An efficient numerical method for solving the Boltzmann equation in multidimensions

Autor: Giacomo Dimarco, Jacek Narski, Thomas Rey, Raphaël Loubère
Přispěvatelé: Department of Mathematics and Computer Science, Università degli Studi di Ferrara (UniFE), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Reliable numerical approximations of dissipative systems (RAPSODI ), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Projet Gallileo G14, ANR-14-CE23-0007,MOONRISE,MOdèles, Oscillations et SchEmas NUmeriques(2014), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Dipartimento di Matematica e Informatica = Department of Mathematics and Computer Science [Ferrara] (DMCS), Università degli Studi di Ferrara = University of Ferrara (UniFE), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Physics and Astronomy (miscellaneous)
Semi-Lagrangian schemes
Kinetic scheme
GPU
CUDA
010103 numerical & computational mathematics
Computational fluid dynamics
01 natural sciences
NO
82B40
76P05
65M70
65M08
65Y05
65Y20
Boltzmann equation
symbols.namesake
Operator (computer programming)
FOS: Mathematics
Applied mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Limit (mathematics)
Mathematics - Numerical Analysis
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
0101 mathematics
[MATH]Mathematics [math]
3D/3D
Kinetic equations
MPI
OpenMP
Spectral schemes
Computer Science Applications1707 Computer Vision and Pattern Recognition
Variable (mathematics)
Numerical Analysis
business.industry
Applied Mathematics
Numerical analysis
Numerical Analysis (math.NA)
Computer Science Applications
Euler equations
010101 applied mathematics
Computational Mathematics
Modeling and Simulation
symbols
business
MSC: 82B40
76P05
65M70
65M08
65Y05
65Y20
Zdroj: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2018, 353, pp.46-81. ⟨10.1016/j.jcp.2017.10.010⟩
Journal of Computational Physics, 2018, 353, pp.46-81. ⟨10.1016/j.jcp.2017.10.010⟩
ISSN: 0021-9991
1090-2716
DOI: 10.1016/j.jcp.2017.10.010⟩
Popis: In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) [J. Comput. Phys., Vol. 255, 2013, pp 680-698] originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the $3$D$\times 3$D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.
Comment: 39 pages, 21 figures, 7 tables
Databáze: OpenAIRE
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