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| - Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations
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| Abstract
| - We design efficient numerical schemes for approximating the MHD equations in multi-dimensions. 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 multi-dimensional (GMD) framework of [S. Mishra and E. Tadmor, Commun. Comput. Phys. 9 (2010) 688-710; S. Mishra and E. Tadmor, SIAM J. Numer. Anal. 49 (2011) 1023-1045]. 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. First- and 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.
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| - © EDP Sciences, SMAI, 2012
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