A Roe scheme for ideal MHD equations on 2D adaptively refined triangular grids

In this paper we present a second order finite volume method for the resolu tion of the bidimensional ideal MHD equations on adaptively refined triangu lar meshes. Our numerical flux function is based on a multidimensional exte nsion of the Roe scheme proposed by Cargo and Gallice for the 1D MHD system . If the mesh is only composed of triangles, our scheme is proved to be wea kly consistent with the condition del . B = 0. This property fails on a car tesian grid. The efficiency of our refinement procedure is shown on 2D MHD shock capturing simulations. Numerical results are compared in case of the interaction of a supersonic plasma with a cylinder on the adapted grid and several non-refined grids. We also present a mass loading simulation which corresponds to a 2D version of the interaction between the solar wind and a comet. (C) 1999 Academic Press.