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

by S. Mishra and E. Tadmor

(Report number 2009-33)

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 [31, 32]. 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:

@Techreport{MT09_414,
  author = {S. Mishra and E. Tadmor},
  title = {Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional central schemes for MHD equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-33},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-33.pdf },
  year = {2009}
}

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