Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, p. 661-680

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.

DOI : https://doi.org/10.1051/m2an/2011059
Classification:  65M06,  35L65
Keywords: multidimensional evolution equations, magnetohydrodynamics, constraint transport, central difference schemes, potential-based fluxes
@article{M2AN_2012__46_3_661_0,
author = {Mishra, Siddhartha and Tadmor, Eitan},
title = {Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {46},
number = {3},
year = {2012},
pages = {661-680},
doi = {10.1051/m2an/2011059},
mrnumber = {2877370},
language = {en},
url = {http://www.numdam.org/item/M2AN_2012__46_3_661_0}
}

Mishra, Siddhartha; Tadmor, Eitan. Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, pp. 661-680. doi : 10.1051/m2an/2011059. http://www.numdam.org/item/M2AN_2012__46_3_661_0/

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