Mathematical model and numerical discretization for the simulation of two-material two-temperature compressible flows

In this work, we investigate the mathematical model and the numerical method for two-material two-temperature compressible flows based on the Eulerian framework. First, we present the two-material two-temperature model equations with its basic mathematical properties. In particular, in order to close the model equations, three different closure laws and the corresponding properties related to well-posedness are discussed in detail. Then, a Weighted Essentially Non-Oscillatory (WENO) finite volume discretization is developed for the discretization of the model equations on both planar geometry and spherical axisymmetric geometry. More importantly, aiming at revealing the underlying reasons for the occurrence of spurious numerical oscillations near the material interface, a theoretical analysis of the numerical discretization coupled with the three different closure laws is carried out. Finally, a variety of typical test cases are presented to illustrate the performance of the numerical method for the proposed model equations.