Relaxation and numerical approximation of a two-fluid two-pressure diphasic model

This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach