The coupling of homogeneous models for two-phase flows

We consider the numerical coupling at a fixed spatial interface of two homogeneous models used for describing non isothermal compressible two phase flows. More precisely, we concentrate on the numerical coupling of the homogeneous equilibrium model and the homogeneous relaxation model in the context of finite volume methods. Three methods of coupling are presented. They are based on one of the following requirements: continuity of the conservative variable through the coupling interface, continuity of the primitive variable and global conservation of mass, momentum and energy. At the end, several numerical experiments are presented in order to illustrate the ability of each method to provide results in agreement with their principle of construction.