Some Aspects of Numerical Modeling of Shock-Wave Processes in a Two-Phase Gas-Dispersed Mixture

Issues concerning the construction of mathematical models and numerical methods of solving dynamic problems for a two-phase medium consisting of a gas and fine inclusions (particles) are discussed. The particles are assumed to be rigid, incompressible, and nondeformable. As a mathematical model, we use the Rakhmatulin–Nigmatulin nonequilibrium continuum model, which is proved to coincide with the Baer–Nunziato model with nonlocal relaxation. Based on splitting into physical processes, a discrete model is proposed that is reduced at each time step to two strictly hyperbolic conservative subsystems of equations. These subsystems are solved numerically by applying Godunov-type difference schemes based on HLL- and HLLC-type Riemann solvers. The proposed numerical method is verified by computing particle layer transfer, velocity relaxation in an infinite two-phase flow, and the Sedov point blast problem in a gas-dispersed medium. In the last case, the results of two-dimensional computations are compared with an exact self-similar solution.