Modelling and numerical approximation for the nonconservative bitemperature Euler model

Denise Aregba-Driollet (1) , J. Breil (2) , Stéphane Brull (3, 1) , B. Dubroca (2) , Elise Estibals (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 CELIA - Centre d'Etudes Lasers Intenses et Applications
3 Équipe Calcul scientifique et Modélisation
4 CASTOR - Control, Analysis and Simulations for TOkamak Research

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. 1991 Mathematics Subject Classification. 65M08, 35L60, 35L65. Secondary: 82D10, 76X05. The dates will be set by the publisher.

Mots clés: nonconservative hyperbolic system; entropy dissipation; Relaxation method; hydrodynamic limit; kinetic schemes; BGK models

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Denise Aregba-Driollet, J. Breil, Stéphane Brull, B. Dubroca, Elise Estibals. Modelling and numerical approximation for the nonconservative bitemperature Euler model. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (4), pp.1353-1383. ⟨10.1051/m2an/2017007⟩. ⟨hal-01934313⟩