Relaxation of fluid systems

Frédéric Coquel (1) , Edwige Godlewski (2) , Nicolas Seguin (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LJLL - Laboratoire Jacques-Louis Lions

We propose a relaxation framework for general fluid models which can be understood as a natural ex- tension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibirum model. Discrete entropy inequalities are established under a natural Gibbs principle.

Mots clés: Hyperbolic system; fluid model; relaxation approximation; finite volume scheme; Godunov-type scheme

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

Frédéric Coquel, Edwige Godlewski, Nicolas Seguin. Relaxation of fluid systems. Mathematical Models and Methods in Applied Sciences, 2012, 22 (8), pp.52. ⟨10.1142/S0218202512500145⟩. ⟨hal-00776822⟩