Quasi-gasdynamic heterogeneous model for describing a mixture of compressible fluids. Two-dimensional case

The reduced four-equation model for dynamics of the heterogeneous compressible two-fluid mixture with equations of state of a stiffened gas is considered. A further reduced form of this model with the excluded volume concentrations and a quadratic equation for the common pressure of the components can be called a quasi-homogeneous form. A finite difference algorithm, built with the finite volume method for the regularized gas dynamics equations, is used. Using examples of solving two-dimensional problems, it is shown that the presented algorithm is a stable and reliable way to model problems with strong shock waves.