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We deal with the reduced four-equation model for the dynamics ofheterogeneous compressible binary mixtures with the stiffened gas equations ofstate. We study its further reduced form, with the excluded volumeconcentrations, and with a quadratic equation for the common pressure of thecomponents; this form can be called a quasi-homogeneous form. We prove newproperties of the equation, derive simple formulas for the squared speed ofsound and present an alternative proof for a formula that relates it to thesquared Wood speed of sound; also, a short derivation of the pressure balanceequation is given. For the first time, we introduce regularizations of theheterogeneous model (in the quasi-homogeneous form). Previously,regularizations of such type were developed only for the homogeneous mixturesof perfect polytropic gases, and it was unclear how to cover the caseconsidered here. In the 1D case, based on these regularizations, we constructnew explicit two-level in time and symmetric three-point in spacefinite-difference schemes without limiters, and provide numerical results forvarious flows with shock waves.

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