Numerical model of multiphase flows based on sub-cell resolution of fluid interfaces

Compressible multiphase flows with resolved interfaces are numerically simulated. The Baer–Nunziato relaxation model, which is nonequilibrium with respect to velocity, pressure, and temperature, is used. The basic elements of the proposed approach are a simple model for local sub-cell reconstruction of the interface near a cell face and the simulation of relaxation processes in mixed cells by solving the composite Riemann problem. Two approximate solutions of this problem are proposed that take into account the interaction of primary waves and the formation of secondary waves based on HLL- and HLLC-type Riemann solvers. The method does not require any special relaxation parameters and supports, in fact, a diffusion-free interface resolution, which is demonstrated by numerically solving test problems.