Exact and approximate Riemann solvers for compressible two-phase flows

A numerical method for solving the two-phase hydrodynamics equations that describe the flow of dispersed solid and gas mixture is considered. The Godunov method is applied to approximate numerical fluxes with implementing solutions to the Riemann problem. The formulations of these problems for the solid and gas phases are given, their exact analytical solutions are described and possible simplified approximate solutions are discussed. The obtained theoretical results are applied to construction of the discrete model which leads to extension of well-known Godunov-type and Rusanov-type methods to the system of Baer–Nunziato equations for non-equilibrium twophase flows. Numerical results concern the method verification on generalized Sod problems with analytical self-similar solutions of two-phase equations.