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

Andreas  Hiltebrand; Siddhartha  Mishra; Andreas  Hiltebrand; Siddhartha  Mishra

doi:10.3934/nhm.2016.11.145

Networks and Heterogeneous Media

2016, Volume 11, Issue 1: 145-162. doi: 10.3934/nhm.2016.11.145

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

Andreas Hiltebrand ^{1
,},
Siddhartha Mishra ^{1
,}

1.
Seminar for Applied Mathematics (SAM), Department of Mathematics, ETH Zurich, 8092 Zurich

Received: 01 April 2015 Revised: 01 July 2015
Primary: 65M60, 35L60.

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.
- Well-balancedness,
- entropy stability,
- space-time DG,
- shallow water equations,
- bottom topography
Citation: Andreas Hiltebrand, Siddhartha Mishra. Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography[J]. Networks and Heterogeneous Media, 2016, 11(1): 145-162. doi: 10.3934/nhm.2016.11.145

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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.

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