behind a Circular cylinder
NASA Astrophysics Data System (ADS)
Holmes, Keith; Green, Melissa
2012-11-01
The unsteady wake behind a circular cylinder is numerically simulated and analyzed utilizing various Eulerian methods and the Lagrangian finite-time Lyapunov exponent (FTLE). The objective is to identify and distinguish among shed vortices in the wake, and particular attention is given to the near wake immediately downstream of the cylinder. The Eulerian methods capably determine regions of the flow associated with greatest magnitude of vorticity in the near wake, as has been shown previously. Ridges of the FTLE field are able to objectively identify structures in the near wake by outlining the boundaries between vortices. This includes boundaries among structures of the same sign, a distinction not possible using the Eulerian methods. The formation of these boundaries help to distinguish between structures still developing around the cylinder surface and those that have been shed from the cylinder. Syracuse University
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
NASA Astrophysics Data System (ADS)
Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.
2016-01-01
An approach for Eulerian-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 Eulerian 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 Eulerian 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.
Simulation on gasification of forestry residues in fluidized beds by Eulerian-Lagrangian approach.
Xie, Jun; Zhong, Wenqi; Jin, Baosheng; Shao, Yingjuan; Liu, Hao
2012-10-01
A comprehensive three-dimensional numerical model is developed to simulate forestry residues gasification in a fluidized bed reactor using Eulerian-Lagrangian approach. The complex granular flow behaviors and chemical reaction characteristics are addressed simultaneously. The model uses an Eulerian 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 Eulerian 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.
NASA Astrophysics Data System (ADS)
Clayton, John
2013-06-01
Thermodynamic potentials of conventional Lagrangian nonlinear elasticity incorporate the right Cauchy-Green strain, itself a function of the deformation gradient. In this work, an alternative theory is advanced for anisotropic solids incorporating an Eulerian strain, in material coordinates, that is a function of the inverse deformation gradient. This strain, which has historically shown promise for hydrostatic compression, is applied to problems with both volume change and shear, e.g. shock compression. A general theory accounting for elastic and plastic deformations is formulated, extending a purely elastic theory developed recently. A solution for the anisotropic shock response is derived for solids with an internal energy function quartic in strain and linear in entropy. Predictions of Eulerian and Lagrangian theories for single crystal ceramics-quartz, sapphire, and diamond-and metals-aluminum, copper, and magnesium-are compared, with Eulerian solutions demonstrating key advantages in some cases.
Using the scalable nonlinear equations solvers package
Gropp, W.D.; McInnes, L.C.; Smith, B.F.
1995-02-01
SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.
On code verification of RANS solvers
NASA Astrophysics Data System (ADS)
Eça, L.; Klaij, C. M.; Vaz, G.; Hoekstra, M.; Pereira, F. S.
2016-04-01
This article discusses Code Verification of Reynolds-Averaged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddy-viscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple one-dimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for non-orthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.
NASA Astrophysics Data System (ADS)
Diggs, Angela; Balachandar, Sivaramakrishnan
2015-06-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-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 Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian 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 Eulerian 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.
Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows
NASA Technical Reports Server (NTRS)
He, Guowei; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The Eulerian 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 Eulerian 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.
Equations of nonlinear dynamics of elastic shells in cylindrical Eulerian coordinates
NASA Astrophysics Data System (ADS)
Zubov, L. M.
2016-05-01
The equations of dynamics of elastic shells subjected to large deformations are formulated. The Eulerian coordinates on a circular cylinder and time are accepted as independent variables, and one of the unknown functions is the distance from a point of the shell surface to the cylinder axis. The equations of dynamics of nonlinearly elastic shells in the Eulerian coordinates are convenient for exact formulation of the problem on the interaction of strongly deformable shells with moving fluids and gases. The equations obtained can be used for dynamic calculations of fluids and gases flowings in pipelines, blood vessels, hoses, and other nonlinearly deformable thin-walled tubular elements of constructions.
jShyLU Scalable Hybrid Preconditioner and Solver
2012-09-11
ShyLU is numerical software to solve sparse linear systems of equations. ShyLU uses a hybrid direct-iterative Schur complement method, and may be used either as a preconditioner or as a solver. ShyLU is parallel and optimized for a single compute Solver node. ShyLU will be a package in the Trilinos software framework.
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver 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 solver algorithms for these types of problems. The results of numerical experiments will be presented.
Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers
NASA Technical Reports Server (NTRS)
Guru Prasad, K.; Kane, J. H.
1992-01-01
The computational advantages associated with the utilization of preconditined iterative equation solvers 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 solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.
A real-time impurity solver for DMFT
NASA Astrophysics Data System (ADS)
Kim, Hyungwon; Aron, Camille; Han, Jong E.; Kotliar, Gabriel
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 solvers have been developed over the past two decades to tackle equilibrium situations, the status of real-time impurity solvers that could compete with Matsubara-frequency solvers and be readily generalizable to non-equilibrium situations is still premature. We present a real-time solver 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 solver 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.
Parallel solver for trajectory optimization search directions
NASA Technical Reports Server (NTRS)
Psiaki, M. L.; Park, K. H.
1992-01-01
A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the search step solver. This is one piece of an algorithm whose overall goal is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter or the National Aerospace Plane. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration to determine the search step. In the trajectory optimization case, the QP has a special dynamic programming structure. The algorithm exploits this special structure with a divide- and conquer type of parallel implementation. The algorithm solves a (p.N)-stage problem on N processors in O(p + log2 N) operations. The algorithm yields a factor of 8 speed-up over the fastest known serial algorithm when solving a 1024-stage test problem on 32 processors.
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Xu, Jinchao
2014-12-01
In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.
Optimising a parallel conjugate gradient solver
Field, M.R.
1996-12-31
This work arises from the introduction of a parallel iterative solver 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.
General purpose nonlinear system solver based on Newton-Krylov method.
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
NASA Astrophysics Data System (ADS)
Liu, Yan; Shen, Weidong; Tian, Baolin; Mao, De-kang
2015-03-01
We develop a new and more general formula for the construction of two dimensional nodal Riemann solver for a cell-centered Lagrangian scheme developed by Maire and his co-workers which allows us to use general one dimensional Riemann solvers that have intermediate velocity and pressure in the construction. The old formula for the scheme used in the papers of Maire et al. is only a special case of our new formula. We present an entropy discussion, which indicates that the schemes with nodal solvers constructed following the old formula, which can only use the 1D Riemann solvers satisfying our strong entropy condition, are usually numerically very dissipative. To develop numerically less dissipative schemes we introduce a so-called weak entropy condition, and present a one dimensional Riemann solver that satisfies the weak entropy condition but not the strong entropy condition. Analysis shows that the scheme using this 1D solver is numerically less dissipative than the schemes using solvers satisfying the strong condition. Finally, several numerical examples are presented to show that our new formula works well and the scheme using the one dimensional solver satisfying the weak entropy condition improves the accuracy in smooth region, resolution around rarefaction waves and two dimensional symmetry; however it sometimes produces small velocity oscillations and mesh distortions.
Eulerian mean surface velocity field derived by combining drifter and satellite altimeter data
NASA Astrophysics Data System (ADS)
Uchida, Hiroshi; Imawaki, Shiro
2003-03-01
Combining surface drifter and satellite altimeter data,we estimate Eulerian mean sea-surface velocity with a resolution of quarter degrees in both latitude and longitude. The Eulerian mean velocity is calculated by subtracting the altimeter-derived velocity anomaly (i.e., deviation from the temporal mean) at the time when a drifter measured the surface velocity, from this drifter-measured velocity. The method is applied to the surface flow of the North Pacific, using TOPEX/POSEIDON and ERS-1/2 altimeter data, and WOCE-TOGA surface drifter data obtained during October 1992 to January 2001. The estimated Eulerian mean velocities for the Kuroshio south of Japan and the Kuroshio Extension region tend to be smaller than simple averages of drifter-derived velocities by 20 to 50 cm sec-1. The instantaneous velocities are obtained every ten days as sums of the Eulerian mean velocities and velocity anomalies. They agree well with in situ surface velocities measured by acoustic Doppler current profilers.
Eulerian simulation of the perforation of aluminum plates by nondeforming projectiles
Silling, S.A.
1992-03-01
A new algorithm for the treatment of sliding interfaces between solids with or without friction in an Eulerian 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.
The "Preface to the Special Edition on Model Evaluation: Evaluation of Urban and Regional Eulerian 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...
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers 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 solvers 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 solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver 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.
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver 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 solver 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)
Multi-GPU kinetic solvers using MPI and CUDA
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2014-12-01
This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the DSMC module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with adaptive Mesh Refinement (AMR). Double digit speedup on single GPU and good scaling for multi-GPU has been demonstrated.
Generic task problem solvers in Soar
NASA Technical Reports Server (NTRS)
Johnson, Todd R.; Smith, Jack W., Jr.; Chandrasekaran, B.
1989-01-01
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 solvers 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.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
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 solver. 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.
NASA Technical Reports Server (NTRS)
Raju, Manthena S.
1998-01-01
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) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. 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.
Performance of NASA Equation Solvers on Computational Mechanics Applications
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1996-01-01
This paper describes the performance of a new family of NASA-developed equation solvers used for large-scale (i.e. 551,705 equations) structural analysis. To minimize computer time and memory, the solvers 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 solvers, 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 solver timings reside on World Wide Web with a challenge to beat them.
Two-dimensional time dependent Riemann solvers for neutron transport
Brunner, Thomas A. . E-mail: tabrunn@sandia.gov; Holloway, James Paul
2005-11-20
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P{sub 1} equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A.
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver 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 solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. 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.
A survey of deterministic solvers for rarefied flows (Invited)
NASA Astrophysics Data System (ADS)
Mieussens, Luc
2014-12-01
Numerical simulations of rarefied gas flows are generally made with DSMC methods. Up to a recent period, deterministic numerical methods based on a discretization of the Boltzmann equation were restricted to simple problems (1D, linearized flows, or simple geometries, for instance). In the last decade, several deterministic solvers have been developed in different teams to tackle more complex problems like 2D and 3D flows. Some of them are based on the full Boltzmann equation. Solving this equation numerically is still very challenging, and 3D solvers are still restricted to monoatomic gases, even if recent works have proved it was possible to simulate simple flows for polyatomic gases. Other solvers are based on simpler BGK like models: they allow for much more intensive simulations on 3D flows for realistic geometries, but treating complex gases requires extended BGK models that are still under development. In this paper, we discuss the main features of these existing solvers, and we focus on their strengths and inefficiencies. We will also review some recent results that show how these solvers can be improved: - higher accuracy (higher order finite volume methods, discontinuous Galerkin approaches) - lower memory and CPU costs with special velocity discretization (adaptive grids, spectral methods) - multi-scale simulations by using hybrid and asymptotic preserving schemes - efficient implementation on high performance computers (parallel computing, hybrid parallelization) Finally, we propose some perspectives to make these solvers more efficient and more popular.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
Darlington, R
1999-12-01
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian 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.
Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
Villa, Eleonora; Maino, Davide; Matarrese, Sabino E-mail: sabino.matarrese@pd.infn.it
2014-06-01
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian 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 Eulerian to the Lagrangian frame in the Newtonian approximation.
NASA Astrophysics Data System (ADS)
Rubin, M. B.; Nadler, B.
2016-03-01
An Eulerian formulation has been developed for the constitutive response of a group of materials that includes anisotropic elastic and viscoelastic solids and viscous fluids. The material is considered to be a composite of an elastic solid and a viscous fluid. Evolution equations are proposed for a triad of vectors m i that represent the stretches and orientations of material line elements in the solid component. Evolution equations for an orthonormal triad of vectors s i are also proposed to characterize anisotropy of the fluid component. In particular, for an elastic solid it is shown that the material response is totally characterized by the functional form of the strain energy and by the current values of m i , which are measurable in the current state of the material. Moreover, it is shown that the proposed Eulerian formulation removes unphysical arbitrariness of the choice of the reference configuration in the standard formulation of constitutive equations for anisotropic elastic solids.
Simulation of the dispersion of nuclear contamination using an adaptive Eulerian grid model.
Lagzi, I; Kármán, D; Turányi, T; Tomlin, A S; Haszpra, L
2004-01-01
Application of an Eulerian model using layered adaptive unstructured grids coupled to a meso-scale meteorological model is presented for modelling the dispersion of nuclear contamination following the accidental release from a single but strong source to the atmosphere. The model automatically places a finer resolution grid, adaptively in time, in regions were high spatial numerical error is expected. The high-resolution grid region follows the movement of the contaminated air over time. Using this method, grid resolutions of the order of 6 km can be achieved in a computationally effective way. The concept is illustrated by the simulation of hypothetical nuclear accidents at the Paks NPP, in Central Hungary. The paper demonstrates that the adaptive model can achieve accuracy comparable to that of a high-resolution Eulerian model using significantly less grid points and computer simulation time. PMID:15149762
The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves
NASA Technical Reports Server (NTRS)
Takahashi, M.; Uryu, M.
1981-01-01
The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane. It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant. Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height. In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height. In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations.
Simulation of an orifice scrubber performance based on Eulerian/Lagrangian method.
Mohebbi, A; Taheri, M; Fathikaljahi, J; Talaie, M R
2003-06-27
A mathematical model based on Eulerian/Lagrangian method has been developed to predict particle collection efficiency from a gas stream in an orifice scrubber. This model takes into account Eulerian approach for particle dispersion, Lagrangian approach for droplet movement and particle-source-in-cell (PSI-CELL) model for calculating droplet concentration distribution. In order to compute fluid velocity profiles, the normal k-epsilon turbulent flow model with inclusion of body force due to drag force between fluid and droplets has been used. Experimental data of Taheri et al. [J. Air Pollut. Control Assoc. 23 (11) (1973) 963] have been used to test the results of the mathematical model. The results from the model are in good agreement with the experimental data. After validating the model the effect of operating parameters such as liquid to gas flow rate ratio, gas velocity at orifice opening, and particle diameter were obtained on the collection efficiency.
Simulations of needle insertion by using a Eulerian hydrocode FEM and the experimental validations.
Kataoka, Hiroyuki; Noda, Shigeho; Yokota, Hideo; Takagi, Shu; Himeno, Ryutaro; Okazawa, Shigenobu
2008-01-01
In this paper, simulations for needle insertion were performed by using a novel Eulerian hydrocode FEM, which was adaptive for large deformation and tissue fracture. We also performed experiments for the same needle insertion with silicon rubbers and needles, which had conical tips of different angles in order to investigate the accuracy of the simulations. The resistance forces in the simulations accurately followed those in the experiments until the conical portion of the needle was inside the rubbers, and the validation of the Eulerian hydrocode was revealed. However, the present simulation showed that after the conical portion was inside the tissue, the simulated resistance forces became lower than the experimental ones. The proportional increase of the friction forces and the roughly flatness of the tip force along the time were simulated. It was predicted that the tightening force along the needle side was underestimated. PMID:18982649
Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows
NASA Astrophysics Data System (ADS)
Barlow, Andrew J.; Maire, Pierre-Henri; Rider, William J.; Rieben, Robert N.; Shashkov, Mikhail J.
2016-10-01
This paper reviews recent developments in Arbitrary Lagrangian Eulerian (ALE) methods for modeling high speed compressible multimaterial flows in complex geometry on general polygonal meshes. We only consider the indirect ALE approach which consists of three key stages: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, in which the nodes of the computational mesh are moved to improve grid quality; and a remapping stage, in which the Lagrangian solution is transferred to the rezoned mesh.
A robust multilevel simultaneous eigenvalue solver
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1993-01-01
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 solver. 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.
A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing
NASA Technical Reports Server (NTRS)
Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo
2009-01-01
The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers 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 solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.
Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie
2016-01-01
The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian 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 Eulerian 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 Eulerian 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 Eulerian 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 Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian 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 Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian 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. PMID:26871161
NASA Astrophysics Data System (ADS)
Jacobitz, Frank G.; Schneider, Kai; Bos, Wouter J. T.; Farge, Marie
2016-01-01
The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian 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 Eulerian 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 Eulerian 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 Eulerian 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 Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian 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 Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian 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.
NASA Astrophysics Data System (ADS)
Fan, Xiaofeng; Wang, Jiangfeng
2016-06-01
The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.
Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments
NASA Astrophysics Data System (ADS)
Chitta, Subhashini; Steinhoff, John
2015-11-01
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 Eulerian 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 Eulerian solution of the wave equation. However, conventional Eulerian 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.
Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow
NASA Astrophysics Data System (ADS)
Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro
2010-03-01
For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full Eulerian finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the Eulerian frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present Eulerian approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.
An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces
NASA Astrophysics Data System (ADS)
Pooley, Benjamin C.; Robinson, James C.
2016-06-01
In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-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 Eulerian-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 Eulerian-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.
Unit physics performance of a mix model in Eulerian fluid computations
Vold, Erik; Douglass, Rod
2011-01-25
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 Eulerian 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 Eulerian 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 Eulerian 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.
On Eulerian constitutive equations for modeling growth and residual stresses in arteries.
Volokh, K Y
2005-06-01
Recently Volokh and Lev (2005) argued that residual stresses could appear in growing arteries because of the arterial anisotropy. This conclusion emerged from a continuum mechanics theory of growth of soft biological tissues proposed by the authors. This theory included Lagrangian constitutive equations, which were formulated directly with respect to the reference configuration. Alternatively, it is possible to formulate Eulerian constitutive equations with respect to the current configuration and to 'pull them back' to the reference configuration. Such possibility is examined in the present work. The Eulerian formulation of the constitutive equations is used for a study of arterial growth. It is shown, particularly, that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery in vitro as it is observed in experiments. It is remarkable that the results of the present study, based on the Eulerian constitutive equations, are very similar to the results of Volokh and Lev (2005), based on the Lagrangian constitutive equations. This strengthens the authors' argument that anisotropy is a possible reason for accumulation of residual stresses in arteries. This argument appears to be invariant with respect to the mathematical description.
NASA Astrophysics Data System (ADS)
Daude, F.; Galon, P.
2016-01-01
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-Eulerian 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 solver 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 solver. 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.
Quantitative analysis of numerical solvers for oscillatory biomolecular system models
Quo, Chang F; Wang, May D
2008-01-01
Background This article provides guidelines for selecting optimal numerical solvers 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 solvers 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 solvers. We use MATLAB numerical solvers because they are optimized and widely used by the modeling community. We have also conducted a systematic study of numerical solver 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 solvers. Thus, it is important to intelligently select numerical solvers 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 solver(s) 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 solvers with quantitative performance assessment metric, we show that it is possible
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian 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 (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian 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 Eulerian 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 Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
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 Eulerian 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 Eulerian 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
EUPDF-II: An Eulerian Joint Scalar Monte Carlo PDF Module : User's Manual
NASA Technical Reports Server (NTRS)
Raju, M. S.; Liu, Nan-Suey (Technical Monitor)
2004-01-01
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 solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with 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 solvers. The source code of EUPDF-II will be available with National Combustion Code (NCC) as a complete package.
Performance Models for the Spike Banded Linear System Solver
Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; Grama, Ananth
2011-01-01
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 solvers 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 solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers 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 solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, 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 solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. 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
The novel high-performance 3-D MT inverse solver
NASA Astrophysics Data System (ADS)
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver 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 solver. As a forward modelling engine a modern scalable solver 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 solver 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.
Adaptive kinetic-fluid solvers for heterogeneous computing architectures
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2015-12-01
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 Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers 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 solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver 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.
A multiple right hand side iterative solver for history matching
Killough, J.E.; Sharma, Y.; Dupuy, A.; Bissell, R.; Wallis, J.
1995-12-31
History matching of oil and gas reservoirs can be accelerated by directly calculating the gradients of observed quantities (e.g., well pressure) with respect to the adjustable reserve parameters (e.g., permeability). This leads to a set of linear equations which add a significant overhead to the full simulation run without gradients. Direct Gauss elimination solvers can be used to address this problem by performing the factorization of the matrix only once and then reusing the factor matrix for the solution of the multiple right hand sides. This is a limited technique, however. Experience has shown that problems with greater than few thousand cells may not be practical for direct solvers because of computation time and memory limitations. This paper discusses the implementation of a multiple right hand side iterative linear equation solver (MRHS) for a system of adjoint equations to significantly enhance the performance of a gradient simulator.
Gpu Implementation of a Viscous Flow Solver on Unstructured Grids
NASA Astrophysics Data System (ADS)
Xu, Tianhao; Chen, Long
2016-06-01
Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.
Two Solvers for Tractable Temporal Constraints with Preferences
NASA Technical Reports Server (NTRS)
Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)
2002-01-01
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 solvers based on two different approaches for solving the same tractable subclass. For each solver 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 solvers highlighting the tradeoff between performance and representational power.
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
NASA Astrophysics Data System (ADS)
Gonzalez, Juan; Núñez, Rafael C.
2009-07-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
Numerical System Solver Developed for the National Cycle Program
NASA Technical Reports Server (NTRS)
Binder, Michael P.
1999-01-01
As part of the National Cycle Program (NCP), a powerful new numerical solver 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 solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.
Profile solver in C for finite element equations
NASA Astrophysics Data System (ADS)
Hededal, O.; Krenk, S.
1994-08-01
This paper presents an efficient, pointer based profile solver with standard matrix indexing. Constrained equations Ax = b where x contains known and unknown values are solved and the full vectors x and b are obtained. Pseudo-code algorithms are formulated for a row oriented form of the LDL(sup T) factorization and implemented directly as a C code. The solver is implemented in C because of the close relation between two-dimensional arrays and pointers which makes it possible to write a clear and efficient code.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (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 Eulerian 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 Eulerian 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.
Preliminary Benchmarking of Plinian Eruption Simulations Using an Adaptive Grid Eulerian Technique
NASA Astrophysics Data System (ADS)
Peterson, A. H.; Ogden, D. E.; Wohletz, K. H.; Gisler, G.; Glatzmaier, G. A.
2005-12-01
The SAGE (SAIC Adaptive Grid Eulerian) code is an Eulerian 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-Eulerian 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.
A Eulerian-Lagrangian Model to Simulate Two-Phase/Particulate Flows
NASA Technical Reports Server (NTRS)
Apte, S. V.; Mahesh, K.; Lundgren, T.
2003-01-01
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 Eulerian-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 Eulerian-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 Eulerian-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.
Lagrangian and arbitrary Lagrangian Eulerian simulations of complex roll-forming processes
NASA Astrophysics Data System (ADS)
Crutzen, Yanick; Boman, Romain; Papeleux, Luc; Ponthot, Jean-Philippe
2016-04-01
The Arbitrary Lagrangian Eulerian (ALE) formalism is a breakthrough technique in the numerical simulation of the continuous-type roll-forming process. In contrast to the classical Lagrangian approach, the ALE formalism can compute the hopefully stationary state for the entire mill length with definitely effortless set-up tasks thanks to a nearly-stationary mesh. In this paper, advantages of ALE and Lagrangian formalisms are extensively discussed for simulating such continuous-type processes. Through a highly complex industrial application, the ease of use of ALE modelling is illustrated with the in-house code METAFOR. ALE and Lagrangian results are in good agreement with each other.
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
NASA Astrophysics Data System (ADS)
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
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-Eulerian (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.
The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
Leung, Shingyu
2013-12-15
We propose a simple Eulerian approach to compute the moderate to long time flow map for approximating the Lyapunov exponent of a (periodic or aperiodic) dynamical system. The idea is to generalize a recently proposed backward phase flow method which is specially designed for long time level set propagation. Unlike the original phase flow method or the backward phase flow method, which is applicable only to autonomous systems, the current approach can also be applied to any time-dependent (periodic or aperiodic) flow. We will discuss the stability of the proposed method. Numerical examples will be given to demonstrate the effectiveness of the algorithm.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
NASA Astrophysics Data System (ADS)
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Elman, Howard C
2013-01-27
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 solvers for models of computational fluid dynamics (CFD).
Intellectual Abilities That Discriminate Good and Poor Problem Solvers.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
1981-01-01
This study compared good and poor fourth-grade problem solvers 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. (MP)
Coordinate Projection-based Solver for ODE with Invariants
2008-04-08
CPODES is a general purpose (serial and parallel) solver 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.
NASA Astrophysics Data System (ADS)
Ergun, Sule
In the case of a postulated loss of coolant accident (LOCA) in a nuclear reactor, an accurate prediction of clad temperature is needed to determine the safety margins. The large break LOCA analyses can be divided in to three time periods. These periods are blowdown, refill and reflood. During the blowdown and reflood phases of the LOCA, when the local void fraction is greater than 80% and the wall is at a temperature above minimum film boiling temperature (Tmin), heat is transferred from the fuel rod to a continuous vapor flow with dispersed droplets. The high void fraction mixture of droplets and vapor provide cooling to prevent the clad temperature from exceeding the safety limit. The heat transfer process for high void fraction mixture is called dispersed flow film boiling (DFFB). This thesis has been modeled DFFB in the reflood phase of a LOCA in a pressurized water reactor (PWR) rod bundle. In this study, the modifications and modification requirements for the COBRA-TF code to obtain a five field Eulerian - Eulerian modeling for two-phase DFFB is described. COBRA-TF is a best estimate code developed for the rod bundle analysis and has four fields, namely, vapor, entrained drop and continuous liquid film. COBRA-TF has a detailed reflood package which takes effect of spacer grids on heat transfer into account. This study has a detailed description of code's solution scheme and the models used for dispersed flow film boiling. The dispersed flow film boiling heat transfer model of the COBRA-TF code has been modified by adding a small droplet field to the code as the fifth field. The effect of smaller, thermally more active droplets on heat, mass and momentum transfer during DFFB has been modeled. Since the large drop break up due to spacer grids is one of the reasons for small droplet generation, the spacer grid models of the COBRA-TF have been revised and modified. In addition to small droplet generation, the spacer grid rewet is an important aspect of heat
Candy, J.; Waltz, R.E.
2006-03-15
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 Eulerian 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 Eulerian 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.
Towards Modeling Local Foam Drainage Using the Arbitrary Lagrangian Eulerian Method
NASA Astrophysics Data System (ADS)
Brandon, Andrew; Ananth, Ramagopal
2014-11-01
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 Eulerian 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 Eulerian method, the novel method used for moving the domain in time, and results from this model development effort.
Numerical Simulation of the Friction Stir Welding Process Using Coupled Eulerian Lagrangian Method
NASA Astrophysics Data System (ADS)
Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.
2016-08-01
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 Eulerian 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 Eulerian Lagrangian method.
Reuge, N; Cadoret, L.; Pannala, Sreekanth; Syamlal, M; Coufort, C; Caussat, B
2008-01-01
Computational fluid dynamic (CFD) models must be thoroughly validated before they can be used with confidence for designing fluidized bed reactors. In this study, validation data were collected from a fluidized bed of (Geldart's group B) alumina particles operated at different gas velocities involving two fluidization hydrodynamic regimes (bubbling and slugging). The bed expansion, height of bed fluctuations, and frequency of fluctuations were measured from a videos of the fluidized bed. The Eulerian-Eulerian two fluid model MFIX was then used to simulate the experiments. Two different models for the particle stresses - Schaeffer (Syamlal et al., (1993), Schaeffer (1987)) and Princeton (Srivastava and Sundaresan (2003)) models - and different values of the restitution coefficient and internal angle of friction were evaluated. 3-D simulations are required for getting quantitative and qualitative agreement with experimental data. The results from the Princeton model are in better agreement with data than from the Schaeffer model. Both free-slip and Johnson-Jackson boundary conditions give nearly identical results. An increase in e from 0.8 to 1 leads to larger bed expansions and lower heights of fluctuations in the bubbling regime whereas it leads to unchanged bed expansion and to a massive reduction in the height of fluctuations in the slugging regime. The angle of internal friction (φ) in the range 10 -40 does not affect the bed expansion, but its reduction significantly reduces the height of fluctuations.
Modeling of combustion processes of stick propellants via combined Eulerian-Lagrangian approach
NASA Technical Reports Server (NTRS)
Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.
1988-01-01
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 Eulerian-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 Eulerian 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.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
NASA Astrophysics Data System (ADS)
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers 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 solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' 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 solvers. 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).
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers 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 solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' 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 solvers. 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)
Migration of vectorized iterative solvers to distributed memory architectures
Pommerell, C.; Ruehl, R.
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. 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 solvers 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 solvers 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 solvers 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 solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj
2010-01-01
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) solvers. Z3 is a state-of-the-art SMT solver. 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 solvers, including the solver 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 solvers. Proceedings
Efficient three-dimensional Poisson solvers in open rectangular conducting pipe
NASA Astrophysics Data System (ADS)
Qiang, Ji
2016-06-01
Three-dimensional (3D) Poisson solver 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 solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers 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 solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.
Eulerian frequency analysis of structural vibrations from high-speed video
NASA Astrophysics Data System (ADS)
Venanzoni, Andrea; De Ryck, Laurent; Cuenca, Jacques
2016-06-01
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 Eulerian 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 Eulerian 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 Eulerian 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
ASHEE: a compressible, Equilibrium-Eulerian model for volcanic ash plumes
NASA Astrophysics Data System (ADS)
Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.
2015-10-01
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 Eulerian 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 Eulerian), is significantly faster than the N-phase Eulerian 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
ASHEE-1.0: a compressible, equilibrium-Eulerian model for volcanic ash plumes
NASA Astrophysics Data System (ADS)
Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.
2016-02-01
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 Eulerian transport equations 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, valid for low-concentration regimes (particle volume fraction less than 10-3) and particle Stokes number (St - i.e., the ratio between relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas-particle non-equilibrium effects. Direct Numerical Simulation accurately reproduces the dynamics of isotropic, compressible turbulence in subsonic regimes. 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 the presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce the 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 the 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 model reduces to the so-called dusty-gas model. However
A parallel-vector equation solver for unsymmetric matrices on supercomputers
NASA Technical Reports Server (NTRS)
Qin, J.; Mei, C.; Nguyen, D. T.; Gray, C. E., Jr.
1991-01-01
A parallel-vector unsymmetric equation solver is presented. The solver exploits both vector and parallel capabilities provided by modern, high-performance supercomputers. A special storage scheme and loop-unrolling technique are used to optimize the vector performance. A parallel FORTRAN language is used to develop the solver on the CRAY 2 and CRAY Y-MP multiple processing computer environment. Three numerical examples are presented which demonstrate the efficiency and accuracy of this equation solver. The first two examples demonstrate the improved performance, and the third example utilizes the proposed solver to solve a highly nonlinear, unsymmetric finite element formulation for panel flutter.
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2015-03-15
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, Eulerian, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected.
Carter, H H; Okubo, A; Wilson, R E; Sanderson, B; Pritchard, D W
1980-07-01
This research project addresses a fundamental problem in turbulence theory, the relation between Lagrangian and Eulerian 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 Eulerian 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 Eulerian 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 Eulerian (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.
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
NASA Astrophysics Data System (ADS)
Leung, Shingyu; Qian, Jianliang
2010-11-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian 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 Eulerian 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.
Rethinking Electrostatic Solvers in Particle Simulations for the Exascale Era
NASA Astrophysics Data System (ADS)
Deca, Jan; Markidis, Stefano; Lapenta, Giovanni; Járleberg, Erik; Apostolov, Rossen; Laure, Erwin
2012-10-01
In preparation to the exascale era, an alternative approach to calculate the electrostatic forces in Particle Mesh (PM) methods is proposed. While the traditional techniques are based on the calculation of the electrostatic potential by solving the Poisson equation, in the new approach the electric field is calculated by solving Ampère's law. When the Ampere's law is discretized explicitly in time, the electric field values on the mesh are simply updated from the previous values. In this way, the electrostatic solver becomes an embarrassingly parallel problem, making the algorithm extremely scalable and suitable for exascale computing platforms. An implementation PM code with the new electrostatic solver is presented to show that the proposed method produces correct results. It is a very promising algorithm for exascale PM simulations.
LDRD report : parallel repartitioning for optimal solver performance.
Heaphy, Robert; Devine, Karen Dragon; Preis, Robert; Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar
2004-02-01
We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver 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.
Benchmarking ICRF Full-wave Solvers for ITER
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
2011-01-06
Abstract Benchmarking of full-wave solvers 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 solver 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.
An exact solver for the DCJ median problem.
Zhang, Meng; Arndt, William; Tang, Jijun
2009-01-01
The "double-cut-and-join" (DCJ) model of genome rearrangement proposed by Yancopoulos et al. uses the single DCJ operation to account for all genome rearrangement events. Given three signed permutations, the DCJ median problem is to find a fourth permutation that minimizes the sum of the pairwise DCJ distances between it and the three others. In this paper, we present a branch-and-bound method that provides accurate solution to the multichromosomal DCJ median problems. We conduct extensive simulations and the results show that the DCJ median solver performs better than other median solvers for most of the test cases. These experiments also suggest that DCJ model is more suitable for real datasets where both reversals and transpositions occur.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
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 solvers 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 solvers.
Scalable Out-of-Core Solvers on Xeon Phi Cluster
D'Azevedo, Ed F; Chan, Ki Shing; Su, Shiquan; Wong, Kwai
2015-01-01
This paper documents the implementation of a distributive out-of-core (OOC) solver 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 solver 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.
A functional implementation of the Jacobi eigen-solver
Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E. )
1993-01-01
In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver 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-solvers to the functional sub-set of the language.
A functional implementation of the Jacobi eigen-solver
Boehm, A.P.W.; Hiromoto, R.E.
1993-02-01
In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver 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-solvers to the functional sub-set of the language.
A spectral Poisson solver for kinetic plasma simulation
NASA Astrophysics Data System (ADS)
Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf
2011-10-01
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 solver 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 solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver 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 solver 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.
On improving linear solver performance: a block variant of GMRES
Baker, A H; Dennis, J M; Jessup, E R
2004-05-10
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver 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.
Verification and Validation Studies for the LAVA CFD Solver
NASA Technical Reports Server (NTRS)
Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.
2013-01-01
The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver 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 solver 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.
An Upwind Solver for the National Combustion Code
NASA Technical Reports Server (NTRS)
Sockol, Peter M.
2011-01-01
An upwind solver 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 solver 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.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Kolev, Tzanio V.; Vassilevski, Panayot S.
2012-12-18
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 solver (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 solver 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.
Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics
NASA Astrophysics Data System (ADS)
Spiegelman, M. W.; May, D.; Wilson, C. R.
2014-12-01
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 solvers. 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
Recent developments of the arbitrary Lagrangian-Eulerian containment code ALICE-II. [LMFBR
Wang, C.Y.; Zeuch, W.R.
1983-01-01
The ANL arbitrary Lagrangian Eulerian 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.
NASA Astrophysics Data System (ADS)
Anderson, Robert; Pember, Richard; Elliott, Noah
2001-11-01
We present a method, ALE-AMR, for modeling unsteady compressible flow that combines a staggered grid arbitrary Lagrangian-Eulerian (ALE) scheme with structured local adaptive mesh refinement (AMR). The ALE method is a three step scheme on a staggered grid of quadrilateral cells: Lagrangian advance, mesh relaxation, and remap. The AMR scheme uses a mesh hierarchy that is dynamic in time and is composed of nested structured grids of varying resolution. The integration algorithm on the hierarchy is a recursive procedure in which the coarse grids are advanced a single time step, the fine grids are advanced to the same time, and the coarse and fine grid solutions are synchronized. The novel details of ALE-AMR are primarily motivated by the need to reconcile and extend AMR techniques typically employed for stationary rectangular meshes with cell-centered quantities to the moving quadrilateral meshes with staggered quantities used in the ALE scheme. Solutions of several test problems are discussed.
Direct numerical simulation of rigid bodies in multiphase flow within an Eulerian framework
NASA Astrophysics Data System (ADS)
Rauschenberger, P.; Weigand, B.
2015-06-01
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 Eulerian 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.
Anderson, R W; Pember, R B; Elliott, N S
2001-10-22
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (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.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
A new method that combines staggered grid arbitrary Lagrangian-Eulerian (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.
BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts
NASA Astrophysics Data System (ADS)
Polettini, Matteo
2015-09-01
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 Eulerian 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.
Implementation of a High Explosive Equation of State into an Eulerian Hydrocode
NASA Astrophysics Data System (ADS)
Littlefield, David L.; Baker, Ernest L.
2004-07-01
The implementation of a high explosive equation of state into the Eulerian hydrocode CTH is described. The equation of state is an extension to JWL referred to as JWLB, and is intended to model the thermodynamic state of detonation products from a high explosive reaction. The EOS was originally cast in a form p = p(ρ, e), where p is the pressure, ρ is the density and e is the internal energy. However, the target application code requires an EOS of the form p = p(ρ, T), where T is the temperature, so it was necessary to reformulate the EOS in a thermodynamically consistent manner. A Helmholtz potential, developed from the original EOS, insures this consistency. Example calculations are shown that illustrate the veracity of this implementation.
NASA Astrophysics Data System (ADS)
Cullis, I. G.; Church, P. D.; Townsley, R.; Greenwood, P.; Proud, W. G.
2006-08-01
The Goldthorpe Path Dependent Failure (PDF) model has been incorporated into the GRIM Eulerian hydrocode and has been applied to a number of dynamic fracture scenarios. The model has allowed a step change improvement in the simulation of fracture processes in an Euler scheme. The applications include shear plugging of a plate due to ballistic impact, prediction of the so-called V{50} for a small mass projectile and the impact of a generic EFP against an aluminium plate target. It has been noted that the prediction of temperature in hydrocodes, still requires more effort, particularly when materials approach the melt point. In addition there is also significant batch to batch variation in the fracture properties in materials, which needs to be taken into account when simulating a given application scenario. The paper discusses these points and recognises that GRIM is now an integral part of the design process for new ballistic designs.
Scaling Algebraic Multigrid Solvers: On the Road to Exascale
Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M
2010-12-12
Algebraic Multigrid (AMG) solvers 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.
A chemical reaction network solver for the astrophysics code NIRVANA
NASA Astrophysics Data System (ADS)
Ziegler, U.
2016-02-01
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 solver 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 solver 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
An automatic ordering method for incomplete factorization iterative solvers
Forsyth, P.A.; Tang, W.P. . Dept. of Computer Science); D'Azevedo, E.F.D. )
1991-01-01
The minimum discarded fill (MDF) ordering strategy for incomplete factorization iterative solvers is developed. MDF ordering is demonstrated for several model son-symmetric problems, as well as a water-flooding simulation which uses an unstructured grid. The model problems show a three to five fold decrease in the number of iterations compared to natural orderings. Greater than twofold improvement was observed for the waterflooding simulation. 26 refs., 7 figs., 3 tabs.
A contribution to the great Riemann solver debate
NASA Technical Reports Server (NTRS)
Quirk, James J.
1992-01-01
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 solvers.
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver 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.
Direct linear programming solver in C for structural applications
NASA Astrophysics Data System (ADS)
Damkilde, L.; Hoyer, O.; Krenk, S.
1994-08-01
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 solvers 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 solver written in C, which can handle a combination of non-negative variables and unlimited variables. The LP solver 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 solver will at the same time give both a more direct problem formulation and a more efficient program.
A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles
NASA Technical Reports Server (NTRS)
Dejong, Frederik J.; Meyyappan, Meyya
1993-01-01
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 Eulerian-Lagrangian technique, in which Eulerian 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.
NASA Astrophysics Data System (ADS)
Georgiev, K.; Zlatev, Z.
2010-11-01
The Danish Eulerian Model (DEM) is an Eulerian 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.
Dynamics of multibody systems in space environment; Lagrangian vs. Eulerian approach
NASA Astrophysics Data System (ADS)
Santini, P.; Gasbarri, P.
2004-01-01
The paper describes the motion of a multibody in space environment: by space environment we mean space-varying gravity, gradient forces, control forces, if any. In the Eulerian approach, the motion of each individual member is described through kinematic parameters: (a) position of its CM with respect to the inertial frame; (b) rotation of the members with respect to the inertial frame; amplitude of the elastic modes (free-free). The said parameters are of different order of magnitudes, and therefore an adequate separation of them is highly desirable. Therefore, individual positions are replaced by overall position of the system (of the order of Earth's radius), and by the motion of each bar relative to it (of the order of members dimension), and for modes amplitudes modal equations are used.It should be noted, however, that the above-described motion parameters are redundant, and we must introduce: (a) reactions between members, (b) equations of compatibility of the same number of reactions.In summary, (i) the set of unknowns is: motion parameters, reactions, control forces; (ii) the equations are equilibrium, compatibility, control. Control is introduced by prescribing the motion of some members, produced by control moments of forces. By simple matrix algebra, it is reduced to a system with motion parameters (overall + local) only. In the Lagrangian approach, motion parameters are selected which are already consistent with compatibility conditions. In this case, as customarily, the expression of kinetic, potential, elastic energy is written, and the application of Lagrangian techniques provides directly the solving system. No reactions and compatibility equations appear here, however; for control purpose, prescribed motion law must again be introduced. Comparison of the two approaches shows perfect agreement (as one should have expected), since they are both exact models referring to the same physical system. In general, however, the Eulerian approach lends
Transonic Drag Prediction Using an Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Levy, David W.
2001-01-01
This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver 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 solver 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 solver on inexpensive clusters of commodity computers is also demonstrated.
Fast linear solvers for variable density turbulent flows
NASA Astrophysics Data System (ADS)
Pouransari, Hadi; Mani, Ali; Darve, Eric
2015-11-01
Variable density flows are ubiquitous in variety of natural and industrial systems. Two-phase and multi-phase flows in natural and industrial processes, astrophysical flows, and flows involved in combustion processes are such examples. For an ideal gas subject to low-Mach approximation, variations in temperature can lead to a non-uniform density field. In this work, we consider radiatively heated particle-laden turbulent flows as an example application in which density variability is resulted from inhomogeneities in the heat absorption by an inhomogeneous particle field. Under such conditions, the divergence constraint of the fluid is enforced through a variable coefficient Poisson equation. Inversion of the discretized variable coefficient Poisson operator is difficult using the conventional linear solvers as the size of the problem grows. We apply a novel hierarchical linear solve algorithm based on low-rank approximations. The proposed linear solver could be applied to variety of linear systems arising from discretized partial differential equations. It can be used as a standalone direct-solver with tunable accuracy and linear complexity, or as a high-accuracy pre-conditioner in conjunction with other iterative methods.
A Survey of Solver-Related Geometry and Meshing Issues
NASA Technical Reports Server (NTRS)
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
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 solver 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 solver 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 solver 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.
QED multi-dimensional vacuum polarization finite-difference solver
NASA Astrophysics Data System (ADS)
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
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 solver 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 solver. As an illustration of the properties of the solver, 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
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M.; Walker, H.F.
1996-12-31
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 solver 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 solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver 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.
NASA Astrophysics Data System (ADS)
Long, Matthew H.; Berg, Peter; Falter, James L.
2015-05-01
The net ecosystem metabolism of the seagrass Thalassia testudinum was studied across a nutrient and productivity gradient in Florida Bay, Florida, using the Eulerian control volume, eddy covariance, and biomass addition techniques. In situ oxygen fluxes were determined by a triangular Eulerian control volume with sides 250 m long and by eddy covariance instrumentation at its center. The biomass addition technique evaluated the aboveground seagrass productivity through the net biomass added. The spatial and temporal resolutions, accuracies, and applicability of each method were compared. The eddy covariance technique better resolved the short-term flux rates and the productivity gradient across the bay, which was consistent with the long-term measurements from the biomass addition technique. The net primary production rates from the biomass addition technique, which were expected to show greater autotrophy due to the exclusion of sediment metabolism and belowground production, were 71, 53, and 30 mmol carbon m-2 d-1 at 3 sites across the bay. The net ecosystem metabolism was 35, 25, and 11 mmol oxygen m-2 d-1 from the eddy covariance technique and 10, -103, and 14 mmol oxygen m-2 d-1 from the Eulerian control volume across the same sites, respectively. The low-flow conditions in the shallow bays allowed for periodic stratification and long residence times within the Eulerian control volume that likely reduced its precision. Overall, the eddy covariance technique had the highest temporal resolution while producing accurate long-term flux rates that surpassed the capabilities of the biomass addition and Eulerian control volume techniques in these shallow coastal bays.
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.
2015-02-01
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 solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Hyperbolic self-gravity solver for large scale hydrodynamical simulations
NASA Astrophysics Data System (ADS)
Hirai, Ryosuke; Nagakura, Hiroki; Okawa, Hirotada; Fujisawa, Kotaro
2016-04-01
A new computationally efficient method has been introduced to treat self-gravity in Eulerian hydrodynamical simulations. It is applied simply by modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method cannot only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids, and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.
NASA Astrophysics Data System (ADS)
Guo, Xiaocheng
2015-06-01
By revisiting the derivation of the previously developed HLLC Riemann solver for magneto-hydrodynamics (MHD), the paper presents an extended HLLC Riemann solver specifically designed for the MHD system in which the magnetic field can be decomposed into a strong internal magnetic field and an external component. The derived HLLC Riemann solver satisfies the conservation laws. The numerical tests show that the extended solver deals with the global MHD simulation of the Earth's magnetosphere well, and maintains high numerical resolution. It recovers the previously developed HLLC Riemann solver for the MHD as long as the internal field is set to zero. Thus, it is backward compatible with the previous HLLC solver, and suitable for the MHD simulations no matter whether a strong internal magnetic field is included or not.
Application of Aeroelastic Solvers Based on Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
2001-01-01
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 solver is required. A finite volume based Navier-Stokes solver 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 solver 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
A New Robust Solver for Saturated-Unsaturated Richards' Equation
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Tartakovsky, D. M.
2012-12-01
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 solvers in both one- and two-dimensional simulations. These solvers 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 solver 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.
A computationally efficient Multicomponent Equilibrium Solver for Aerosols (MESA)
NASA Astrophysics Data System (ADS)
Zaveri, Rahul A.; Easter, Richard C.; Peters, Leonard K.
2005-12-01
Development and application of a new Multicomponent Equilibrium Solver for Aerosols (MESA) is described for systems containing H+, NH4+, Na+, Ca2+, SO42-, HSO4-, NO3-, and Cl- ions. The equilibrium solution is obtained by integrating a set of pseudo-transient ordinary differential equations describing the precipitation and dissolution reactions for all the possible salts to steady state. A comprehensive temperature dependent mutual deliquescence relative humidity (MDRH) parameterization is developed for all the possible salt mixtures, thereby eliminating the need for a rigorous numerical solution when ambient RH is less than MDRH(T). The solver is unconditionally stable, mass conserving, and shows robust convergence. Performance of MESA was evaluated against the Web-based AIM Model III, which served as a benchmark for accuracy, and the EQUISOLV II solver for speed. Important differences in the convergence and thermodynamic errors in MESA and EQUISOLV II are discussed. The average ratios of speeds of MESA over EQUISOLV II ranged between 1.4 and 5.8, with minimum and maximum ratios of 0.6 and 17, respectively. Because MESA directly diagnoses MDRH, it is significantly more efficient when RH < MDRH. MESA's superior performance is partially due to its "hard-wired" code for the present system as opposed to EQUISOLV II, which has a more generalized structure for solving any number and type of reactions at temperatures down to 190 K. These considerations suggest that MESA is highly attractive for use in 3-D aerosol/air-quality models for lower tropospheric applications (T > 240 K) in which both accuracy and computational efficiency are critical.
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.; Sauer, Jeremy A.
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver 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 solver. 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 solver 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.
Reformulation of the Fourier-Bessel steady state mode solver
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver 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.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1989-01-01
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 solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
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 solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.
Algorithms for parallel flow solvers on message passing architectures
NASA Astrophysics Data System (ADS)
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- 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 solver 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 solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
Hierarchically parallelized constrained nonlinear solvers with automated substructuring
NASA Technical Reports Server (NTRS)
Padovan, J.; Kwang, A.
1991-01-01
This paper develops a parallelizable multilevel constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure, both sequential, 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 capacity to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.
Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring
NASA Technical Reports Server (NTRS)
Padovan, Joe; Kwang, Abel
1994-01-01
This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. 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.
Advances in the hydrodynamics solver of CO5BOLD
NASA Astrophysics Data System (ADS)
Freytag, Bernd
Many features of the Roe solver 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.
FDIPS: Finite Difference Iterative Potential-field Solver
NASA Astrophysics Data System (ADS)
Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang
2016-06-01
FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.
Object-Oriented Design for Sparse Direct Solvers
NASA Technical Reports Server (NTRS)
Dobrian, Florin; Kumfert, Gary; Pothen, Alex
1999-01-01
We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.
Performance issues for iterative solvers in device simulation
NASA Technical Reports Server (NTRS)
Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai
1994-01-01
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 solver on a variety of problems.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
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 solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method
NASA Astrophysics Data System (ADS)
Kruglyakov, M.; Geraskin, A.; Kuvshinov, A.
2016-11-01
We present a novel, open source 3-D MT forward solver based on a method of integral equations (IE) with contracting kernel. Special attention in the solver is paid to accurate calculations of Green's functions and their integrals which are cornerstones of any IE solution. The solver 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.
NASA Astrophysics Data System (ADS)
Jarauta, Alex; Ryzhakov, Pavel; Secanell, Marc; Waghmare, Prashant R.; Pons-Prats, Jordi
2016-08-01
An embedded Eulerian-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an Eulerian 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.
Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Padovan, Joe; Krishna, Lala
1986-01-01
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. 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 solvers. 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 solvers, results are presented for several benchmark examples.
A GPU-accelerated flow solver for incompressible two-phase fluid flows
NASA Astrophysics Data System (ADS)
Codyer, Stephen; Raessi, Mehdi; Khanna, Gaurav
2011-11-01
We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2013-01-01
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 Eulerian 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 Eulerian 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 Eulerian 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 Eulerian scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.
NASA Astrophysics Data System (ADS)
Li, K. F.; Yao, K.; Taketa, C.; Zhang, X.; Liang, M. C.; Jiang, X.; Newman, C. E.; Tung, K. K.; Yung, Y. L.
2015-12-01
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 Eulerian 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.
Flow-driven cloud formation and fragmentation: results from Eulerian and Lagrangian simulations
NASA Astrophysics Data System (ADS)
Heitsch, Fabian; Naab, Thorsten; Walch, Stefanie
2011-07-01
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 Eulerian 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.
An Eulerian scheme for the second-order approximation of subsurface transport moments
NASA Astrophysics Data System (ADS)
Naff, R. L.
1994-05-01
The moments of a conservative tracer cloud migrating in a mean uniform flow field are estimated using an operator approximation scheme; results are presented for the second, third, and fourth central moments in the mean flow direction. It is assumed that the spatially variable flow field, and therefore the tracer migration problem itself, is amenable to a probabilistic description; the effects of local dispersion on cloud migration are neglected in this study. Variation in the flow field is assumed to be the result of spatial variation in the hydraulic conductivity; spatial variation in porosity is assumed negligible. The operator approximation scheme, as implemented in this study, is second-order correct, which requires a second-order correct approximation of the velocity field correlation structure. Because estimation of the velocity correlation structure is decidedly the most difficult aspect of second-order analysis, an ad hoc extension of the imperfectly stratified approximation developed earlier is implemented for this purpose. The first-order approximation resulting from the operator expansion scheme is equivalent to small perturbation Eulerian results presented earlier (Naff, 1990, 1992). The infinite-order approximation resulting from this scheme is equivalent to the exponential operator results obtained by Van Kampen (1976).
NASA Astrophysics Data System (ADS)
Alver, Morten Omholt; Broch, Ole Jacob; Melle, Webjørn; Bagøien, Espen; Slagstad, Dag
2016-08-01
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 Eulerian 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.
NASA Astrophysics Data System (ADS)
Dhir, Gaurav; Suman, Sawan
2015-11-01
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-Eulerian 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.
Sulfur distribution and transport studies in East Asia using eulerian model
NASA Astrophysics Data System (ADS)
Wang, Zifa; Huang, Meiyuan; He, Dongyang; Xu, Huaying; Zhou, Ling
1996-08-01
A three-dimensional regional Eulerian model of sulfur deposition and transport is developed. Processes treated in the model include emission, transport, diffusion, gas-phase and aqueous-phase chemical process, dry deposition, rainout and washout of sulfur. A “looking up table” method is provided to deal with the gas-phase chemical process including sulfur transfer. Dry-depositon velocity considers the influence of underlying surface, wind, degree of stability by parameterization. Model calculated values reasonably agrees with observation. Distribution of sulfur deposition and transport in East Asia are also analyzed in this paper. Some amount of sulfur emission of different countries transport across boundaries, but the main origin of sulfur deposition in each country in East Asia is from itself. Furthermore, some transport paths on different layers and outlet or inlet zones are found. According to sulfur balance and budget we concluded that sulfur outlets are bigger than inlets across boundary and emissions are more than deposition in most places of East Asia.
NASA Astrophysics Data System (ADS)
Li, King-Fai; Yao, Kaixuan; Taketa, Cameron; Zhang, Xi; Liang, Mao-Chang; Jiang, Xun; Newman, Claire; Tung, Ka-Kit; Yung, Yuk L.
2016-04-01
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 Eulerian 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.
Arbitrary Lagrangian Eulerian simulations of stationary and non-stationary metal forming processes
NASA Astrophysics Data System (ADS)
Boman, R.; Ponthot, J.-P.
2013-12-01
Accurate modelling of sheet metal forming processes, such as cold roll forming, by the finite element method using the classical Lagrangian formulation usually requires a very large mesh leading to huge CPU times. In order to model industrial roll forming lines including many tools in a reasonable time, the sheet has to be shortened or the element size has to be increased leading to inaccurate results. An alternative method is given by the Arbitrary Lagrangian Eulerian (ALE) formalism which consists in decoupling the motion of the material and the mesh, the nodes of which are fixed in the rolling direction but are free to move on perpendicular plane, following the geometrical boundary of the sheet. The whole forming line can then be modelled using a limited number of brick and contact elements because the mesh is only refined near the tools where bending and contact occur. In this paper, ALE results are compared to previous Lagrangian simulations and experimental measurement on a U-channel, including springback. Advantages of the ALE method are finally demonstrated by the simulation of a tubular rocker panel on a 16-stands forming mill.
Eulerian Multiphase CFD Analysis of Particle Transport and Deposition in the Human Lung
NASA Astrophysics Data System (ADS)
Haworth, D. C.; Kunz, R. F.; Leemhuis, L. S.; Davison, A. C.
2002-11-01
An Eulerian n-fluid CFD model is used to model the transport and deposition of particles in the human lung. Separate continuity, momentum, energy and turbulence model equations are carried for an arbitrary number of fluid phases. Physical models for non-equilibrium interfacial transfer are incorporated to account for particle dispersion, drag, lift and wall deposition. The numerical scheme combines a fully unstructured second-order spatial discretization, distributed-memory scalable parallelism, and a novel coupled phasic exchange algorithm to accommodate the significant influence of inter-field transfer on discretization, operator splitting and linear solution elements of the algorithm. Here there is one carrier phase (air) and multiple particulate fields representing particles of different sizes. Current geometric models include an idealized three-generation branching duct configuration, and a more biologically realistic configuration that extends from the mouth down to approximately the seventh generation of branching in the lung. The models have been exercised to determine the fraction of particles of different sizes that are deposited as a function of depth in the lung. Initial wall deposition results from steady-flow calculations reveal qualitatively good agreement with limited available experimental data and phenomenological models.
Simulation of atmospheric dispersion of radionuclides using an Eulerian-Lagrangian modelling system.
Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N
2008-12-01
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 Eulerian 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.
Numerical study of plasma-wall transition using an Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Shoucri, M.; Cardinali, A.; Matte, J. P.; Spigler, R.
2004-07-01
A one-dimensional Eulerian Vlasov code is used to study the self-consistent solution of a plasma facing a floating collector, in the absence of an external magnetic field. Both electrons and ions are treated with a kinetic equation. A Bhatnagar-Gross-Krook (BGK) collision term is used to describe the collisions. Acceleration of the ion flow at the Debye sheath entrance is observed together with the formation of a stable steep negative electric field in front of the floating collector. This negative electric field acts to accelerate the positive ions towards the plate, pushing back the negative electrons, such that at steady state the total current collected at the plate is zero. The codes are run for a sufficiently long time on the ions time scale to ensure the ions (argon) distribution function is reaching a steady state. For the different parameters used, the solution shows the existence of persistent regular oscillations of constant amplitude when the electron collisions are very small or negligible. These oscillations will be studied. The increase in the electron collisions damps these oscillations and helps the system reach an equilibrium.
The detection of breathing behavior using Eulerian-enhanced thermal video.
Bennett, Stephanie L; Goubran, Rafik; Knoefel, Frank
2015-01-01
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 Eulerian 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.
Shoucri, M.; Matte, J.-P.; Vidal, F.
2015-05-15
We apply an Eulerian 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}
Modelling Cavitating Flows using an Eulerian-Lagrangian Approach and a Nucleation Model
NASA Astrophysics Data System (ADS)
Ma, Jingsen; Hsiao, Chao-Tsung; Chahine, Georges L.
2015-12-01
An Eulerian/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.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (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.
Implementation of the TEPLA Damage Model in a 3D Eulerian Hydrocode
NASA Astrophysics Data System (ADS)
Holian, Kathleen S.; Clancy, Sean P.; Maudlin, Paul J.
2007-06-01
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 Eulerian 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.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Staten, Matthew L.; Owen, Steven James
2010-09-01
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 Eulerian-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.
A Methodology to Validate 3-D Arbitrary Lagrangian Eulerian Codes with Applications to Alegra
Chhabildas, L.C.; Duggins, B.D.; Konrad, C.H.; Mosher, D.A.; Perry, J.S.; Reinhart, W.D.; Summers, R.M.; Trucano, T.G.
1998-11-04
In this study we provided an experimental test bed for validating features of the Arbitrary Lagrangian Eulerian Grid for Research Applications (ALEGRA) code over a broad range of strain rates with overlapping diagnostics that encompass the multiple responses. A unique feature of the ALEGRA code is that it allows simultaneous computational treatment, within one code, of a wide range of strain-rates varying from hydrodynamic to structural conditions. This range encompasses strain rates characteristic of shock-wave propagation (107/s) and those characteristics of structural response (102/s). Most previous code validation experimental &udies, however, have been restricted to simulating or investigating a single strain-rate regime. What is new and different in this investigation is that we have performed well-controlled and well-instrumented experiments, which capture features relevant to both hydrodynamic and structural response in a single experiment. Aluminum was chosen for use in this study because it is a well-characterized material. The current experiments span strain rate regimes of over 107/s to less than 102/s in a single experiment. The input conditions were extremely well defined. Velocity interferometers were used to record the high' strain-rate response, while low strain rate data were collected using strain gauges. Although the current tests were conducted at a nominal velocity of - 1.5 km/s, it is the test methodology that is being emphasized herein. Results of a three-dimensional experiment are also presented.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (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
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
Atzberger, Paul J.
2011-04-20
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.
NASA Astrophysics Data System (ADS)
Burkett, Michael W.; Clancy, Sean P.; Maudlin, Paul J.; Holian, Kathleen S.
2004-07-01
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 Eulerian 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.
NASA Astrophysics Data System (ADS)
Burkett, Michael; Clancy, Sean; Maudlin, Paul; Holian, Kathleen
2001-06-01
: 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, Eulerian 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.
Rain scavenging of tritiated water vapour: a numerical Eulerian stationary model.
Atanassov, D; Galeriu, D
2011-01-01
The tradition in tritium washout modeling is to unite the washout model with a Gaussian plume model describing dispersion of tritium vapour in the atmosphere. In the present study, an alternative approach is proposed. A numerical Eulerian model that describes washout independently of dispersion is developed. The sensitivity analysis to model parameters has shown that the washout process is influenced most significantly by rainfall parameters and air temperature: different raindrop size distributions cause differences of up to about 70% in the washout outputs; a change of 15°C in the air temperature causes an effect of about 50%. Results are presented showing calculated values of washout outputs (tritium concentration in rain, tritium downward flux, washout coefficient) for different tritium vapour profiles, rainfall rates and air temperatures. The general conclusion is that the washout process is too complex to be described comprehensively by the simple washout coefficient concept. We suggest the approach proposed here for directly calculating the tritium downward flux and concentration in the rainwater is preferable.
Efficient simulation of pitch angle collisions in a 2+2-D Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.
2014-10-01
Here we discuss pitch angle scattering collisions in the context of the Eulerian-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.
Arbitrary Lagrangian-Eulerian simulations of particle and bubble dynamics in non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Yue, Pengtao
2013-11-01
Fluid rheology affects particle-bubble interaction in various ways. For example, it modifies the migration of a single particle and a single bubble as well as the film drainage when they get close. In this talk, we will investigate these non-Newtonian effects using an arbitrary Lagrangian-Eulerian method which simultaneously tracks rigid particle surfaces and deformable bubble surfaces. The gas motion inside each bubble is neglected, and we only consider the bubble pressure which is determined by the isothermal ideal gas law. The particle motion and the fluid motion are solved in a unified Galerkin finite-element framework, in which the hydrodynamic forces and moments between the particle and the surrounding fluid cancel out. Mesh refinement is enforced where the surface curvature is high and where two boundary segments are close; the latter guarantees a sufficient resolution of the film drainage process. Numerical results on bubble migration and particle-bubble interaction in viscoelastic fluids and shear-thinning fluids will be presented.
ICECO-CEL: a coupled Eulerian-Lagrangian code for analyzing primary system response in fast reactors
Wang, C.Y.
1981-02-01
This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian 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 Eulerian 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.
NASA Astrophysics Data System (ADS)
You, Guoqiao; Leung, Shingyu
2014-06-01
We propose a new Eulerian tool to study complicated dynamical systems based on the average growth in the surface area of a family of level surfaces represented implicitly by a level set function. Since this proposed quantity determines the temporal variation of the averaged surface area of all level surfaces, we name the quantity the Variation of the Integral over Area of Level Surfaces (VIALS). Numerically, all these infinitely many level surfaces are advected according to the given dynamics by solving one single linear advection equation. To develop a computationally efficient approach, we apply the coarea formula and rewrite the surface area integral as a simple integral relating the total variation (TV) of the level set function. The proposed method can be easily incorporated with a recent Eulerian algorithm for efficient computation of flow maps to speed up our approach. We will also prove that the proposed VIALS is closely related to the computation of the finite time Lyapunov exponent (FTLE) in the Lagrangian coherent structure (LCS) extraction. This connects our proposed Eulerian approach to widely used Lagrangian techniques for understanding complicated dynamical systems.
NASA Astrophysics Data System (ADS)
Jaishree, J.; Haworth, D. C.
2010-11-01
Transported probability density function (PDF) methods offer compelling advantages for modeling chemically reacting turbulent flows, and Lagrangian particle-based Monte Carlo algorithms have become the predominant method for solving modeled PDF transport equations. Significant progress has been made in Lagrangian particle methods to facilitate their implementation into conventional Eulerian computational fluid dynamics (CFD) codes. Still, it would be desirable to realize the advantages of PDF methods using more conventional numerical algorithms and/or at lower computational cost. Toward these ends, Eulerian field methods have been proposed as alternatives to particle-based methods for solving modeled PDF transport equations. Here we apply Lagrangian particle and Eulerian field (both stochastic and deterministic) PDF methods to a hierarchy of three piloted methane-air nonpremixed turbulent jet flames where turbulence/chemistry interactions become progressively more important. Both accuracy and computational efficiency are assessed. Based on these results, we provide recommendations on how to apply each method most effectively, and we identify outstanding issues requiring future research.
NASA Astrophysics Data System (ADS)
Frei, S.; Richter, T.; Wick, T.
2016-09-01
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 Eulerian (ALE) coordinates and in Eulerian 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 Eulerian and ALE approaches as well as convergence studies.
Riemann solvers and Alfven waves in black hole magnetospheres
NASA Astrophysics Data System (ADS)
Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip
2016-09-01
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 solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, 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.
A massively parallel fractional step solver for incompressible flows
Houzeaux, G. Vazquez, M. Aubry, R. Cela, J.M.
2009-09-20
This paper presents a parallel implementation of fractional solvers 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 solvers 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.
Using computer algebra and SMT solvers in algebraic biology
NASA Astrophysics Data System (ADS)
Pineda Osorio, Mateo
2014-05-01
Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT Solvers 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 Solver. 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.
Matrix decomposition graphics processing unit solver for Poisson image editing
NASA Astrophysics Data System (ADS)
Lei, Zhao; Wei, Li
2012-10-01
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) solver (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 solver (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.
Agglomeration Multigrid for an Unstructured-Grid Flow Solver
NASA Technical Reports Server (NTRS)
Frink, Neal; Pandya, Mohagna J.
2004-01-01
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 solver. Efficiency and robustness of the multigrid-enhanced flow solver 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.
An efficient chemical kinetics solver using high dimensional model representation
Shorter, J.A.; Ip, P.C.; Rabitz, H.A.
1999-09-09
A high dimensional model representation (HDMR) technique is introduced to capture the input-output behavior of chemical kinetic models. The HDMR expresses the output chemical species concentrations as a rapidly convergent hierarchical correlated function expansion in the input variables. In this paper, the input variables are taken as the species concentrations at time t{sub i} and the output is the concentrations at time t{sub i} + {delta}, where {delta} can be much larger than conventional integration time steps. A specially designed set of model runs is performed to determine the correlated functions making up the HDMR. The resultant HDMR can be used to (1) identify the key input variables acting independently or cooperatively on the output, and (2) create a high speed fully equivalent operational model (FEOM) serving to replace the original kinetic model and its differential equation solver. A demonstration of the HDMR technique is presented for stratospheric chemical kinetics. The FEOM proved to give accurate and stable chemical concentrations out to long times of many years. In addition, the FEOM was found to be orders of magnitude faster than a conventional stiff equation solver. This computational acceleration should have significance in many chemical kinetic applications.
User documentation for PVODE, an ODE solver for parallel computers
Hindmarsh, A.C., LLNL
1998-05-01
PVODE is a general purpose ordinary differential equation (ODE) solver 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 solver 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
The SX Solver: A Computer Program for Analyzing Solvent-Extraction Equilibria: Version 3.0
Lumetta, Gregg J.
2002-01-17
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel and uses the built-in Solver function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributyl phosphate has been modeled to illustrate the programs use.
A block iterative LU solver for weakly coupled linear systems. [in fluid dynamics equations
NASA Technical Reports Server (NTRS)
Cooke, C. H.
1977-01-01
A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
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 solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. 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 solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver 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.
The Quasi-Eulerian Hydrophone: A New Approach for Ocean Acoustics
NASA Astrophysics Data System (ADS)
Matsumoto, H.; Dziak, R. P.; Fowler, M. J.; Hammond, S. R.; Meinig, C.
2005-12-01
For the last 10 years Oregon State University and NOAA/Pacific Marine Environmental Laboratory have successfully operated and maintained autonomous hydrophone arrays to monitor low frequency acoustic energy of earthquakes and marine mammal calls in remote ocean areas where no historical record existed. These hydrophones are moored at mid-water depth and require a routine servicing cruise to retrieve the stored data. The system is robust, but it is not real-time and it takes up to a year before acoustic events can be identified from the raw acoustic data. As a result, we frequently miss opportunities to observe ocean acoustic events as they occur. A new type of autonomous hydrophone called a Quasi-Eulerian hydrophone (QUEphone) is under development at OSU/PMEL. This instrument allows near-real-time monitoring of a selected study area. It is a tether-free float with a built-in hydrophone monitoring system and a buoyancy controller. It is capable of repeat ascent/descent cycles in up to 2000 m of water. In contrast to the conventional Lagrangean float, the QUEphone float stays in the same area by maintaining negative buoyancy and remaining on the seafloor for most of its life span. While on the seafloor the QUEphone runs an intelligent event detection algorithm, and upon detection of a significant number of events will surface to transmit a small data file to shore. We have conducted brief test deployments of the QUEphone in both a fresh-water lake and marine waters off Oregon coast, and the results of these tests will be discussed and compared with other hydrophone data. Once fully developed the QUEphone is expected to provide near real-time analysis capability of earthquakes that affect seafloor hydrothermal vents and their associated ecosystems. Such fast reaction will allow for a rapid response to seismic events, enabling researchers to examine how changes in hydrothermal activity affect deep-ocean vent ecosystems.
SIMULATION OF GEOMATERIALS USING CONTINUUM DAMAGE MODELS ON AN EULERIAN GRID
Lomov, I; Antoun, T H
2004-09-17
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 Eulerian 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.
Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F
2016-02-01
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 Eulerian-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. PMID:26753780
NASA Astrophysics Data System (ADS)
Eibern, Hendrik; Schmidt, Hauke
1999-08-01
The inverse problem of data assimilation of tropospheric trace gas observations into an Eulerian chemistry transport model has been solved by the four-dimensional variational technique including chemical reactions, transport, and diffusion. The University of Cologne European Air Pollution Dispersion Chemistry Transport Model 2 with the Regional Acid Deposition Model 2 gas phase mechanism is taken as the basis for developing a full four-dimensional variational data assimilation package, on the basis of the adjoint model version, which includes the adjoint operators of horizontal and vertical advection, implicit vertical diffusion, and the adjoint gas phase mechanism. To assess the potential and limitations of the technique without degrading the impact of nonperfect meteorological analyses and statistically not established error covariance estimates, artificial meteorological data and observations are used. The results are presented on the basis of a suite of experiments, where reduced records of artificial "observations" are provided to the assimilation procedure, while other "data" is retained for performance control of the analysis. The paper demonstrates that the four-dimensional variational technique is applicable for a comprehensive chemistry transport model in terms of computational and storage requirements on advanced parallel platforms. It is further shown that observed species can generally be analyzed, even if the "measurements" have unbiased random errors. More challenging experiments are presented, aiming to tax the skill of the method (1) by restricting available observations mostly to surface ozone observations for a limited assimilation interval of 6 hours and (2) by starting with poorly chosen first guess values. In this first such application to a three-dimensional chemistry transport model, success was also achieved in analyzing not only observed but also chemically closely related unobserved constituents.
Predictions of plume dispersion in complex terrain: Eulerian versus Lagrangian models
NASA Astrophysics Data System (ADS)
Nguyen, K. C.; Noonan, J. A.; Galbally, I. E.; Physick, W. L.
Simulations of dispersion from an elevated point source in complex terrain and non-stationary flow are presented using the Lagrangian atmospheric dispersion model (LADM, Physick et al., 1992, Air Pollution Modeling and its Applications, Vol. IX, pp. 725-729, Plenum Press, New York; 1994 CSIRO Division of Atmospheric Research Technical Paper No. 24) and the Eulerian grid-based model (CALGRID, Yamartino et al., 1989, CALGRID: a mesoscale photochemical grid model, Vol. I; model formation document, Report, Sacarmento, California). Both models use the same predicted windfields. We find that • the different algorithms used for release of pollutants into the model domains lead to initial concentrations at the release height in LADM one-third higher than in CALGRID. • The CALGRID plume spreads laterally over a larger region than does the LADM plume due to the finite-difference approach of CALGRID. The pollutant mass in the extra volume occupied by the CALGRID plume is less than 10% of that released. • The essentials of morning fumigation are simulated more realistically under the Lagrangian approach. In LADM the elevated plume is mixed down to the ground rapidly, causing a sharp increase in ground-level concentrations (glc), whereas, in CALGRID glc increase more gradually over a few hours. • The use of hourly averaged windfields in CALGRID compared to 10 min windfields in LADM leads to a relative separation of the two modelled plumes of 5 km at a distance of roughly 6 km downwind from the sources at 1500 LST. Consequently in complex terrain and non-stationary conditions, the plumes are subjected to different three-dimensional wind regimes. For the particular terrain studied, roughly 3% of the pollutant mass emitted into CALGRID during the day is transported above 3000 m after 1700 LST whereas only 0.8% is transported above this height in LADM. • During the daytime the CALGRID simulation produces maximum glc which are about 40% smaller than those predicted by LADM.
Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F
2016-02-01
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 Eulerian-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.
NASA Astrophysics Data System (ADS)
Mahoney, A. R.; Hutchings, J. K.; Haas, C.; Eicken, H.
2014-12-01
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 Eulerian-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.
A Eulerian nutrient to fish model of the Baltic Sea — A feasibility-study
NASA Astrophysics Data System (ADS)
Radtke, Hagen; Neumann, Thomas; Fennel, Wolfgang
2013-09-01
A nutrient-to-fish-model with an explicit two-way interaction between a biogeochemical model of the lower food web and a fish model component is presented for the example of the Baltic Sea, demonstrating the feasibility of a consistent coupling of the upper and lower parts of the food web in a Eulerian model system. In the Baltic Sea, the fish stock is dominated by two prey species (sprat and herring) and one predator (cod). The dynamics of the fish model is driven by size (mass-class) dependent predator-prey interactions while the interaction between the biogeochemical and Fish model component is established through feeding of prey fish on zooplankton and recycling of fish biomass to nutrients and detritus. The fish model component is coupled to an advanced three dimensional biogeochemical model (ERGOM, Neumann et al., 2002). A horizontally explicit representation of fish requires the implementation of fish behavior. As a first step, we propose an algorithm to stimulate fish migration by letting the fish follow the food. Moreover, fish species are guided to their respective spawning areas. Results of first three-dimensional simulations are presented with emphasis on the transport of matter by moving fish. The spawning areas of cod and sprat are in the deep basins, which are not well reached by advective transport. Hence the deposition of matter in these areas by spawning fish could play some role in the distribution of matter. The approach is not limited to applications for the Baltic and the model can be transferred also to other systems.
Prediction of turbulent gas-solids flow in curved ducts using the Eulerian-Lagrangian method
NASA Astrophysics Data System (ADS)
Naik, S.; Bryden, I. G.
1999-10-01
The flow of particulate two-phase flow mixtures occur in several components of solid fuel combustion systems, such as the pressurised fluidised bed combustors (PFBC) and suspension-fired coal boilers. A detailed understanding of the mixture characteristics in the conveying component can aid in refining and optimising its design. In this study, the flow of an isothermal, dilute two-phase particulate mixture has been examined in a high curvature duct, which can be representative of that transporting the gas-solid mixture from the hot clean-up section to the gas turbine combustor in a PFBC plant. The numerical study has been approached by utilising the Eulerian-Lagrangian methodology for describing the characteristics of the fluid and particulate phases. By assuming that the mixture is dilute and the particles are spherical, the governing particle momentum equations have been solved with appropriately prescribed boundary conditions. Turbulence effects on the particle dispersion were represented by a statistical model that accounts for both the turbulent eddy lifetime and the particle transit time scales. For the turbulent flow condition examined it was observed that mixtures with small particle diameters had low interphase slip velocities and low impaction probability with the pipe walls. Increasing the particle diameters (>50 m) resulted in higher interphase slip velocities and, as expected, their impaction probability with the pipe walls was significantly increased. The particle dispersion is significant for the smaller sizes, whereas the larger particles are relatively insensitive to the gas turbulence. The main particle impaction region, and locations most prone to erosion damage, is estimated to be within an outer duct length of two to six times the duct diameter, when the duct radius of curvature to the duct diameter ratio is equal to unity. Copyright
NASA Astrophysics Data System (ADS)
Meyer, Daniel W.; Tchelepi, Hamdi A.; Jenny, Patrick
2010-05-01
In risk analysis applications involving heterogeneous formations, the knowledge of the solute concentration probability density function (PDF) at different spatial locations and times is crucial. We propose a new joint velocity-concentration PDF method applicable for highly heterogeneous porous media that accounts for advective transport, pore-scale dispersion and molecular diffusion. Unlike in low order approximation (LOA) methods that are valid for low conductivity variances ?Y 2 and where the one-point velocity PDF is typically assumed to be a Gaussian, the proposed joint PDF method honors the increasingly non-Gaussian velocity one-point PDF and the long-term velocity correlations that were reported in different Monte Carlo (MC) studies for ?Y 2 > 0.5 [e.g., Salandin, P. and V. Fiorotto, WRR, 1998. 34(5) and Trefry, M.G., F.P. Ruan, and D. McLaughlin, WRR, 2003. 39(3)]. Furthermore, the new joint PDF method does not involve any a-priori assumption about the shape of the resulting marginal concentration PDF. LOA methods that provide information on the concentration mean and variance [Fiori, A. and G. Dagan, Journal of Contaminant Hydrology, 2000. 45(1-2)] on the other hand are typically complemented by assuming that the concentration PDF has a β-PDF shape [Bellin, A. and D. Tonina, Journal of Contaminant Hydrology, 2007. 94(1-2)]. The Eulerian joint velocity-concentration PDF transport equation in our model is numerically solved with a computationally efficient particle method. The suggested joint PDF method is validated by comparison with MC data reported by Caroni and Fiorotto for Péclet numbers ranging from 10 to 104 and ?Y 2 = 1 and 2 [Caroni, E. and V. Fiorotto, Transport in Porous Media, 2005. 59(1)].
NASA Astrophysics Data System (ADS)
Storlazzi, C. D.; Messina, A. M.; Cheriton, O. M.; Biggs, T. W.
2014-12-01
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-Eulerian 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.
Lagrangian and Eulerian biventricular strains from anatomical NURBS models using tagged MRI
NASA Astrophysics Data System (ADS)
Tustison, Nicholas J.; Amini, Amir A.
2005-04-01
We present current research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered include Cartesian-based NURBS models with both a cylindrical and prolate-spheroidal parameterization, prolate spheroidal-based NURBS models with a prolate-spheroidal parameterization, and cylindrical-based NURBS models with a cylindrical parameterization. For each frame subsequent to end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent forward displacement fitting from end-diastole to all later time frames. After fitting to all time points of data, lofting the NURBS model at each time point creates a comprehensive 4-D NURBS model. From this model, we can extract 3-D myocardial deformation fields and corresponding strain maps which are local measures of non-rigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian-based NURBS model outperformed its counterparts in predicting normal strain. This model was used to then calculate normal Lagrangian and Eulerian strains in canine data.
Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver.
Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.
2010-08-01
Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver 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 solver. 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 solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
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 solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver 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.
High-performance equation solvers and their impact on finite element analysis
NASA Technical Reports Server (NTRS)
Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.
1990-01-01
The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers 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 solvers 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 solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.
Perturbative forward solver software for small localized fluorophores in tissue
Martelli, F.; Bianco, S. Del; Di Ninni, P.
2011-01-01
In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green’s functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated. PMID:22254165
Blade design and analysis using a modified Euler solver
NASA Technical Reports Server (NTRS)
Leonard, O.; Vandenbraembussche, R. A.
1991-01-01
An iterative method for blade design based on Euler solver 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.
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
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 solver 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.
Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
NASA Technical Reports Server (NTRS)
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
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 solver workloads and high performance computing platforms and is useful for tuning these applications.
GPU accelerated FDTD solver and its application in MRI.
Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S
2010-01-01
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 solver 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.
Perturbative forward solver software for small localized fluorophores in tissue.
Martelli, F; Del Bianco, S; Di Ninni, P
2012-01-01
In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green's functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated. PMID:22254165
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1994-01-01
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 solvers 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 speedup 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.
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1993-01-01
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 solvers 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.
Aeroelastic analysis of advanced propellers using an efficient Euler solver
NASA Technical Reports Server (NTRS)
Srivastava, R.; Reddy, T. S. R.; Mehmed, O.
1992-01-01
A 3D Euler solver is coupled with a 3D structural dynamics model to investigate flutter of propfans. A hybrid scheme is used to reduce computational time for the Euler equations and a normal mode analysis is used for flutter calculations. Experimental and calculated flutter results are compared for an advanced propeller propfan which experienced flutter at transonic tip relative velocities. The predicted flutter calculations are in close agreement with the experimental data. A structural damping value of 0.5 percent was required to predict the behavior observed in the experiment. Computations show that the flutter behavior is dominated by the second mode, but coupling with the first mode is required. The addition of other modes to the calculations did not affect the flutter behavior.
Progress in developing Poisson-Boltzmann equation solvers
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-01-01
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 solvers 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
Application of sparse matrix solvers as effective preconditioners
Young, D.P.; Melvin, R.G.; Johnson, F.T.; Bussoletti, J.E.; Wigton, L.B.; Samant, S.S. )
1989-11-01
In this paper the use of a new out-of-core sparse matrix package for the numerical solution of partial differential equations involving complex geometries arising from aerospace applications is discussed. The sparse matrix solver accepts contributions to the matrix elements in random order and assembles the matrix using fast sort/merge routines. Fill-in is reduced through the use of a physically based nested dissection ordering. For very large problems a drop tolerance is used during the matrix decomposition phase. The resulting incomplete factorization is an effective preconditioner for Krylov subspace methods, such as GMRES. Problems involving 200,000 unknowns routinely are solved on the Cray X-MP using 64MW of solid-state storage device (SSD).
Extending the QUDA Library with the eigCG Solver
Strelchenko, Alexei; Stathopoulos, Andreas
2014-12-12
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 solvers, 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
A three-dimensional fast solver for arbitrary vorton distributions
Strickland, J.H.; Baty, R.S.
1994-05-01
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 solver. For 100,000 vortons in the flow, the fast solver obtains solutions in 1 % to 10% of the time required for the direct solution technique depending upon the configuration.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Pernice, M.
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers 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 solver 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.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
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 solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver 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.
NASA Astrophysics Data System (ADS)
Furuichi, M.; Kameyama, M.; Kageyama, A.
2007-12-01
Reproducing a realistic plate tectonics with mantle convection simulation is one of the greatest challenges in computational geophysics. We have developed a three dimensional Eulerian 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 Eulerian 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 Eulerian 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.
Exit of a blast wave from a conical nozzle. [flow field calculations by Eulerian computer code DORF
NASA Technical Reports Server (NTRS)
Kim, K.; Johnson, W. E.
1976-01-01
The Eulerian 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.
GORRAM: Introducing accurate operational-speed radiative transfer Monte Carlo solvers
NASA Astrophysics Data System (ADS)
Buras-Schnell, Robert; Schnell, Franziska; Buras, Allan
2016-06-01
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 solver 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 solvers individually optimized for the intended task. These solvers 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 solver 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 solver. 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 solvers an eligible candidate as forward model in operational-speed retrieval algorithms and data assimilation applications. GORRAM also has the potential to create fast solvers of other integrable equations.
Oasis: A high-level/high-performance open source Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Mortensen, Mikael; Valen-Sendstad, Kristian
2015-03-01
Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver 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 solver. A version of the solver, 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 solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.
The impact of improved sparse linear solvers on industrial engineering applications
Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
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 solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver 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 solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers 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 solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
Acceleration of FDTD mode solver by high-performance computing techniques.
Han, Lin; Xi, Yanping; Huang, Wei-Ping
2010-06-21
A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver 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 solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver 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 solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver 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 solver 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 solvers are no longer applicable due to memory limitation.
The effects of advection solvers on the performance of air quality models
Tanrikulu, S.; Odman, M.T.
1996-12-31
The available numerical solvers for the advection term in the chemical species conservation equation have different properties, and consequently introduce different types of errors. These errors can affect the performance of air quality models and lead to biases in model results. In this study, a large number of advection solvers have been studied and six of them were identified as having potential for use in photochemical models. The identified solvers were evaluated extensively using various numerical tests that are relevant to air quality simulations. Among the solvers evaluated, three of them showed better performance in terms of accuracy and some other characteristics such as conservation of mass and positivity. They are the solvers by Bott, Yuamartino, and Dabdub and Seinfeld. These three solvers were incorporated into the SARMAP Air Quality Model (SAQM) and the August 3-6, 1990 ozone episode in the San Joaquin Valley of California was simulated with each. A model performance analysis was conducted for each simulation using the rich air quality database of the 1990 San Joaquin Valley Air Quality Study. The results of the simulations were compared with each other and the effects of advection solvers on the performance of the model are discussed.
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael
2015-07-01
In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (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
Robust large-scale parallel nonlinear solvers for simulations.
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson
2005-11-01
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 solvers (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 solver, which makes it simple to write
A new set of direct and iterative solvers for the TOUGH2 family of codes
Moridis, G.J.
1995-04-01
Two new solvers are discussed. LUBAND, the first routine is a direct solver 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) solver 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.
A multigrid solver for semi-implicit global shallow-water models
NASA Technical Reports Server (NTRS)
Barros, Saulo R. M.; Dee, Dick P.; Dickstein, Flavio
1990-01-01
A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.
Application of an unstructured grid flow solver to planes, trains and automobiles
NASA Technical Reports Server (NTRS)
Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram
1993-01-01
Rampant, an unstructured flow solver 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 solver 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 solver and presents flow field solutions about a plane, train, and automobile.
An optimal iterative solver for the Stokes problem
Wathen, A.; Silvester, D.
1994-12-31
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 solver 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.
Towards Batched Linear Solvers on Accelerated Hardware Platforms
Haidar, Azzam; Dong, Tingzing Tim; Tomov, Stanimire; Dongarra, Jack J
2015-01-01
As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, 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.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
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 solver 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.
Generation of Minimum-Consistent DFA Using SAT Solver
NASA Astrophysics Data System (ADS)
Inui, Nobuo; Aizawa, Akiko
The purpose of this study is to develop efficient methods for the minimum-consistent DFA (deterministic finite state automaton) problem. The graph-coloring based SAT (satisfiability) approach proposed by Heule is a state of the art method for this problem. It specially achieves high performance computing in dense problems such as in a popular benchmark problem where rich information about labels is included. In contrast, to solve sparse problems is a challenge for the minimum-consistent DFA problem. To solve sparse problems, we propose three approaches to the SAT formulation: a) the binary color representation, b) the dynamic symmetry breaking and c) the hyper-graph coloring constraint. We organized an experiment using the existing benchmark problems and sparse problems made from them. We observed that our symmetry breaking constraints made the speed up the running time of SAT solver. In addition with this, our other proposed methods were showing the possibility to improve the performance. Then we simulated the perfomance of our methods under the condition that we executed the several program set-ups in parallel. Compared with the previous research results, we finally could reduce the average relative time by 66.5% and the total relative time by 7.6% for sparse problems and by 79.7% and 38.5% for dense problems, respectively. These results showed that our proposed methods were effective for difficult problems.
Approximate Riemann Solvers for the Cosmic Ray Magnetohydrodynamical Equations
NASA Astrophysics Data System (ADS)
Kudoh, Yuki; Hanawa, Tomoyuki
2016-08-01
We analyze 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 solver 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. (2006) 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 an 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.
A generalized Poisson solver for first-principles device simulations
NASA Astrophysics Data System (ADS)
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
2016-01-01
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 solver 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.
Cooperative solutions coupling a geometry engine and adaptive solver codes
NASA Technical Reports Server (NTRS)
Dickens, Thomas P.
1995-01-01
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 solvers 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.
Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations
NASA Astrophysics Data System (ADS)
Kudoh, Yuki; Hanawa, Tomoyuki
2016-11-01
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 solver 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.
Development of parallel incompressible NS solver on stretched grids
NASA Astrophysics Data System (ADS)
Jothiprasad, G.; Caughey, D.; Pope, S. B.
2003-11-01
Development of a parallel NS solver for studying DNS and LES of temporal mixing layers is discussed. The equations are cast in strong conservation form on a uniform computational mesh, transformed from a stretched mesh in the physical domain. Variables are defined on a collocated grid, and the transformed equations are solved using a fractional step method. Convective and dissipative terms are treated using explicit Adams-Bashforth and implicit Crank-Nicolson, respectively. Fourth order spatial accuracy is maintained except for hyperviscous subgrid model terms, which are only 2nd order accurate. The block LU analysis of J. B. Perot, extended to fractional step methods on collocated grids, shows that an O(Δ t^2) term involving the pressure gradient must be added to the momentum equations to maintain 2nd order accuracy in time. Using a smaller stencil for the pressure gradients largely simplifies the pressure Poisson equation while still ensuring that discrete continuity is satisfied to appropriate order. Implementation on distributed-memory multiprocessors is achieved using MPI, with care taken to minimize communication overhead.
Verification of continuum drift kinetic equation solvers in NIMROD
Held, E. D.; Ji, J.-Y.; Kruger, S. E.; Belli, E. A.; Lyons, B. C.
2015-03-15
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 solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver 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.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y.
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver 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.
A generalized Poisson solver for first-principles device simulations.
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
2016-01-28
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 solver 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. PMID:26827208
Verification of continuum drift kinetic equation solvers in NIMROD
NASA Astrophysics Data System (ADS)
Held, E. D.; Kruger, S. E.; Ji, J.-Y.; Belli, E. A.; Lyons, B. C.
2015-03-01
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 solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Two-Dimensional Ffowcs Williams/Hawkings Equation Solver
NASA Technical Reports Server (NTRS)
Lockard, David P.
2005-01-01
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 solver.
Incremental planning to control a blackboard-based problem solver
NASA Technical Reports Server (NTRS)
Durfee, E. H.; Lesser, V. R.
1987-01-01
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 solver's real-time response and can enhance cooperation in a distributed problem solving network.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2012-01-01
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 Eulerian 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 Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.
NASA Astrophysics Data System (ADS)
Li, Linmin; Li, Baokuan
2016-08-01
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 Eulerian 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 Eulerian-Lagrangian-LES model provides a valid modeling framework to predict the unsteady gas bubble-slag layer coupled behaviors.
The Danish eulerian hemispheric model — a three-dimensional air pollution model used for the arctic
NASA Astrophysics Data System (ADS)
Christensen, Jesper Heile
A three-dimensional Eulerian hemispheric air pollution model, the Danish Eulerian Hemispheric Model (DEHM), is in development at the National Environmental Research Institute (NERI). The model has been used to study long-range transport of air pollution in the Northern Hemisphere. The present version of the model includes long-range transport of sulphur dioxide (SO 2) and particulate sulphate (SC 42-. The chemistry in the model is described by a simple linear oxidation of SO 2 to SO 42-, and the wet deposition of SO 2 and SO 4- is estimated based on the amount of precipitation, which is calculated from the contents of liquid cloud water (see Christensen, Air Pollution Modelling and its Applicatioons, Vol. X, pp. 119-127, Vol. XI, pp. 249-256, Plenum press, New York; 1995, Ph.D. thesis, National Environmental Research Institute, Denmark). The model has been used to study the air pollution in the Arctic. Results from 3 1/2 yr simulation with an analysis of the results is presented: the model results are verified by comparisons, to measurements not only from the Arctic region but also from Europe and Canada. Some examples of episodes in the Arctic including analysis of the meteorological conditions during the episodes are presented. Finally, the model has been used to estimate the contribution from the different source regions on the northern hemisphere to the Arctic sulphur pollution.
Lomov, I; Liu, B
2005-09-29
Multimaterial Eulerian and Arbitrary Lagragian-Eulerian (ALE) codes usually use volume fractions of materials to track individual components in mixed cells. Material advection usually is calculated either by interface capturing, where a high-order van Leer-like slope reconstruction technique is applied, or interface tracking, where a normal reconstruction technique is applied. The former approach is more appropriate for gas-like substances, and the latter is ideal for solids and liquids, since it does not smear out material interfaces. A wide range of problems involves both diffuse and sharp interfaces between substances and demands a combination of these techniques. It is possible to treat all substances that can diffuse into each other as a single material and only keep mass fractions of the individual components of the mixture. The material response can be determined based on the assumption of pressure and temperature equilibrium between components of the mixture. Unfortunately, it is extremely difficult to solve the corresponding system of equations. In order to avoid these problems one can introduce an effective gamma and employ the ideal gas approximation to calculate mixture response. This method provides reliable results, is able to compute strong shock waves, and deals with complex equations of state. Results from a number of simulations using this scheme are presented.
NASA Astrophysics Data System (ADS)
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian 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 Eulerian 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 Eulerian 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 Eulerian 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 Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
NASA Astrophysics Data System (ADS)
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-11-01
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-01-01
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
NASA Astrophysics Data System (ADS)
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.
2016-05-01
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 solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver 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.
A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
NASA Astrophysics Data System (ADS)
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2016-07-01
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver 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 solver 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 solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu)
Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J
2014-01-01
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
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.; et al
2014-11-27
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.« less
Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J
2014-11-27
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
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
2014-11-27
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 solver 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 solver 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 solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Efficient Implementation of Multigrid Solvers on Message-Passing Parrallel Systems
NASA Technical Reports Server (NTRS)
Lou, John
1994-01-01
We discuss our implementation strategies for finite difference multigrid partial differential equation (PDE) solvers on message-passing systems. Our target parallel architecture is Intel parallel computers: the Delta and Paragon system.
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver 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 solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver 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.
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver 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 solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver 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
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
NASA Technical Reports Server (NTRS)
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers 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 solver. 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.
The SX Solver: A New Computer Program for Analyzing Solvent-Extraction Equilibria.
Lumetta, Gregg J; McNamara, Bruce K; Rapko, Brian M
1999-01-08
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel{reg_sign} and uses the built-in ''Solver'' function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributyl phosphate has been modeled to illustrate the program's use.
The SX Solver: A New Computer Program for Analyzing Solvent-Extraction Equilibria
McNamara, B.K.; Rapko, B.M.; Lumetta, G.J.
1999-02-09
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel{reg_sign} and uses the built-in ''Solver'' function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributylphosphate has been modeled to illustrate the program's use.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver 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 solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
Implementation of a parallel unstructured Euler solver on the CM-5
NASA Technical Reports Server (NTRS)
Morano, Eric; Mavriplis, D. J.
1995-01-01
An efficient unstructured 3D Euler solver 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 solver is discussed.
Maxwell solvers for the simulations of the laser-matter interaction
NASA Astrophysics Data System (ADS)
Nuter, Rachel; Grech, Mickael; Gonzalez de Alaiza Martinez, Pedro; Bonnaud, Guy; d'Humières, Emmanuel
2014-06-01
With the advent of high intensity laser beams, solving the Maxwell equations with a free-dispersive algorithm is becoming essential. Several Maxwell solvers, implemented in Particle-In-Cell codes, have been proposed. We present here some of them by describing their computational stencil in two-dimensional geometry and defining their stability area as well as their numerical dispersion relation. Numerical simulations of Backward Raman amplification and laser wake-field are presented to compare these different solvers.
NASA Astrophysics Data System (ADS)
Willemsen, Bram; Malcolm, Alison; Lewis, Winston
2016-03-01
In a set of problems ranging from 4-D seismic to salt boundary estimation, updates to the velocity model often have a highly localized nature. Numerical techniques for these applications such as full-waveform inversion (FWI) require an estimate of the wavefield to compute the model updates. When dealing with localized problems, it is wasteful to compute these updates in the global domain, when we only need them in our region of interest. This paper introduces a local solver that generates forward and adjoint wavefields which are, to machine precision, identical to those generated by a full-domain solver evaluated within the region of interest. This means that the local solver computes all interactions between model updates within the region of interest and the inhomogeneities in the background model outside. Because no approximations are made in the calculation of the forward and adjoint wavefields, the local solver can compute the identical gradient in the region of interest as would be computed by the more expensive full-domain solver. In this paper, the local solver is used to efficiently generate the FWI gradient at the boundary of a salt body. This gradient is then used in a level set method to automatically update the salt boundary.
Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds
Wiegmann, A.
1999-06-01
FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.
Continuous-time quantum Monte Carlo impurity solvers
NASA Astrophysics Data System (ADS)
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as
Patients as partners, patients as problem-solvers.
Young, Amanda; Flower, Linda
2002-01-01
This article reports our ongoing work in developing a model of health care communication called collaborative interpretation, which we define as a rhetorical practice that generates building blocks for a more complete and coherent diagnostic story and for a collaborative treatment plan. It does this by situating patients as problem-solvers. Our study begins with an analysis of provider-patient interactions in a specific setting-the emergency department (ED) of an urban trauma-level hospital- where we observed patients and providers miscommunicating in at least 3 distinct areas: over the meaning of key terms, in the framing of the immediate problem, and over the perceived role of the ED in serving the individual and the community. From our observations, we argue that all of these miscommunications and missed opportunities are rooted in mismatched expectations on the part of both provider and patient and the lack of explicit comparison and negotiation of expectations-in other words, a failure to see the patient-provider interaction as a rhetorical, knowledge-building event. In the process of observing interactions, conversing with patients and providers, and working with a team of providers and patients, we have developed an operational model of communication that could narrow the gap between the lay public and the medical profession-a gap that is especially critical in intercultural settings like the one we have studied. This model of collaborative interpretation (CI) provides strategies to help patients to represent their medical problems in the context of their life experiences and to share the logic behind their health care decisions. In addition, CI helps both patient and provider identify their goals and expectations in treatment, the obstacles that each party perceives, and the available options. It is adaptableto various settings, including short, structured conversations in the emergency room, extended dialogue between a health educator and a patient in a
A two-dimensional fast solver for arbitrary vortex distributions
Strickland, J.H.; Baty, R.S.
1997-04-01
A method which is capable of an efficient calculation of the two-dimensional stream function and velocity field produced by a large system of vortices is presented in this report. This work is based on the adaptive scheme of Carrier, Greengard, and Rokhlin with the added feature that the evaluation or target points do not have to coincide with the location of the source or vortex positions. A simple algorithm based on numerical experiments has been developed to optimize the method for cases where the number of vortices N{sub V} differs significantly from the number of target points N{sub T}. The ability to specify separate source and target fields provides an efficient means for calculating boundary conditions, trajectories of passive scalar quantities, and stream-function plots, etc. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. For six terms in the series expansions, non-dimensional truncation errors for the magnitudes of the complex potential and velocity fields are on the order of 10{sup {minus}5} and 10{sup {minus}3} respectively. The authors found that the CPU time scales as {radical}(N{sub V}N{sub T}) for N{sub V}/N{sub T} in the range of 0.1 to 10. For {radical}(N{sub V}N{sub T}) less than 200, there is virtually no CPU time savings while for {radical}N{sub V}N{sub T} roughly equal to 20,000, the fast solver obtains solutions in about 1% of the time required for the direct solution technique depending somewhat upon the configuration of the vortex field and the target field.
A Radiation Transfer Solver for Athena Using Short Characteristics
NASA Astrophysics Data System (ADS)
Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
Efficient IMRT inverse planning with a new L1-solver: template for first-order conic solver
NASA Astrophysics Data System (ADS)
Kim, Hojin; Suh, Tae-Suk; Lee, Rena; Xing, Lei; Li, Ruijiang
2012-07-01
Intensity modulated radiation therapy (IMRT) inverse planning using total-variation (TV) regularization has been proposed to reduce the complexity of fluence maps and facilitate dose delivery. Conventionally, the optimization problem with L-1 norm is solved with quadratic programming (QP), which is time consuming and memory expensive due to the second-order Newton update. This study proposes to use a new algorithm, template for first-order conic solver (TFOCS), for fast and memory-efficient optimization in IMRT inverse planning. The TFOCS utilizes dual-variable updates and first-order approaches for TV minimization without the need to compute and store the enlarged Hessian matrix required for Newton update in the QP technique. To evaluate the effectiveness and efficiency of the proposed method, two clinical cases were used for IMRT inverse planning: a head and neck case and a prostate case. For comparison, the conventional QP-based method for the TV form was adopted to solve the fluence map optimization problem in the above two cases. The convergence criteria and algorithm parameters were selected to achieve similar dose conformity for a fair comparison between the two methods. Compared with conventional QP-based approach, the proposed TFOCS-based method shows a remarkable improvement in computational efficiency for fluence map optimization, while maintaining the conformal dose distribution. Compared with QP-based algorithms, the computational speed using TFOCS for fluence optimization is increased by a factor of 4 to 6, and at the same time the memory requirement is reduced by a factor of 3 to 4. Therefore, TFOCS provides an effective, fast and memory-efficient method for IMRT inverse planning. The unique features of the approach should be particularly important in inverse planning involving a large number of beams, such as in VMAT and dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT).
Browne, P.L.
1986-02-01
This report derives, then shows the equivalence of, the Lagrangian and Eulerian equations by use of Reynolds' Transport Theorem. The differential forms of the equations are also deduced from the integral forms. Finally, some common simplifications of the equations are derived. 3 refs., 1 fig.
NASA Astrophysics Data System (ADS)
Hao, J.; Lin, Y. J.; Nie, Y.; Wu, M.; Ludwig, A.
2015-06-01
A 3-phase Eulerian approach is used to model the macrosegregation during solidification in direct chill (DC) casting of binary bronze (Cu-Sn). The three phases are the melt, the solidifying columnar dendrites and the equiaxed grains. The thermodynamic information of Cu-Sn is included based on published thermodynamic data, which are coupled with the 3-phase solidification model. The occurrence of columnar-to-equiaxed transition (CET), phase interactions, feeding flow, equiaxed sedimentation and their influence on macrosegregation are considered in the model. The model is applied to a laboratory DC casting process of bronze as a benchmark to demonstrate the model potentials. The simulation results of mixed columnar and equiaxed solidification as well as the formation of macrosegregation are presented. The focus of this work is to analyze and discuss the macrosegregation mechanisms by different flow including feeding flow and crystal sedimentation.
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
NASA Astrophysics Data System (ADS)
Alvarado, Matthew James; Wang, Chien; Prinn, Ronald G.
2009-05-01
Global-scale models of atmospheric chemistry (GACMs) "mix" biomass burning emissions into grid boxes with horizontal scales of 10-200 km. This ignores the complex nonlinear transformations that take place in the young smoke plumes. Here we use a new gas- and aerosol-phase chemistry model called Aerosol Simulation Program (ASP) and a 3-D Eulerian smoke plume model to simulate the fluid dynamics, radiative transfer, gas-phase chemistry, and aerosol-phase chemistry of the Timbavati smoke plume observed during SAFARI 2000. We then compare the results of the 3-D plume model with those of an Eulerian box model, which is used as an analog for the large grid boxes of GACMs. The 3-D plume model matched the observed plume injection height but required a large minimum horizontal diffusion coefficient to match the observed horizontal dispersion of the plume. Absorption and scattering by smoke aerosols reduced the modeled photolysis rates in the plume by 10-20%. Increasing the heterogeneous production of HONO and H2SO4 in the model and including uncharacterized organic species using monoterpenes as a proxy compound improves the model-observation match. Direct measurements of OH in the smoke plumes would be an excellent way to determine if heterogeneous production of HONO is taking place. The automatic dilution of smoke plume emissions into the large grid boxes of global models can result in large errors in predicted concentrations of O3, NOx and aerosol species downwind. We discuss several potential approaches that could reduce these errors.
Tassev, Svetlin
2014-06-01
We present a pedagogical systematic investigation of the accuracy of Eulerian and Lagrangian perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theory to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by Eulerian Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. I. HYDRODYNAMICS AND SELF-GRAVITY
Almgren, A. S.; Beckner, V. E.; Bell, J. B.; Day, M. S.; Lijewski, M. J.; Nonaka, A.; Howell, L. H.; Singer, M.; Joggerst, C. C.; Zingale, M.
2010-06-01
We present a new code, CASTRO, that solves the multicomponent compressible hydrodynamic equations for astrophysical flows including self-gravity, nuclear reactions, and radiation. CASTRO uses an Eulerian grid and incorporates adaptive mesh refinement (AMR). Our approach to AMR uses a nested hierarchy of logically rectangular grids with simultaneous refinement in both space and time. The radiation component of CASTRO will be described in detail in the next paper, Part II, of this series.
Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications
NASA Technical Reports Server (NTRS)
Sun, Xian-He
1997-01-01
Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm
Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening
NASA Technical Reports Server (NTRS)
Diskin, Boris
1999-01-01
This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation
A Computationally Efficient Multicomponent Equilibrium Solver for Aerosols (MESA)
Zaveri, Rahul A.; Easter, Richard C.; Peters, Len K.
2005-12-23
This paper describes the development and application of a new multicomponent equilibrium solver for aerosol-phase (MESA) to predict the complex solid-liquid partitioning in atmospheric particles containing H+, NH4+, Na+, Ca2+, SO4=, HSO4-, NO3-, and Cl- ions. The algorithm of MESA involves integrating the set of ordinary differential equations describing the transient precipitation and dissolution reactions for each salt until the system satisfies the equilibrium or mass convergence criteria. Arbitrary values are chosen for the dissolution and precipitation rate constants such that their ratio is equal to the equilibrium constant. Numerically, this approach is equivalent to iterating all the equilibrium reactions simultaneously with a single iteration loop. Because CaSO4 is sparingly soluble, it is assumed to exist as a solid over the entire RH range to simplify the algorithm for calcium containing particles. Temperature-dependent mutual deliquescence relative humidity polynomials (valid from 240 to 310 K) for all the possible salt mixtures were constructed using the comprehensive Pitzer-Simonson-Clegg (PSC) activity coefficient model at 298.15 K and temperature-dependent equilibrium constants in MESA. Performance of MESA is evaluated for 16 representative mixed-electrolyte systems commonly found in tropospheric aerosols using PSC and two other multicomponent activity coefficient methods – Multicomponent Taylor Expansion Method (MTEM) of Zaveri et al. [2004], and the widely-used Kusik and Meissner method (KM), and the results are compared against the predictions of the Web-based AIM Model III or available experimental data. Excellent agreement was found between AIM, MESA-PSC, and MESA-MTEM predictions of the multistage deliquescence growth as a function of RH. On the other hand, MESA-KM displayed up to 20% deviations in the mass growth factors for common salt mixtures in the sulfate-poor cases while significant discrepancies were found in the predicted multistage
Yeh, Gour-Tsyh; Carpenter, S.L.; Hopkins, P.L.; Siegel, M.D.
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Storaasli, Olaf O.
2004-01-01
Of several iterative and direct equation solvers evaluated previously for computations in aeroacoustics, the most promising was the NASA-developed General-Purpose Solver (winner of NASA's 1999 software of the year award). This paper presents detailed, single-processor statistics of the performance of this solver, which has been tailored and optimized for large-scale aeroacoustic computations. The statistics, compiled using an SGI ORIGIN 2000 computer with 12 Gb available memory (RAM) and eight available processors, are the central processing unit time, RAM requirements, and solution error. The equation solver is capable of solving 10 thousand complex unknowns in as little as 0.01 sec using 0.02 Gb RAM, and 8.4 million complex unknowns in slightly less than 3 hours using all 12 Gb. This latter solution is the largest aeroacoustics problem solved to date with this technique. The study was unable to detect any noticeable error in the solution, since noise levels predicted from these solution vectors are in excellent agreement with the noise levels computed from the exact solution. The equation solver provides a means for obtaining numerical solutions to aeroacoustics problems in three dimensions.
Finite Element Interface to Linear Solvers (FEI) version 2.9 : users guide and reference manual.
Williams, Alan B.
2005-02-01
The Finite Element Interface to Linear Solvers (FEI) is a linear system assembly library. Sparse systems of linear equations arise in many computational engineering applications, and the solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver package capable of solving all of the linear systems that arise. This motivates the need to switch an application from one solver library to another, depending on the problem being solved. The interfaces provided by various solver libraries for data assembly and problem solution differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application can be greatly reduced by having an abstraction layer that puts a 'common face' on various solver libraries. The FEI has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory. The original FEI offered several advantages over using linear algebra libraries directly, but also imposed significant limitations and disadvantages. A new set of interfaces has been added with the goal of removing the limitations of the original FEI while maintaining and extending its strengths.
Using a multifrontal sparse solver in a high performance, finite element code
NASA Technical Reports Server (NTRS)
King, Scott D.; Lucas, Robert; Raefsky, Arthur
1990-01-01
We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.
Wavelet-based Poisson Solver for use in Particle-In-CellSimulations
Terzic, B.; Mihalcea, D.; Bohn, C.L.; Pogorelov, I.V.
2005-05-13
We report on a successful implementation of a wavelet based Poisson solver for use in 3D particle-in-cell (PIC) simulations. One new aspect of our algorithm is its ability to treat the general(inhomogeneous) Dirichlet boundary conditions (BCs). The solver 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 further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modeling of the Fermilab/NICADD and AES/JLab photoinjectors.
Implementation of An Implicit Unsplit Staggered Mesh MHD Solver in FLASH
NASA Astrophysics Data System (ADS)
Xia, G.; Lee, D.
2010-11-01
FLASH is a publicly available community code designed to solve highly compressible multi-physics reactive flows. We have been adding capabilities to FLASH to make it an open science code for the academic HEDP community. A key need is to provide a computationally efficient time-stepping integration method that overcomes the stiffness that arises in the equations describing a physical problem when there are disparate time scales. To address this problem, we are developing a fully implicit solver based on a Jacobian-Free Newton-Krylov implicit formulation. The method has been integrated into a robust, efficient, and high-order accurate Unsplit Staggered Mesh MHD (USM) solver. We are also integrating this solver into an anisotropic Spitzer-Braginskii conductivity model to treat thermal heat conduction along magnetic field lines, and into a treatment of the Biermann Battery effect that accounts for spontaneous generation of magnetic fields in the presence of non-parallel temperature and density gradients.
Prediction of ship resistance in head waves using RANS based solver
NASA Astrophysics Data System (ADS)
Islam, Hafizul; Akimoto, Hiromichi
2016-07-01
Maneuverability prediction of ships using CFD has gained high popularity over the years because of its improving accuracy and economics. This paper discusses the estimation of calm water and added resistance properties of a KVLCC2 model using a light and economical RaNS based solver, called SHIP_Motion. The solver solves overset structured mesh using finite volume method. In the calm water test, total drag coefficient, sinkage and trim values were predicted together with mesh dependency analysis and compared with experimental data. For added resistance in head sea, short wave cases were simulated and compared with experimental and other simulation data. Overall the results were well predicted and showed good agreement with comparative data. The paper concludes that it is well possible to predict ship maneuverability characteristics using the present solver, with reasonable accuracy utilizing minimum computational resources and within acceptable time.
Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver
Shonibare, Olabanji Y.; Wardle, Kent E.
2015-01-01
A novel hybrid multiphase flow solver has been used to conduct simulations of a vertical plunging liquid jet. This solver combines a multifluid methodology with selective interface sharpening to enable simulation of both the initial jet impingement and the long-time entrained bubble plume phenomena. Models are implemented for variable bubble size capturing and dynamic switching of interface sharpened regions to capture transitions between the initially fully segregated flow types into the dispersed bubbly flow regime. It was found that the solver was able to capture the salient features of the flow phenomena under study and areas for quantitative improvement havemore » been explored and identified. In particular, a population balance approach is employed and detailed calibration of the underlying models with experimental data is required to enable quantitative prediction of bubble size and distribution to capture the transition between segregated and dispersed flow types with greater fidelity.« less
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
NASA Technical Reports Server (NTRS)
Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.
Frequency Domain Modelling by a Direct-Iterative Solver: A Space and Wavelet Approach
NASA Astrophysics Data System (ADS)
Hustedt, B.; Operto, S.; Virieux, J.
2002-12-01
Seismic forward modelling of wave propagation phenomena in complex rheologic media using a frequency domain finite-difference (FDFD) technique is of special interest for multisource experiments and waveform inversion schemes, because the complete wavefield solution can be computed in a fast and efficient way. FDFD modelling requires the inversion of an extremely large matrix-equation A x x = b, by either a direct or an iterative solver. The direct solver computes an effective inverse of A, called LU factorization. The main handicap is additional computer memory required for storing matrix fill-in coefficients, that are created during the factorization process. Iterative solvers are not limited by memory constraints (additional coefficients), but the convergence depends on a good initial solution difficult to guess before hand. For both solvers, available computer resources has limited wide-spread FDFD modelling applications to mainly two-dimensional (2D) and rarely three-dimensional (3D) problems. In order to overcome these limits, we propose the combination of a direct solver and an iterative solver, called Direct-Iterative Solver (DIS). The direct solver is used to compute an exact wavefield solution on a coarse discretized grid. We use a multifrontal decomposition technique. The coarse-grid size is determined preliminary by limits of the available computer resources, rather than by the wave simulation problem. We project the exact coarse-grid solution on a fine-grid, and use it as an initial solution for an iterative solver, which convergences to an acceptable approximation of the desired fine-grid solution. Two different DIS schemes have been implemented and tested for numerical accuracy and computational performance. The first approach, called the Direct-Iterative-Space Solver (DISS), projects the coarse-grid solution on the fine-grid by a bilinear interpolation. Though the interpolated solution nicely approximates the desired fine-grid solution, still for
Flutter and Forced Response Analyses of Cascades using a Two-Dimensional Linearized Euler Solver
NASA Technical Reports Server (NTRS)
Reddy, T. S. R.; Srivastava, R.; Mehmed, O.
1999-01-01
Flutter and forced response analyses for a cascade of blades in subsonic and transonic flow is presented. The structural model for each blade is a typical section with bending and torsion degrees of freedom. The unsteady aerodynamic forces due to bending and torsion motions. and due to a vortical gust disturbance are obtained by solving unsteady linearized Euler equations. The unsteady linearized equations are obtained by linearizing the unsteady nonlinear equations about the steady flow. The predicted unsteady aerodynamic forces include the effect of steady aerodynamic loading due to airfoil shape, thickness and angle of attack. The aeroelastic equations are solved in the frequency domain by coupling the un- steady aerodynamic forces to the aeroelastic solver MISER. The present unsteady aerodynamic solver showed good correlation with published results for both flutter and forced response predictions. Further improvements are required to use the unsteady aerodynamic solver in a design cycle.
3-D seakeeping analysis with water on deck and slamming. Part 1: Numerical solver
NASA Astrophysics Data System (ADS)
Greco, M.; Lugni, C.
2012-08-01
A three-dimensional seakeeping numerical solver is developed to handle occurrence and effects of water-on-deck and bottom slamming. It couples (A) the rigid-ship motions with (B) the water flowing along the deck and (C) bottom slamming events. Problem A is studied with a 3-D weakly nonlinear potential flow solver based on the weak-scatterer hypothesis. Problem B, and so local and global induced green-water loads, are investigated by assuming shallow-water conditions onto the deck. Problem C is examined through a Wagner-type wedge-impact analysis. Within the coupling between A and B: the external seakeeping problem furnishes the initial and boundary conditions to the in-deck solver in terms of water level and velocity along the deck profile; in return the shallow-water problem makes available to the seakeeping solver the green-water loads to be introduced as additional loads into the rigid-motion equations. Within the coupling between A and C: the instantaneous ship configuration and its kinematic and dynamic conditions with respect to the incident waves will fix the parameters for the local impact problem; in return the slamming and water-entry pressures are integrated in the vessel region of interest and introduced as additional loads into the rigid-motion equations. The resulting numerical solver can study efficiently the ship interaction with regular and irregular sea states and the forward motion with limited speed of the vessel. This is crucial to perform reliable and feasible statistical investigations of vessel behavior. Main elements of the solver are described and validated against reference numerical solutions and model tests.
Wavelet-based Poisson solver for use in particle-in-cell simulations.
Terzić, Balsa; Pogorelov, Ilya V
2005-06-01
We report on a successful implementation of a wavelet-based Poisson solver 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 solver to test problems in accelerator physics and astrophysics. PMID:15980304
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
NASA Technical Reports Server (NTRS)
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
Newton-Raphson preconditioner for Krylov type solvers on GPU devices.
Kushida, Noriyuki
2016-01-01
A new Newton-Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs. However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. The developed preconditioner is based on the BFGS Hessian matrix approximation technique, which is well known as a robust and fast nonlinear equation solver. Because the Hessian matrix in the BFGS represents the coefficient matrix of a system of linear equations in some sense, the approximated Hessian matrix can be a preconditioner. On the other hand, BFGS is required to store dense matrices and to invert them, which should be avoided on modern computers and supercomputers. To overcome these disadvantages, we therefore introduce a limited memory BFGS, which requires less memory space and less computational effort than the BFGS. In addition, a limited memory BFGS can be implemented with BLAS libraries, which are well optimized for target architectures. There are advantages and disadvantages to the Hessian matrix approximation becoming better as the Krylov solver iteration continues. The preconditioning matrix varies through Krylov solver iterations, and only flexible Krylov solvers can work well with the developed preconditioner. The GCR method, which is a flexible Krylov solver, is employed because of the prevalence of GCR as a Krylov solver with a variable preconditioner. As a result of the performance investigation, the new preconditioner indicates the following benefits: (1) The new preconditioner is robust; i.e., it converges while conventional preconditioners (the diagonal scaling, and the SSOR preconditioners) fail. (2) In the best case scenarios, it is over 10 times faster than conventional preconditioners on a CPU. (3) Because it requries only simple operations, it performs well on a GPGPU. In
Trust-region based solver for nonlinear transport in heterogeneous porous media
NASA Astrophysics Data System (ADS)
Wang, Xiaochen; Tchelepi, Hamdi A.
2013-11-01
We describe a new nonlinear solver for immiscible two-phase transport in porous media, where viscous, buoyancy, and capillary forces are significant. The flux (fractional flow) function, F, is a nonlinear function of saturation and typically has inflection points and can be non-monotonic. The non-convexity and non-monotonicity of F are major sources of difficulty for nonlinear solvers of coupled multiphase flow and transport in natural porous media. We describe a modified Newton algorithm that employs trust regions of the flux function to guide the Newton iterations. The flux function is divided into saturation trust regions delineated by the inflection, unit-flux, and end points. The updates are performed such that two successive iterations cannot cross any trust-region boundary. If a crossing is detected, the saturation value is chopped back to the appropriate trust-region boundary. The proposed trust-region Newton solver, which is demonstrated across the parameter space of viscous, buoyancy and capillary effects, is a significant extension of the inflection-point strategy of Jenny et al. (JCP, 2009) [5] for viscous dominated flows. We analyze the discrete nonlinear transport equation obtained using finite-volume discretization with phase-based upstream weighting. Then, we prove convergence of the trust-region Newton method irrespective of the timestep size for single-cell problems. Numerical results across the full range of the parameter space of viscous, gravity and capillary forces indicate that our trust-region scheme is unconditionally convergent for 1D transport. That is, for a given choice of timestep size, the unique discrete solution is found independently of the initial guess. For problems dominated by buoyancy and capillarity, the trust-region Newton solver overcomes the often severe limits on timestep size associated with existing methods. To validate the effectiveness of the new nonlinear solver for large reservoir models with strong heterogeneity
Parallel H1-based auxiliary space AMG solver for H(curl) problems
Kolev, T V; Vassilevski, P S
2006-06-30
This report describes a parallel implementation of the auxiliary space methods for definite Maxwell problems proposed in [4]. The solver, named AMS, extends our previous study [7]. AMS uses ParCSR sparse matrix storage and the parallel AMG (algebraic multigrid) solver BoomerAMG [1] from the hypre library. It is designed for general unstructured finite element discretizations of (semi)definite H(curl) problems discretized by Nedelec elements. We document the usage of AMS and illustrate its parallel scalability and overall performance.
Newton-Raphson preconditioner for Krylov type solvers on GPU devices.
Kushida, Noriyuki
2016-01-01
A new Newton-Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs. However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. The developed preconditioner is based on the BFGS Hessian matrix approximation technique, which is well known as a robust and fast nonlinear equation solver. Because the Hessian matrix in the BFGS represents the coefficient matrix of a system of linear equations in some sense, the approximated Hessian matrix can be a preconditioner. On the other hand, BFGS is required to store dense matrices and to invert them, which should be avoided on modern computers and supercomputers. To overcome these disadvantages, we therefore introduce a limited memory BFGS, which requires less memory space and less computational effort than the BFGS. In addition, a limited memory BFGS can be implemented with BLAS libraries, which are well optimized for target architectures. There are advantages and disadvantages to the Hessian matrix approximation becoming better as the Krylov solver iteration continues. The preconditioning matrix varies through Krylov solver iterations, and only flexible Krylov solvers can work well with the developed preconditioner. The GCR method, which is a flexible Krylov solver, is employed because of the prevalence of GCR as a Krylov solver with a variable preconditioner. As a result of the performance investigation, the new preconditioner indicates the following benefits: (1) The new preconditioner is robust; i.e., it converges while conventional preconditioners (the diagonal scaling, and the SSOR preconditioners) fail. (2) In the best case scenarios, it is over 10 times faster than conventional preconditioners on a CPU. (3) Because it requries only simple operations, it performs well on a GPGPU. In
Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles
NASA Astrophysics Data System (ADS)
Moffitt, Nicholas J.
This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate
NASA Astrophysics Data System (ADS)
Li, Shao-Meng; Anlauf, K. G.; Wiebe, H. A.; Bottenheim, J. W.; Puckett, K. J.
Using a principal component analysis technique and data on atmospheric gases and aerosols at a rural site in Ontario, Canada from the Eulerian model evaluation field study (EMEFS), the Eulerian acid deposition and oxidant model (ADOM) is evaluated. Seventy-nine and 76% of the variances in the data and model output, respectively, are explained by three principal components. They are a chemically aged/ transported component, a diurnal cycle component, and an area emission component, all characterized by their ratios of gases and temporal variation patterns. The ADOM component contributions to sulphur species are in general agreement with the EMEFS components, but with notable differences for key photochemical species including O 3. The temporal variations of the ADOM components are close to those of the EMEFS components. The EMEFS chemically aged/transported component shows a high degree of photochemical processing, with the ratios [NO x]/[TNO y]=0.3 and [O 3]/([TNO y]-[NO x])=9±1. The corresponding ADOM component predicts lower G[NO x]/[TNO y] and [NO 3]/([TNO y]-[NO x]) ratios, probably caused by a chemical mechanism in the model that is too fast, and lower contributions to O 3, NO 2, TNO 3, PAN, TNO y, and HCHO, probably caused by model grid dilution or lower model emissions. The EMEFS diurnal component owes its variance to the daily photochemistry and nighttime dry deposition of the chemical species. In comparison, the matching ADOM component underpredicts the ratio [O 3]/([TNO y]-[NO x]) and the NO 2 consumption and O 3 production but overpredicts the contributions to the other species. The EMEFS emission component represents emissions from local/regional area sources. The corresponding ADOM component underpredicts TNO y by 44% and the fraction of TNO y as NO x compared to the EMEFS component, suggesting that the model has lower emissions of NO x and a photochemical mechanism that converts NO x faster than indicated by the EMEFS results.
NASA Astrophysics Data System (ADS)
Shippee, N. J.; Atkinson, D. E.
2014-12-01
The idea of considering the "end user perspective" regarding storm activity and objective tracking methods used to compile information on their behaviour is particularly important in the Alaskan region. Annually, coastal regions in the North are exposed to stormy conditions, though most impacts occur during periods where multiple storms track over the same area in a short period of time (serial cyclones) or where strong storms occur without the presence of a protective sea ice buffer. From a fixed perspective (i.e. Eulerian), a storm may be identified more by the impacts that it generates at that location (winds, sea state, erosion). From a Lagrangian (tracking) view, the intensity, duration, and characteristics of the synoptic environment may prove more relevant for understanding. The overall "effectiveness" of an objective tracking method depends on the intended use of the provided information. While pitting different methods against each other is not necessarily a fruitful exercise (Mesquita et al. 2009), the reality is that one method may better reflect the reality of storm activity and impacts to those experiencing the weather first hand. One of the more subtle points in extra-tropical cyclone tracking and comparison work is the method by which a storm is defined. Most cyclones are analyzed on MSLP fields; others define a cyclone by relative vorticity (ζ) maxima at 850 hPa (NH) and minima (SH). Storms can also be defined by wind events, or even impacts, at a location. Using counts of strong wind events at a grid point or location can account for pressure gradients both associated with storms and absent of a synoptic event. Three separate tracking algorithms are analyzed to determine the method most likely to produce a long-term homogeneous dataset that can be used to train a statistical seasonal prediction method. These methods include the Serreze algorithm, Hodges TRACK algorithm, and Atkinson algorithm. Both the Serreze and Hodges methods provide a tracking
NASA Technical Reports Server (NTRS)
Carmichael, G. R.; Peters, L. K.
1984-01-01
A three-dimensional, time dependent Eulerian atmospheric SO2 and sulfate transport/transformation/removal model is described and applied to the eastern U.S. The model was developed in anticipation of increased input to the atmospheric sulfur content by coal-burning power plants in the near future and is intended as an aid in identifying sources of SO2. The Eulerian transport model incorporates functions for chemical transformations, dry deposition, spatial topographical variations, spatial and temporal variations of mixing layer heights, the wind field, eddy diffusivities, deposition velocities, and temperature and water concentration profiles. Attention is also given to the SO2 photochemical oxidation mechanism and rates. Results from a 72-hr simulation of SO(x) transport over the eastern U.S., using actual 1974 meteorological data, illustrate the model's capability to depict interactions between emissions, transport, chemistry and removal. Concentration distributions are demonstrated to have significant spatial and temporal variations.
Mastin, Larry G.; Randall, Michael J.; Schwaiger, Hans F.; Denlinger, Roger P.
2013-01-01
Ash3d is a three-dimensional Eulerian atmospheric model for tephra transport, dispersal, and deposition, written by the authors to study and forecast hazards of volcanic ash clouds and tephra fall. In this report, we explain how to set up simulations using both a web interface and an ASCII input file, and how to view and interpret model output. We also summarize the architecture of the model and some of its properties.
Ganshin, A; Oda, T; Saito, M; Maksyutov, S; Valsala, V; Andres, Robert Joseph; Fischer, R; Lowry, D; Lukyanov, A; Matsueda, H; Nisbet, E; Rigby, M; Sawa, Y; Toumi, R; Tsuboi, K; Varlagin, A; Zhuravlev, R
2012-01-01
Abstract. We designed a method to simulate atmospheric CO2 concentrations at several continuous observation sites around the globe using surface fluxes at a very high spatial resolution. The simulations presented in this study were performed using the Global Eulerian-Lagrangian Coupled Atmospheric model (GELCA), comprising a Lagrangian particle dispersion model coupled to a global atmospheric tracer transport model with prescribed global surface CO2 flux maps at a 1 1 km resolution. The surface fluxes used in the simulations were prepared by assembling the individual components of terrestrial, oceanic and fossil fuel CO2 fluxes. This experimental setup (i.e. a transport model running at a medium resolution, coupled to a high-resolution Lagrangian particle dispersion model together with global surface fluxes at a very high resolution), which was designed to represent high-frequency variations in atmospheric CO2 concentration, has not been reported at a global scale previously. Two sensitivity experiments were performed: (a) using the global transport model without coupling to the Lagrangian dispersion model, and (b) using the coupled model with a reduced resolution of surface fluxes, in order to evaluate the performance of Eulerian-Lagrangian coupling and the role of high-resolution fluxes in simulating high-frequency variations in atmospheric CO2 concentrations. A correlation analysis between observed and simulated atmospheric CO2 concentrations at selected locations revealed that the inclusion of both Eulerian-Lagrangian coupling and highresolution fluxes improves the high-frequency simulations of the model. The results highlight the potential of a coupled Eulerian-Lagrangian model in simulating high-frequency atmospheric CO2 concentrations at many locations worldwide. The model performs well in representing observations of atmospheric CO2 concentrations at high spatial and temporal resolutions, especially for coastal sites and sites located close to sources of
A Navier-Stokes solver using the LU-SSOR TVD algorithm
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan
1987-01-01
A new Navier-Stokes solver is developed by combining the efficiency of the LU-SSOR scheme and the accuracy of the flux-limited dissipation scheme. Application to laminar and turbulent flows and hypersonic flows proves the reliability of the new algorithm.
Experimental validation of a coupled neutron-photon inverse radiation transport solver.
Mattingly, John K.; Harding, Lee; Mitchell, Dean James
2010-03-01
Forward radiation transport is the problem of calculating the radiation field given a description of the radiation source and transport medium. In contrast, inverse transport is the problem of inferring the configuration of the radiation source and transport medium from measurements of the radiation field. As such, the identification and characterization of special nuclear materials (SNM) is a problem of inverse radiation transport, and numerous techniques to solve this problem have been previously developed. The authors have developed a solver based on nonlinear regression applied to deterministic coupled neutron-photon transport calculations. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5-kg sphere of alpha-phase, weapons-grade plutonium. The source was measured in six different configurations: bare, and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses of 1.27, 2.54, 3.81, 7.62, 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 solver to characterize the solver's ability to correctly infer the configuration of the source from its measured signatures.
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Study of the microbunching instability in single-pass systemsusing a direct 2D Vlasov solver
Venturini, Marco
2007-06-30
We apply a recently developed Vlasov solver to the study ofthemicrobunching instability generated by shot noise in the beamdeliverysystems of x-ray Free Electron Lasers (FELs). We discusstwo latticespresently under consideration for the FEL FERMI project at Elettra andshow that at least one of the two lattices appears capable of deliveringa beam with the desired quality in the longitudinal phasespace.
NASA Astrophysics Data System (ADS)
Wang, Y.; Shu, C.; Huang, H. B.; Teo, C. J.
2015-01-01
A multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this paper for incompressible multiphase flows with low- and large-density-ratios. In the solver, the flow variables at cell centers are given from the solution of macroscopic governing differential equations (Navier-Stokes equations recovered by multiphase lattice Boltzmann (LB) model) by the finite volume method. At each cell interface, the viscous and inviscid fluxes are evaluated simultaneously by local reconstruction of solution for the standard lattice Boltzmann equation (LBE). The forcing terms in the governing equations are directly treated by the finite volume discretization. The phase interfaces are captured by solving the phase-field Cahn-Hilliard equation with a fifth order upwind scheme. Unlike the conventional multiphase LB models, which restrict their applications on uniform grids with fixed time step, the MLBFS has the capability and advantage to simulate multiphase flows on non-uniform grids. The proposed solver is validated by several benchmark problems, such as two-phase co-current flow, Taylor-Couette flow in an annulus, Rayleigh-Taylor instability, and droplet splashing on a thin film at density ratio of 1000 with Reynolds numbers ranging from 20 to 1000. Numerical results show the reliability of the proposed solver for multiphase flows with high density ratio and high Reynolds number.
NASA Astrophysics Data System (ADS)
Heil, Matthias; Hazel, Andrew L.; Boyle, Jonathan
2008-12-01
We compare the relative performance of monolithic and segregated (partitioned) solvers for large- displacement fluid structure interaction (FSI) problems within the framework of oomph-lib, the object-oriented multi-physics finite-element library, available as open-source software at
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Das, Raja; Saltz, Joel; Vermeland, R. E.
1992-01-01
An efficient three dimensional unstructured Euler solver is parallelized on a Cray Y-MP C90 shared memory computer and on an Intel Touchstone Delta distributed memory computer. This paper relates the experiences gained and describes the software tools and hardware used in this study. Performance comparisons between two differing architectures are made.
Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows
Technology Transfer Automated Retrieval System (TEKTRAN)
Several new techniques are proposed to overcome the deficiencies in the conventional formulation of the approximate Riemann solvers for one-dimensional open channel flows, which include numerical imbalance and inaccuracy in the solution of discharge. The former arises in the case of irregular geomet...
NASA Astrophysics Data System (ADS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-12-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5-3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.
A fast parallel solver for the forward problem in electrical impedance tomography.
Jehl, Markus; Dedner, Andreas; Betcke, Timo; Aristovich, Kirill; Klöfkorn, Robert; Holder, David
2015-01-01
Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and the resulting surface voltages are measured. It has the potential to distinguish between ischaemic and haemorrhagic stroke with a portable and inexpensive device. The image reconstruction relies on an accurate forward model of the experimental setup. Because of the relatively small signal in stroke EIT, the finite-element modeling requires meshes of more than 10 million elements. To study the requirements in the forward modeling in EIT and also to reduce the time for experimental image acquisition, it is necessary to reduce the run time of the forward computation. We show the implementation of a parallel forward solver for EIT using the Dune-Fem C++ library and demonstrate its performance on many CPU's of a computer cluster. For a typical EIT application a direct solver was significantly slower and not an alternative to iterative solvers with multigrid preconditioning. With this new solver, we can compute the forward solutions and the Jacobian matrix of a typical EIT application with 30 electrodes on a 15-million element mesh in less than 15 min. This makes it a valuable tool for simulation studies and EIT applications with high precision requirements. It is freely available for download. PMID:25069109
Flowfield Comparisons from Three Navier-Stokes Solvers for an Axisymmetric Separate Flow Jet
NASA Technical Reports Server (NTRS)
Koch, L. Danielle; Bridges, James; Khavaran, Abbas
2002-01-01
To meet new noise reduction goals, many concepts to enhance mixing in the exhaust jets of turbofan engines are being studied. Accurate steady state flowfield predictions from state-of-the-art computational fluid dynamics (CFD) solvers are needed as input to the latest noise prediction codes. The main intent of this paper was to ascertain that similar Navier-Stokes solvers run at different sites would yield comparable results for an axisymmetric two-stream nozzle case. Predictions from the WIND and the NPARC codes are compared to previously reported experimental data and results from the CRAFT Navier-Stokes solver. Similar k-epsilon turbulence models were employed in each solver, and identical computational grids were used. Agreement between experimental data and predictions from each code was generally good for mean values. All three codes underpredict the maximum value of turbulent kinetic energy. The predicted locations of the maximum turbulent kinetic energy were farther downstream than seen in the data. A grid study was conducted using the WIND code, and comments about convergence criteria and grid requirements for CFD solutions to be used as input for noise prediction computations are given. Additionally, noise predictions from the MGBK code, using the CFD results from the CRAFT code, NPARC, and WIND as input are compared to data.
An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations
NASA Technical Reports Server (NTRS)
Singh, Jatinder; Taylor, Stephen
1997-01-01
This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.
2005-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.
A Flexible CUDA LU-based Solver for Small, Batched Linear Systems
Tumeo, Antonino; Gawande, Nitin A.; Villa, Oreste
2014-06-09
This chapter presents the implementation of a batched CUDA solver based on LU factorization for small linear systems. This solver may be used in applications such as reactive flow transport models, which apply the Newton-Raphson technique to linearize and iteratively solve the sets of non linear equations that represent the reactions for ten of thousands to millions of physical locations. The implementation exploits somewhat counterintuitive GPGPU programming techniques: it assigns the solution of a matrix (representing a system) to a single CUDA thread, does not exploit shared memory and employs dynamic memory allocation on the GPUs. These techniques enable our implementation to simultaneously solve sets of systems with over 100 equations and to employ LU decomposition with complete pivoting, providing the higher numerical accuracy required by certain applications. Other currently available solutions for batched linear solvers are limited by size and only support partial pivoting, although they may result faster in certain conditions. We discuss the code of our implementation and present a comparison with the other implementations, discussing the various tradeoffs in terms of performance and flexibility. This work will enable developers that need batched linear solvers to choose whichever implementation is more appropriate to the features and the requirements of their applications, and even to implement dynamic switching approaches that can choose the best implementation depending on the input data.
A Comparison of the Intellectual Abilities of Good and Poor Problem Solvers: An Exploratory Study.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
This study examined a selected sample of fourth-grade students who had been previously identified as good or poor problem solvers. The pupils were compared on variables considered as "reference tests" for Verbal, Induction, Numerical, Word Fluency, Memory, Spatial Visualization, and Perceptual Speed abilities. The data were compiled to indicate…
Mahinthakumar, G.; Saied, F.; Valocchi, A.J.
1997-03-01
Some popular iterative solvers for non-symmetric systems arising from the finite-element discretization of three-dimensional groundwater contaminant transport problem are implemented and compared on distributed memory parallel platforms. This paper attempts to determine which solvers are most suitable for the contaminant transport problem under varied conditions for large scale simulations on distributed parallel platforms. The original parallel implementation was targeted for the 1024 node Intel paragon platform using explicit message passing with the NX library. This code was then ported to SGI Power Challenge Array, Convex Exemplar, and Origin 2000 machines using an MPI implementation. The performance of these solvers is studied for increasing problem size, roughness of the coefficients, and selected problem scenarios. These conditions affect the properties of the matrix and hence the difficulty level of the solution process. Performance is analyzed in terms of convergence behavior, overall time, parallel efficiency, and scalability. The solvers that are presented are BiCGSTAB, GMRES, ORTHOMIN, and CGS. A simple diagonal preconditioner is used in this parallel implementation for all the methods. The results indicate that all methods are comparable in performance with BiCGSTAB slightly outperforming the other methods for most problems. The authors achieved very good scalability in all the methods up to 1024 processors of the Intel Paragon XPS/150. They demonstrate scalability by solving 100 time steps of a 40 million element problem in about 5 minutes using either BiCGSTAB or GMRES.
Determining the Optimal Values of Exponential Smoothing Constants--Does Solver Really Work?
ERIC Educational Resources Information Center
Ravinder, Handanhal V.
2013-01-01
A key issue in exponential smoothing is the choice of the values of the smoothing constants used. One approach that is becoming increasingly popular in introductory management science and operations management textbooks is the use of Solver, an Excel-based non-linear optimizer, to identify values of the smoothing constants that minimize a measure…
Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines
NASA Technical Reports Server (NTRS)
Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.
1994-01-01
The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less
VDJSeq-Solver: in silico V(D)J recombination detection tool.
Paciello, Giulia; Acquaviva, Andrea; Pighi, Chiara; Ferrarini, Alberto; Macii, Enrico; Zamo', Alberto; Ficarra, Elisa
2015-01-01
In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(D)J rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/. PMID:25799103
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
NASA Astrophysics Data System (ADS)
Fisicaro, G.; Genovese, L.; Andreussi, O.; Marzari, N.; Goedecker, S.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Briere, E.; Larrauri, D.; Olive, J.
1995-09-01
For about four years, Electricite de France has been developing a 3-D computer code for the Eulerian simulation of two-phase flows. This code, named ASTRID, is based on the six-equation two-fluid model. Boiling water flows, such as those encountered in nuclear reactors, are among the main applications of ASTRID. In order to provide ASTRID with closure laws and boundary conditions suitable for boiling flows, a boiling model has been developed by EDF and the Institut de Mecanique des Fluides de Toulouse. In the fluid, the heat and mass transfer between a bubble and the liquid is being modelled. At the heating wall, the incipient boiling point is determined according to Hsu`s criterion and the boiling heat flux is split into three additive terms: a convective term, a quenching term and a vaporisation term. This model uses several correlations. EDF`s program in boiling two-phase flows also includes experimental studies, some of which are performed in collaboration with other laboratories. Refrigerant subcooled boiling both in tubular (DEBORA experiment, CEN Grenoble) and in annular geometry (Arizona State University Experiment) have been computed with ASTRID. The simulations show the satisfactory results already obtained on void fraction and liquid temperature. Ways of improvement of the model are drawn especially on the dynamical part.
NASA Astrophysics Data System (ADS)
Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song
2015-09-01
An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.
Saenz, Juan A.; Chen, Qingshan; Ringler, Todd
2015-05-19
Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWAmore » framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, we verify our analysis by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.« less
Park, Byoung Yoon; Leavy, Richard Brian; Niederhaus, John Henry J.
2013-03-01
The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the Eulerian frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by less than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.
Saenz, Juan A.; Chen, Qingshan; Ringler, Todd
2015-05-19
Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWA framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, we verify our analysis by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.
NASA Astrophysics Data System (ADS)
López Ortega, A.; Scovazzi, G.
2011-07-01
This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian-Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to conservative remap. Unique to the proposed method is the direct incorporation of the geometric conservation law (GCL) in the resulting numerical scheme. It is shown here that the geometric conservation law allows the method to inherit the positivity preserving and local extrema diminishing (LED) properties typical of FCT schemes. The proposed framework is extended to the systems of equations that typically arise in meteorological and compressible flow computations. The proposed algorithm remaps the vector fields associated with these problems by means of a synchronized strategy. The present paper also complements and extends the work of the second author on nodal-based methods for shock hydrodynamics, delivering a fully integrated suite of Lagrangian/remap algorithms for computations of compressible materials under extreme load conditions. Extensive testing in one, two, and three dimensions shows that the method is robust and accurate under typical computational scenarios.
Short, Mark; Aslam, Tariq D
2010-01-01
The detonation structure in many insensitive high explosives consists of two temporally disparate zones of heat release. In PBX 9502, there is a fast reaction zone ({approx} 25 ns) during which reactants are converted to gaseous products and small carbon clusters, followed by a slower regime ({approx} 250 ns) of carbon coagulation. A hybrid approach for determining the propagation of two-stage heat release detonations has been developed that utilizes a detonation shock dynamics (DSD) based strategy for the fast reaction zone with a direct hydrodynamic simulation of the flow in the slow zone. Unlike a standard DSD/programmed bum formulation, the evolution of the fast zone DSD-like surface is coupled to the flow in the slow reaction zone. We have termed this formulation flow integrated detonation shock dynamics (FIDSD). The purpose of the present paper is to show how the FIDSD formulation can be applied to detonation propagation on an Eulerian grid using an algorithm based on level set interface tracking and a ghost fluid approach.
Healy, R.W.; Russell, T.F.
1992-01-01
A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.
Wang, H.; Man, S.; Ewing, R.E.; Qin, G.; Lyons, S.L.; Al-Lawatia, M.
1999-06-10
Many difficult problems arise in the numerical simulation of fluid flow processes within porous media in petroleum reservoir simulation and in subsurface contaminant transport and remediation. The authors develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are full mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.
Wang, C.Y.
1993-06-01
This paper describes fluid-structure-interaction and structure response analyses of a reactor vessel subjected to loadings associated with postulated accidents, using the hybrid Lagrangian-Eulerian code ALICE-II. This code has been improved recently to accommodate many features associated with innovative designs of reactor vessels. Calculational capabilities have been developed to treat water in the reactor cavity outside the vessel, internal shield structures and internal thin shells. The objective of the present analyses is to study the cover response and potential for missile generation in response to a fuel-coolant interaction in the core region. Three calculations were performed using the cover weight as a parameter. To study the effect of the cavity water, vessel response calculations for both wet- and dry-cavity designs are compared. Results indicate that for all cases studied and for the design parameters assumed, the calculated cover displacements are all smaller than the bolts` ultimate displacement and no missile generation of the closure head is predicted. Also, solutions reveal that the cavity water of the wet-cavity design plays an important role of restraining the downward displacement of the bottom head. Based on these studies, the analyses predict that the structure integrity is maintained throughout the postulated accident for the wet-cavity design.
Wang, C.Y.
1993-01-01
This paper describes fluid-structure-interaction and structure response analyses of a reactor vessel subjected to loadings associated with postulated accidents, using the hybrid Lagrangian-Eulerian code ALICE-II. This code has been improved recently to accommodate many features associated with innovative designs of reactor vessels. Calculational capabilities have been developed to treat water in the reactor cavity outside the vessel, internal shield structures and internal thin shells. The objective of the present analyses is to study the cover response and potential for missile generation in response to a fuel-coolant interaction in the core region. Three calculations were performed using the cover weight as a parameter. To study the effect of the cavity water, vessel response calculations for both wet- and dry-cavity designs are compared. Results indicate that for all cases studied and for the design parameters assumed, the calculated cover displacements are all smaller than the bolts' ultimate displacement and no missile generation of the closure head is predicted. Also, solutions reveal that the cavity water of the wet-cavity design plays an important role of restraining the downward displacement of the bottom head. Based on these studies, the analyses predict that the structure integrity is maintained throughout the postulated accident for the wet-cavity design.
NASA Astrophysics Data System (ADS)
Akiki, G.; Balachandar, S.
2016-02-01
This study presents a technique to incorporate spheres in a channel flow that uses a non-uniform Eulerian grid using immersed boundary methods with direct forcing. An efficient algorithm is presented which distributes the Lagrangian markers non-uniformly to match the fluid grid and keep the number of markers optimized. Also a novel method to calculate the area weights of the Lagrangian markers is given. It is observed that even the best available algorithms for uniform distribution of markers on a sphere result in a finite error. Using vector spherical harmonics, this error is quantified and reduced to machine precision. A series of simulations of a stationary and moving sphere in a periodic channel at Reynolds number range of 1-100 are presented. Results for a sphere in an ambient shear flow in close proximity of a wall are also shown, where the present non-uniform distribution offers an order of magnitude reduction over uniform distribution of Lagrangian markers. Simulations of a random cluster of 640 monodisperse spherical particles show a 77% reduction in Lagrangian markers with an error of 0.135% in computing the total drag.
Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Frink, N. T.; Mavriplis, D. J.; Rausch, R. D.; Milholen, W. E.
2004-01-01
A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not
NASA Astrophysics Data System (ADS)
Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike
The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under
NASA Astrophysics Data System (ADS)
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
Miniati, Francesco
2014-02-10
We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z = 0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h {sup –1} kpc across the virial volume. The probability density functions of various velocity-derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within the R {sub vir}/3 region and 40% beyond that. We compute second- and third-order longitudinal and transverse structure functions for both solenoidal and compressional components in the cluster core, virial region, and beyond. The structure functions exhibit a well-defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases toward the outskirts. Within R {sub vir}/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers's; the flow is mostly solenoidal and statistically rigorously, which is consistent with fully developed homogeneous and isotropic turbulence. Small-scale anisotropy appears due to numerical artifact. Toward the virial region, the flow becomes increasingly compressional, the structure functions become flatter, and modest genuine anisotropy appear particularly close to the injection scale. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution leads to a lack of turbulent power on a small scales, an excess thereof on large scales, and
NASA Astrophysics Data System (ADS)
Doisneau, F.; Laurent, F.; Murrone, A.; Dupays, J.; Massot, M.
2013-02-01
The accurate simulation of polydisperse sprays undergoing coalescence in unsteady gaseous flows is a crucial issue. In solid rocket motors, the internal flow depends strongly on the alumina droplet size distribution, which spreads up with coalescence. Yet solving for unsteady two-phase flows with high accuracy on the droplet sizes is a challenge for both modeling and scientific computing. As an alternative to Lagrangian approaches, a wide range of Eulerian models have been recently developed to describe the disperse liquid phase at a lower cost, with an easier coupling to the gaseous phase and with massively parallel codes. Among these models, the multi-fluid model allows the detailed description of polydispersity and size/velocity correlations by separately solving fluids of size-sorted droplets, the so-called sections. The existing one size moment method, which describes the size distribution with one size moment per section, provides simple and fast resolution for coalescence. On the other hand, a two size moment method has been suggested to reduce the number of sections but it lacks an efficient coalescence resolution method. After introducing a new strategy for two size moment coalescence, the two methods are compared on various configurations in a research code and an industrial-oriented code, in order to conclude on computational accuracy and cost. Then the paper aims at describing the most efficient approach for multi-dimensional unsteady and eventually coalescing rocket chamber simulations. Its objective is threefold: first, to validate the two size moment method by comparing simulations to reference solutions and dedicated experimental measurements conducted at ONERA, second to study the efficiency and robustness of both methods, third, to draw some firm conclusions about the necessity to use the one size moment or two size moment method to simulate solid propellant alumina sprays. We finally perform the first simulations of coalescence in realistic 2D
Kota, Sri Harsha; Ying, Qi; Zhang, Yunlong
2013-06-01
In this study, the TAMNROM-3D model, a 3D Eulerian near-road air quality model with vehicle induced turbulence parameterization and a MOVES based emission preprocessor, is tested using near-road gaseous pollutants data collected near a rural freeway with 34% heavy duty vehicle traffic. Exhaust emissions of gasses from the vehicles are estimated using a lumped vehicle classification scheme based on the number of vehicle axles and the default county-level MOVES vehicle fleet database. The predicted dilution of CO and NOx in the downwind direction agrees well with observation, although the total NOx emission has to be scaled to 85% of its original emission rate estimated by the MOVES model. Using the atmospheric turbulent diffusion coefficient parameterization of Degrazia et al. (2000) with variable horizontal turbulent diffusion coefficient (Kxx) leads to slightly better predictions than a traditional non-height-dependent Kxx parameterization. The NO2 concentrations can be better predicted when emission of total NOx is split into NO and NO2 using the NO2 to NOx ratio of 29% measured near the road. Simulations using the SAPRC99 photochemical mechanism do not show significant changes in the predicted NO and NO2 concentrations near the road compared to simulations using a simple three-reaction mechanism that involves only NOx and O3. A regional air quality simulation in Houston, Texas during a high O3 episode in August 2000 shows that using the NO2 to NOx ratio of 29% instead of the traditional 5% leads to as much as 6ppb increase in 8-h O3 predictions.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K.
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
Analysis, tuning and comparison of two general sparse solvers for distributed memory computers
Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.; Li, X.S.
2000-06-30
We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differences in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.
NASA Technical Reports Server (NTRS)
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1996-01-01
The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.
A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations
NASA Astrophysics Data System (ADS)
Popinet, Stéphane
2015-12-01
The Serre-Green-Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in particular for the treatment of wetting/drying and equilibrium states. The linear system of coupled vector equations governing the dispersive SGN momentum sources is solved simply and efficiently using a generic multigrid solver. This approach generalises automatically to adaptive quadtree meshes. Adaptive mesh refinement is shown to provide orders-of-magnitude gains in speed and memory when applied to the dispersive propagation of waves during the Tohoku tsunami. The source code, test cases and examples are freely available.
An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Erickson, Larry L.
1994-01-01
A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.
NASA Technical Reports Server (NTRS)
Yarrow, Maurice; Vastano, John A.; Lomax, Harvard
1992-01-01
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2005-01-01
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.
1994-01-01
An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.
Generating Combinatorial Test Cases by Efficient SAT Encodings Suitable for CDCL SAT Solvers
NASA Astrophysics Data System (ADS)
Banbara, Mutsunori; Matsunaka, Haruki; Tamura, Naoyuki; Inoue, Katsumi
Generating test cases for combinatorial testing is to find a covering array in Combinatorial Designs. In this paper, we consider the problem of finding optimal covering arrays by SAT encoding. We present two encodings suitable for modern CDCL SAT solvers. One is based on the order encoding that is efficient in the sense that unit propagation achieves the bounds consistency in CSPs. Another one is based on a combination of the order encoding and Hnich's encoding. CDCL SAT solvers have an important role in the latest SAT technology. The effective use of them is essential for enhancing efficiency. In our experiments, we found solutions that can be competitive with the previously known results for the arrays of strength two to six with small to moderate size of components and symbols. Moreover, we succeeded either in proving the optimality of known bounds or in improving known lower bounds for some arrays.
Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases
NASA Astrophysics Data System (ADS)
Zengler, Christoph; Küchlin, Wolfgang
We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.
Linear optical response of finite systems using multishift linear system solvers
Hübener, Hannes; Giustino, Feliciano
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Linear optical response of finite systems using multishift linear system solvers.
Hübener, Hannes; Giustino, Feliciano
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Pandyna, Mohagna J.; Frink, Neal T.; Noack, Ralph W.
2005-01-01
A static and dynamic Chimera overset-grid capability is added to an established NASA tetrahedral unstructured parallel Navier-Stokes flow solver, USM3D. Modifications to the solver primarily consist of a few strategic calls to the Donor interpolation Receptor Transaction library (DiRTlib) to facilitate communication of solution information between various grids. The assembly of multiple overlapping grids into a single-zone composite grid is performed by the Structured, Unstructured and Generalized Grid AssembleR (SUGGAR) code. Several test cases are presented to verify the implementation, assess overset-grid solution accuracy and convergence relative to single-grid solutions, and demonstrate the prescribed relative grid motion capability.
A steady-state solver and stability calculator for nonlinear internal wave flows
NASA Astrophysics Data System (ADS)
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
Li, Xiaoye S.; Demmel, James W.
2002-03-27
In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
O. Kononenko
2015-02-17
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
NASA Astrophysics Data System (ADS)
Cerroni, D.; Fancellu, L.; Manservisi, S.; Menghini, F.
2016-06-01
In this work we propose to study the behavior of a solid elastic object that interacts with a multiphase flow. Fluid structure interaction and multiphase problems are of great interest in engineering and science because of many potential applications. The study of this interaction by coupling a fluid structure interaction (FSI) solver with a multiphase problem could open a large range of possibilities in the investigation of realistic problems. We use a FSI solver based on a monolithic approach, while the two-phase interface advection and reconstruction is computed in the framework of a Volume of Fluid method which is one of the more popular algorithms for two-phase flow problems. The coupling between the FSI and VOF algorithm is efficiently handled with the use of MEDMEM libraries implemented in the computational platform Salome. The numerical results of a dam break problem over a deformable solid are reported in order to show the robustness and stability of this numerical approach.
Multitasking domain decomposition fast Poisson solvers on the Cray Y-MP
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Fatoohi, Rod A.
1990-01-01
The results of multitasking implementation of a domain decomposition fast Poisson solver on eight processors of the Cray Y-MP are presented. The object of this research is to study the performance of domain decomposition methods on a Cray supercomputer and to analyze the performance of different multitasking techniques using highly parallel algorithms. Two implementations of multitasking are considered: macrotasking (parallelism at the subroutine level) and microtasking (parallelism at the do-loop level). A conventional FFT-based fast Poisson solver is also multitasked. The results of different implementations are compared and analyzed. A speedup of over 7.4 on the Cray Y-MP running in a dedicated environment is achieved for all cases.