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Viscous Shock Capturing in a Time-Explicit DiscontinuousGalerkin Method

Published online by Cambridge University Press:  16 May 2011

A. Klöckner ,
T. Warburton  and
J. S. Hesthaven
A. Klöckner*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
T. Warburton
Affiliation:
Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005
J. S. Hesthaven
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912
*
⋆ Corresponding author. E-mail:[email protected]
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Abstract

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)methods. The output of this detector is a reliably scaled, element-wise smoothnessestimate which is suited as a control input to a shock capture mechanism. Using anartificial viscosity in the latter role, we obtain a DG scheme for the numerical solutionof nonlinear systems of conservation laws. Building on work by Persson and Peraire, wethoroughly justify the detector’s design and analyze its performance on a number ofbenchmark problems. We further explain the scaling and smoothing steps necessary to turnthe output of the detector into a local, artificial viscosity. We close by providing anextensive array of numerical tests of the detector in use.

Keywords

shock detectionEuler’s equationsdiscontinuous Galerkinexplicit time integrationshock capturingartificial viscosity
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 3: Computational aerodynamics , 2011 , pp. 57 - 83
Copyright
© EDP Sciences, 2011

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