A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms

We propose a way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of b alance laws. In order to reduce the computational cost, we selected the fam ily of flux vector splitting schemes. We reformulate the source terms as no nconservative products and treat them directly in the definition of the num erical fluxes by means of generalized jump relations. This is applied to a ID shallow water system with topography and to a 2D simplified model of two -phase flows with damping effects. Numerical results and comparisons with a classical centered discretizations scheme are supplied. (C) 2000 Elsevier Science Ltd. All rights reserved.