# Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations∗∗∗

Siddhartha Mishra; Eitan Tadmor

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 3, page 661-680
- ISSN: 0764-583X

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topMishra, Siddhartha, and Tadmor, Eitan. "Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations∗∗∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.3 (2012): 661-680. <http://eudml.org/doc/276382>.

@article{Mishra2012,

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.},

author = {Mishra, Siddhartha, Tadmor, Eitan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multidimensional evolution equations; magnetohydrodynamics; constraint transport; central difference schemes; potential-based fluxes; multidimensional evolution equations},

language = {eng},

month = {1},

number = {3},

pages = {661-680},

publisher = {EDP Sciences},

title = {Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations∗∗∗},

url = {http://eudml.org/doc/276382},

volume = {46},

year = {2012},

}

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

DA - 2012/1//

PB - EDP Sciences

VL - 46

IS - 3

SP - 661

EP - 680

AB - 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.

LA - eng

KW - Multidimensional evolution equations; magnetohydrodynamics; constraint transport; central difference schemes; potential-based fluxes; multidimensional evolution equations

UR - http://eudml.org/doc/276382

ER -

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