Numerical investigation of two-phase hyperbolic models

The work is devoted to the numerical study of a finite-volume scheme with an HLLEM flux for solving equations from the family of Baer-Nunziato models. Three versions of the model are considered, differing in the degree of ”nonequilibrium”. A brief description of the models and their differences is provided. To approximate the equations of nonequilibrium models with rigid right-hand sides, which describe the process of mechanical and thermodynamic relaxation, the method of splitting into physical processes is used. Spatial approximations are constructed using the 1st and 2nd order finite volume method (TVD). The HLLEM flux is used as a numerical flux, for which a simple algorithm for determining the method parameter that guarantees the physicality of the solution is proposed. A feature of the work is that all three considered models are applied to analyze virtually the same physical setting.