Second order entropy diminishing scheme for the euler equations
Résumé
In several papers of Bouchut, Bourdarias, Perthame and Coquel, Le Floch a general methodology has been developed to construct second order finite volume schemes for hyperbolic systems of conservation laws satisfying the entire family of entropy inequalities. This approach is mainly based on the construction of an entropy diminishing pro jection. Unfortunately, the explicit computation of this pro jection is not always easy. In the first part of this paper, we carry out this computation in the important case of the Euler equations of gas dynamics. In the second part, we present several numerical applications of the projection in the context of finite volume schemes.
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