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Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography

by A. Hiltebrand and S. Mishra

(Report number 2015-13)

Abstract
We describe a shock-capturing streamline diffusion space-time discontinuous Galerkin (DG) method to discretize the shallow water equations with variable bottom topography. This method, based on the entropy variables as degrees of freedom, is shown to be energy stable as well as well-balanced with respect to the lake at rest steady state. We present numerical experiments illustrating the numerical method.

Keywords: Well-balancedness, entropy stability, space-time DG, shallow water equations, bottom topography.

@Techreport{HM15_603,
  author = {A. Hiltebrand and S. Mishra},
  title = {Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-13.pdf },
  year = {2015}
}

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