A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a nonconservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the r esults of Dal Maso, Le Floch and Murat about nonconservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order li nearized well-balanced scheme in the sense of Greenberg and Le Roux. As a m ain feature, this approach is able to preserve the right asymptotic behavio r of the original inhomogeneous system, which is not an obvious property. N umerical results for the Euler equations are shown to handle correctly thes e equilibria in various situations.