Building a Godunov-type numerical scheme for a model of two-phase flows

Our aim in the paper is to build a Godunov-type numerical scheme for an isentropic model of two-phase flows. First, computational Riemann solvers together with computing algorithms in subsonic and supersonic regions are presented. Then, exact solutions of local Riemann problems are employed to build a Godunov-type scheme. The scheme is shown to be well-balanced in the sense that it can capture exactly stationary waves in both phases. Numerical tests show that the Godunov-type scheme possesses a good accuracy in the subsonic region as well as supersonic regions, where approximate solutions are convergent to the exact solution.