Qualitative Properties of a Model of Two-Phase Media for Description of Dynamics of Collisional Gas Particle Mixtures

A qualitative analysis of the collisional model of a two-phase medium is presented for the description of shock-wave processes in dense gas particle mixtures. In the Euler equations, the chaotic motion of particles and their collisions are integrally taken into account. In general, the system has a composite type. Flow domains in which the system is hyperbolic are determined. The expansion of these domains with respect to the collisionless model is shown. Some numerical solutions of non-conservative equations of composite type with the use of monotonizing schemes of Harten and Gentry-Martin-Daly are obtained. The convergence properties of numerical solutions are established. Examples of shock-wave structures with shocks in the particle phase are demonstrated.