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
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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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⟩

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