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.