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

Published online by Cambridge University Press:  11 January 2012

Siddhartha Mishra  and
Eitan Tadmor
Siddhartha Mishra
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. siddharm@cma.uio.no.
Eitan Tadmor
Affiliation:
Department of Mathematics, Center of Scientific Computation and Mathematical Modeling (CSCAMM), Institute for Physical sciences and Technology (IPST), University of Maryland, 20741-4015 MD, Maryland, USA; tadmor@cscamm.umd.edu
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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.

Keywords

Multidimensional evolution equationsmagnetohydrodynamicsconstraint transportcentral difference schemespotential-based fluxes
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 3: Special volume in honor of Professor David Gottlieb , May 2012 , pp. 661 - 680
Copyright
© EDP Sciences, SMAI, 2012

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