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Entropy-stable space-time DG schemes for non-conservative hyperbolic systems

by A. Hiltebrand and S. Mishra and C. Parés

(Report number 2017-39)

Abstract
We propose a space-time discontinuous Galerkin (DG) method to approximate multi-dimensional non-conservative hyperbolic systems. The scheme is based on a particular choice of interface fluctuations. \emph{The key difference with existing space-time DG methods lies in the fact that our scheme is formulated in entropy variables, allowing us to prove entropy stability for the method}. Additional numerical stabilization in the form of streamline diffusion and shock-capturing terms are added. The resulting method is entropy stable, arbitrary high-order accurate, fully discrete, and able to handle complex domain geometries discretized with unstructured grids. We illustrate the method with representative numerical examples.

Keywords: Non-conservative systems, Entropy stability, space-time DG

@Techreport{HMP17_735,
  author = {A. Hiltebrand and S. Mishra and C. Parés},
  title = {Entropy-stable space-time DG schemes for non-conservative hyperbolic systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-39},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-39.pdf },
  year = {2017}
}

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