About qualitative properties of the collisional model for description of shock-wave dynamics of gas particle suspensions

The theoretical analysis of a model of two-phase medium which takes into account chaotic motion and collisions of particles for the description of shock-wave processes in dense gas particle suspensions is presented. Domains of hyperbolicity or composite type of the governing system of equations are determined. The expansion of the hyperbolicity zones with respect to the collisionless model is shown. An approximate hyperbolized model is presented, and comparative analysis of numerical solutions of the problem of the formation of shock-wave structures of various types is performed. The convergence properties in numerical simulations of non-conservative equations of composite type with the use of monotonizing schemes of Harten and Gentry–Martin–Daly are established. Conditions for the applicability of a hyperbolized model for different types of flows are obtained. They indicate that in general it is advisable to analyze the shock-wave processes in gas particle suspensions within the framework of the full model.