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Potential based constraint preserving genuinely multi-dimensional schemes for systems of conservation laws

by S. Mishra and E. Tadmor

(Report number 2009-34)

Abstract
We survey the new framework developed in [33, 34, 35], for designing genuinely multi-dimensional (GMD) finite volume schemes for systems of conservation laws in two space dimensions. This approach is based on reformulating edge centered numerical fluxes in terms of vertex centered potentials. Any consistent numerical flux can be used in defining the potentials. Suitable choice of the numerical potentials results schemes that preserve discrete forms of interesting constraints like vorticity and divergence. The schemes are very simple to code, exible and have low computational costs. Numerical examples for the Euler equations of gas dynamics and the ideal MHD equations are presented to illustrate the computational efficiency of the schemes.

Keywords:

@Techreport{MT09_415,
  author = {S. Mishra and E. Tadmor},
  title = {Potential based constraint preserving genuinely multi-dimensional schemes for systems of conservation laws},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-34},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-34.pdf },
  year = {2009}
}

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