Geodesic
Modelling and numerical approximation for the nonconservative bitemperature Euler model
Aregba–Driollet, D.1, 2  ; Breil, J.2 ; Brull, S.1  ; Dubroca, B.2  ; Estibals, E.3
1 Univ. Bordeaux, IMB, UMR 5251, 33405 Talence, France
2 Univ. Bordeaux, CELIA, UMR 5107, 33400 Talence, France
3 INRIA Sophia Antipolis Méditerranée, 2004 route des lucioles, 06902 Valbonne, France
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1353-1383

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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.

DOI : 10.1051/m2an/2017007
Classification : 65M08, 35L60, 35L65, 82D10, 76X05
Keywords: Relaxation method, nonconservative hyperbolic system, kinetic schemes, BGK models, hydrodynamic limit, entropy dissipation

Aregba–Driollet, D. 1, 2 ; Breil, J. 2 ; Brull, S. 1 ; Dubroca, B. 2 ; Estibals, E. 3

1 Univ. Bordeaux, IMB, UMR 5251, 33405 Talence, France
2 Univ. Bordeaux, CELIA, UMR 5107, 33400 Talence, France
3 INRIA Sophia Antipolis Méditerranée, 2004 route des lucioles, 06902 Valbonne, France 
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     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},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017007/}
}
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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

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