A simple extension of Roe's scheme for multi-component real gas flows

Abstract

This paper proposes a numerical algorithm to model multi-component real gas flows in local thermodynamic equilibrium (LTE). The approach is based on the solution of the Euler equations for the mixtures which is coupled with the mass conservation equation for each component of fluid. This algorithm is based on the extension of Roe's scheme for real gases introduced in [21], which is robust, efficient and simpler than the other extensions. The Euler equations for the mixture are solved whereas fluid components are updated using a classical upwind approximation. As the solution evolves, the developed method preserves the positivity of the mass fractions of all components. The proposed technique does not directly involve the thermodynamics derivatives at the average state, which avoids assumptions and approximations in the calculation of these derivatives. The pressure oscillation problem appearing in the case of flow fields including material contact has been also discussed. The numerical experiments show the accuracy and robustness of the method in various cases.