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Entropy conservative and entropy stable schemes for non-conservative hyperbolic systems

by M. J. Castro and U. S. Fjordholm and S. Mishra and C. Parés

(Report number 2011-49)

Abstract
The vanishing viscosity limit of non-conservative hyperbolic systems depends heavily on the specic form of the viscosity. Numerical approximations, such as the path consistent schemes of [16], may not converge to the physically relevant solutions of the system. We construct entropy stable path consistent (ESPC) schemes to approximate non-conservative hyperbolic systems by combining entropy conservative discretizations with numerical diffusion operators that are based on the underlying viscous operator. Numerical experiments for the coupled Burgers system and the two-layer shallow water equations demonstrating the robustness of ESPC schemes are presented.

Keywords:

@Techreport{CFMP11_87,
  author = {M. J. Castro and U. S. Fjordholm and S. Mishra and C. Parés},
  title = {Entropy conservative and entropy stable schemes for non-conservative hyperbolic systems },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-49},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-49.pdf },
  year = {2011}
}

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