A two–phase mixture relativistic theory with two different four–velocities

A diffuse interface method (DIM) is developed in order to deduce the relativistic governing equations describing the evolution of a two-fluid, two pressure mixture within the context of two–phase flow modelling. The two components are also assumed to have two distinct four–velocities. The governing system is obtained through the relativistic extension of the method of Baer and Nunziato for the expression of pressure and four–velocity at the interfaces, in absence of mass transfer between the two components. Moreover, weak discontinuity waves compatible with such a system are examined in order to characterize the not–strictly hyperbolic nature of the system.