A W -modification of Godunov's method and its application to two-dimensional non-stationary flows of a dusty gas

A new, more accurate, modification of Godunov's method for two-dimensional conservation laws is proposed. Monotonicity of the scheme in the scalar linear case is proved. The scheme is generalized to the flow of two-phase media in the Euler formulation. Results of a numerical experiment on the interaction of a shock wave with a dust cloud are presented.