Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis

Florent Berthelin (1) , Thierry Goudon (2) , Sebastian Minjeaud (1, 3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment
3 CASTOR - Control, Analysis and Simulations for TOkamak Research

We introduce, in the one-dimensional framework, a new scheme of finite volume type for barotropic Euler equations. The numerical unknowns, namely densities and velocities, are defined on staggered grids. The numerical fluxes are defined by using the framework of kinetic schemes. We can consider general (convex) pressure laws. We justify that the density remains non negative and the total physical entropy does not increase, under suitable stability conditions. Performances of the scheme are illustrated through a set of numerical experiments.

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

Florent Berthelin, Thierry Goudon, Sebastian Minjeaud. Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis. Mathematics of Computation, 2015, 84 (295), pp.2221--2262. ⟨hal-00858252v2⟩