Consistency analysis of a 1D Finite Volume scheme for barotropic Euler models

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

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

This work is concerned with the consistency study of a 1D (staggered kinetic) finite volume scheme for barotropic Euler models. We prove a Lax-Wendroff-like statement: the limit of a converging (and uniformly bounded) sequence of stepwise constant functions defined from the scheme is a weak entropic-solution of the system of conservation laws.

Domaines: Analyse numérique [math.NA]

Florent Berthelin, Thierry Goudon, Sebastian Minjeaud. Consistency analysis of a 1D Finite Volume scheme for barotropic Euler models. J. Fuhrmann, M. Ohlberger, C. Rohde Eds. Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 77, Springer Proc. in Math. \& Stat., pp. 97-106, 2015. ⟨hal-00961615⟩