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.
Mots-clés : 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 }, pages = {661--680}, publisher = {EDP-Sciences}, volume = {46}, number = {3}, year = {2012}, doi = {10.1051/m2an/2011059}, mrnumber = {2877370}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2011059/} }
TY - JOUR AU - Mishra, Siddhartha AU - Tadmor, Eitan TI - Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 661 EP - 680 VL - 46 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2011059/ DO - 10.1051/m2an/2011059 LA - en ID - M2AN_2012__46_3_661_0 ER -
%0 Journal Article %A Mishra, Siddhartha %A Tadmor, Eitan %T Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 661-680 %V 46 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2011059/ %R 10.1051/m2an/2011059 %G en %F 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 , Special volume in honor of Professor David Gottlieb. Numéro spécial, Tome 46 (2012) no. 3, pp. 661-680. doi : 10.1051/m2an/2011059. http://archive.numdam.org/articles/10.1051/m2an/2011059/
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