The paper considers applications of a two-velocity model of hydrody- namics for a two-phase medium for describing natural geological systems, such as movement of magma melts in magma channels, the flow of a river and the erosion of an unfixed sandy river bottom. The study deals with a test problem of spreading a square area with a high content of a dispersed phase.

Non-stationary problems are solved numerically on the basis of a thermody- namically consistent model for two-phase medium which takes into account a wide class of dissipative phenomena. The numerical analysis is based on the application of a completely implicit control volume method for a rectangular uniform grid with a shift in the calculation nodes for velocities.

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