Constraint Preserving Schemes Using Potential - Based Fluxes . Iii . Genuinely Multi - Dimensional Schemes for Mhd Equations ∗

We design efficient numerical schemes for approximating the MHD equations in multidimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multidimensional (GMD) framework of [31, 32]. The schemes are formulated in terms of vertex-centered potentials. A suitable choice of the potential results in GMD schemes that preserve a discrete version of divergence. Firstand second-order divergence preserving GMD schemes are tested on a series of benchmark numerical experiments. They demonstrate the computational efficiency and robustness of the GMD schemes. Résumé. ... AMS Subject Classification. 65M06,35L65.