Non equilibrium relaxation models for two phase relativistic flows

A hierarchy of hyperbolic models describing single–component two–phase relativistic flows is considered. In particular, three different models are examined and compared: one in which the thermodynamic equilibrium is reached through both pressure and temperature relaxation, another in which the pressures of the two phases are supposed to get instantaneously a common equilibrium value and, finally, the one obtained under the hypothesis that thermal and mechanical equilibrium is instantaneously reached. The consistency of the relaxation procedure with the second law of thermodynamics is discussed. Exact hydrodynamic discontinuity wave velocities for these models are obtained and compared. In particular, it is shown that if a model M* arises from a model M through a relaxation procedure, the hydrodynamic discontinuity wave velocities \lambda of the two models are related by \lambda^2_M* <= \lambda^2_M. M 2 M.