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

Abstract

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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.

How to cite

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Mishra, 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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