Second‐order entropy diminishing scheme for the Euler equations

Abstract

Abstract In several papers of Bouchut et al ., Coquel and Le Floch ( Math. Comput. 1996; 65 (216):1439–1461; Numer. Math. 1996; 74 (01):1–34), 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 projection . Unfortunately, the explicit computation of this projection 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. Copyright © 2005 John Wiley & Sons, Ltd.