On a Doubly Reduced Model for Dynamics of Heterogeneous Mixtures of Stiffened Gases, its Regularizations and their Implementations

We deal with the reduced four-equation model for dynamics of the heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations and a quadratic equation for the common pressure of the components, that can be called quasi-homogeneous form. We prove new properties of this equation, derive a simple formula for the squared speed of sound, give an alternative proof for a formula that relates it to the squared Wood speed of sound, and a short derivation of the pressure balance equation. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). In the 1D case, we construct the corresponding explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and present various numerical results for flows with shock waves.