Solveur de Roe positivement conservatif

Abstract

In this paper we fix the main drawback of usual Roe's approximate Riemann solver: the solver may fail by predicting non-physical states with negative density or internal energy. We present a new family of positive Roe's average matrix in Eulerian and Lagrangian forms. These matrices are not based on Jacobian canonical form as it is usual. This approach can be used to compute accurately flows with very low density. Numerical results illustrate the efficiency of the proposed method.