Modelling and entropy satisfying relaxation scheme for the nonconservative bitemperature Euler system with transverse magnetic field

Stéphane Brull (1) , Xavier Lhébrard (2) , Bruno Dubroca (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The present paper concerns the study of the nonconservative bitem-perature Euler system with transverse magnetic field. We firstly introduce an underlying conservative kinetic model coupled to Maxwell equations. The nonconservative bitemperature Euler system with transverse magnetic field is then established from this kinetic model by hydrodynamic limit. Next we present the derivation of a finite volume method to approximate weak solutions. It is obtained by solving a relaxation system of Suliciu type, and is similar to HLLC type solvers. The solver is shown in particular to preserve positivity of density and internal energies. Moreover we use a local minimum entropy principle to prove discrete entropy inequalities, ensuring the robustness of the scheme.

Mots clés: BGK models; hydrodynamic limit; relaxation method; non-conservative hyperbolic system; discrete entropy inequalities; discrete entropy minimum principle

Domaines: Analyse numérique [math.NA]

Stéphane Brull, Xavier Lhébrard, Bruno Dubroca. Modelling and entropy satisfying relaxation scheme for the nonconservative bitemperature Euler system with transverse magnetic field. 2019. ⟨hal-01939165v2⟩