Modeling of the nonlinear motion of saturated granular media

A nonlinear model of the saturated granular media based on a two-phase mixture model of viscous liquids is proposed. A mathematical model of the two-velocity dynamics of a granular medium involves the temperature phase equilibrium and the absence of the pressure phase equilibrium and is consistent from the thermodynamic standpoint. The obtained two-velocity model was verified by comparison with the results of numerical calculations for the one-velocity model. The convective and the pressure flows of the mixture of compressible viscous liquids for various conditions are simulated.