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

Andreas  Hiltebrand; Siddhartha  Mishra

doi:10.3934/nhm.2016.11.145

Article Contents

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, and
Siddhartha Mishra^1,

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

Received: March 31, 2015

Revised: June 30, 2015

Published: February 2016

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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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Mathematics Subject Classification: Primary: 65M60, 35L60.

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