Numerical analysis of two operator splitting methods for an hyperbolic system of conservation laws with stiff relaxation terms

This paper is concerned with the discretization of an hyperbolic system of conservation laws with stiff relaxation source terms that model a two-phase fluid flow. It is shown both theoretically and numerically that the usual operator splitting method poorly computes the propagation of sound waves in a two-phase medium. We propose a new operator splitting, based on physical considerations. This numerical method gives very good results regarding both the propagation velocity and the attenuation coefficient of sound waves in a two-phase medium.