Entropy Correct Spatial Discretizations for 1D Regularized Systems of Equations for Gas Mixture Dynamics

Abstract

One-dimensional regularized systems of equations for the general (multi-velocity and multi-temperature) and one-velocity and one-temperature compressible multicomponent gas mixture dynamics are considered in the absence of chemical reactions. Two types of the regularization are taken. For the latter system, diffusion fluxes between the components of the mixture are taken into account. For both the systems, the important mixture entropy balance equations with non-negative entropy productions are valid. By generalizing a discretization constructed previously in the case of a single-component gas, we suggest new nonstandard symmetric three-point spatial discretizations for both the systems which are not only conservative in mass, momentum, and total energy but also satisfy semi-discrete counterparts of the mentioned entropy balance equations with non-negative entropy productions. Importantly, the basic discretization in the one-velocity and one-temperature case is not constructed directly but by aggregation of the discretization in the case of general mixture, and that is a new approach. In this case, the results of numerical experiments are also presented for contact problems between two different gases for initial pressure jumps up to 2500.