A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes

Authors:
Christophe Berthon;Bruno Dubroca;Afeintou Sangam
Affiliations:
Christophe.Berthon@math.univ-nantes.fr;bruno.dubroca@math.u-bordeaux1.fr;Afeintou.Sangam@unice.fr
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

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Abstract

The present work deals with the establishment of stability conditions of finite volume methods to approximate weak solutions of the general Euler equations to simulate compressible flows. In order to ensure discrete entropy inequalities, we derive a new technique based on a local minimum principle to be satisfied by the specific entropy. Sufficient conditions are exhibited to satisfy the required local minimum entropy principle. Arguing these conditions, a class of entropy preserving schemes is thus derived.