This paper is devoted to the study of the nonconservative bitemperature Euler system. We firstly introduce an underlying two species kinetic model coupled with the Poisson equation. The bitemperature Euler system is then established from this kinetic model according to an hydrodynamic limit. A dissipative entropy is proved to exist and a solution is defined to be admissible if it satisfies the related dissipation property. Next, four different numerical methods are presented. Firstly, the kinetic model gives rise to kinetic schemes for the fluid system. The second approach belongs to the family of the discrete BGK schemes introduced by Aregba–Driollet and Natalini. Finally, a quasi-linear relaxation approach and a Lagrange-remap scheme are considered.
Accepté le :
DOI : 10.1051/m2an/2017007
Mots clés : Relaxation method, nonconservative hyperbolic system, kinetic schemes, BGK models, hydrodynamic limit, entropy dissipation
@article{M2AN_2018__52_4_1353_0,
author = {Aregba{\textendash}Driollet, D. and Breil, J. and Brull, S. and Dubroca, B. and Estibals, E.},
title = {Modelling and numerical approximation for the nonconservative bitemperature {Euler} model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1353--1383},
publisher = {EDP-Sciences},
volume = {52},
number = {4},
year = {2018},
doi = {10.1051/m2an/2017007},
mrnumber = {3875289},
zbl = {1417.65158},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017007/}
}
TY - JOUR AU - Aregba–Driollet, D. AU - Breil, J. AU - Brull, S. AU - Dubroca, B. AU - Estibals, E. TI - Modelling and numerical approximation for the nonconservative bitemperature Euler model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1353 EP - 1383 VL - 52 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017007/ DO - 10.1051/m2an/2017007 LA - en ID - M2AN_2018__52_4_1353_0 ER -
%0 Journal Article %A Aregba–Driollet, D. %A Breil, J. %A Brull, S. %A Dubroca, B. %A Estibals, E. %T Modelling and numerical approximation for the nonconservative bitemperature Euler model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1353-1383 %V 52 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017007/ %R 10.1051/m2an/2017007 %G en %F M2AN_2018__52_4_1353_0
Aregba–Driollet, D.; Breil, J.; Brull, S.; Dubroca, B.; Estibals, E. Modelling and numerical approximation for the nonconservative bitemperature Euler model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1353-1383. doi : 10.1051/m2an/2017007. http://www.numdam.org/articles/10.1051/m2an/2017007/
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