An efficient numerical method for solving the Boltzmann equation in multidimensions

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) 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 o...

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Bibliographic Details
Published in:Journal of computational physics Vol. 353; pp. 46 - 81
Main Authors: Dimarco, Giacomo, Loubère, Raphaël, Narski, Jacek, Rey, Thomas
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 15.01.2018
Elsevier Science Ltd
Elsevier
Subjects:
3D/3D
Analysis of PDEs
Astrophysics
Boltzmann equation
Boltzmann transport equation
Computational physics
CUDA
Fluid mechanics
GPU
Kinetic equations
Kinetics
Lagrange multiplier
Mathematics
Mechanics
MPI
Numerical methods
OpenMP
Physics
Semi-Lagrangian schemes
Semiconductors
Spectral schemes
CUDA
3D/3D
Boltzmann equation
Kinetic equations
OpenMP
MPI
Semi-Lagrangian schemes
Spectral schemes
GPU
spectral schemes
semi-Lagrangian schemes
kinetic equations
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) 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 conservative 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 3D×3D 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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.10.010