Suspension hydrodynamic equations: two-phase models

Two-velocity models of suspension hydrodynamics are considered, using the equality condition for chemical potentials of the phases or without this condition. The model equations are obtained by the conservation law method and are thermodynamically consistent under the assumption of one pressure or two pressure systems. Models are compared numerically on the test problems of discontinuity decay using the TVD method. A comparison was also made with a two-velocity suspension model with an internal energy dependent on the phase volume fractions.