Résumé
The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity twopressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity for the definition of Rankine-Hugoniot jump relations. Each field of the convective system is investigated, providing that the maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two Finite Volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows.