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Volume 27, Issue 4
Vectorial Kinetic Relaxation Model with Central Velocity. Application to Implicit Relaxations Schemes

David Coulette, Clémentine Courtès, Emmanuel Franck & Laurent Navoret

DOI: 10.4208/cicp.OA-2019-0013

Commun. Comput. Phys., 27 (2020), pp. 976-1013.

Published online: 2020-02

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  • Abstract

We apply flux vector splitting (FVS) strategy to the implicit kinetic schemes for hyperbolic systems. It enables to increase the accuracy of the method compared to classical kinetic schemes while still using large time steps compared to the characteristic speeds of the problem. The method also allows to tackle multi-scale problems, such as the low Mach number limit, for which wave speeds with large ratio are involved. We present several possible kinetic relaxation schemes based on FVS and compare them on one-dimensional test-cases. We discuss stability issues for this kind of method.

  • Keywords

Implicit scheme, kinetic, flux vector splitting, Euler equation, relaxation.

  • AMS Subject Headings

(or PACs) To be provided by authors

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

david.coulette@ens-lyon.fr (David Coulette)

clementine.courtes@math.unistra.fr (Clémentine Courtès)

emmanuel.franck@inria.fr (Emmanuel Franck)

laurent.navoret@math.unistra.fr (Laurent Navoret)

  • BibTex
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  • TXT
@Article{CiCP-27-976, author = {Coulette , DavidCourtès , ClémentineFranck , Emmanuel and Navoret , Laurent}, title = {Vectorial Kinetic Relaxation Model with Central Velocity. Application to Implicit Relaxations Schemes }, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {976--1013}, abstract = {

We apply flux vector splitting (FVS) strategy to the implicit kinetic schemes for hyperbolic systems. It enables to increase the accuracy of the method compared to classical kinetic schemes while still using large time steps compared to the characteristic speeds of the problem. The method also allows to tackle multi-scale problems, such as the low Mach number limit, for which wave speeds with large ratio are involved. We present several possible kinetic relaxation schemes based on FVS and compare them on one-dimensional test-cases. We discuss stability issues for this kind of method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0013}, url = {http://global-sci.org/intro/article_detail/cicp/14823.html} }
TY - JOUR T1 - Vectorial Kinetic Relaxation Model with Central Velocity. Application to Implicit Relaxations Schemes AU - Coulette , David AU - Courtès , Clémentine AU - Franck , Emmanuel AU - Navoret , Laurent JO - Communications in Computational Physics VL - 4 SP - 976 EP - 1013 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0013 UR - https://global-sci.org/intro/article_detail/cicp/14823.html KW - Implicit scheme, kinetic, flux vector splitting, Euler equation, relaxation. AB -

We apply flux vector splitting (FVS) strategy to the implicit kinetic schemes for hyperbolic systems. It enables to increase the accuracy of the method compared to classical kinetic schemes while still using large time steps compared to the characteristic speeds of the problem. The method also allows to tackle multi-scale problems, such as the low Mach number limit, for which wave speeds with large ratio are involved. We present several possible kinetic relaxation schemes based on FVS and compare them on one-dimensional test-cases. We discuss stability issues for this kind of method.

Coulette , DavidCourtès , ClémentineFranck , Emmanuel and Navoret , Laurent. (2020). Vectorial Kinetic Relaxation Model with Central Velocity. Application to Implicit Relaxations Schemes . Communications in Computational Physics. 27 (4). 976-1013. doi:10.4208/cicp.OA-2019-0013
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