A ROE SOLVER FOR THE MAGNETOHYDRODYNAMICS EQUATIONS

During the last 10 years, upwind numerical schemes have been very popu lar methods for solving, non-linear hyperbolic systems especially when discontinuities exist in the solution. Among many methods applied to the problems in gas dynamics, Roe's scheme stands out by its simplicit y and clarity of the underlying physical model. Thus it is natural to extend it to the system of magnetohydrodynamics. The application of th is scheme relies on a linearization of the equations of magnetohydrody namics in each cell of the mesh. A crucial step in this procedure lies in the construction of a Roe's matrix. We describe in this paper how to obtain such a matrix and therefore construct a Roe's type scheme.