Godunov's method for a multivelocity model of heterogeneous medium

This article uses a model of heterogeneous media accounting for an additional state of the medium as a mixture characterized by averaged quantities. The equations describing this state coincide with the equations of gas dynamics. Additional equations express conservation laws, but only for the components with the local speed of sound lower than in the mixture; we assume that other waves are absorbed by the media and form waves in the mixture. Since the equations are not in divergence form, the original Godunov's method is inapplicable. We suggest a modified Godunov's method to integrate the nondivergent system of equations for a multivelocity heterogeneous mixture. We use a linearized Riemann solver for Riemann problems.