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shock detection

Mathematical Modelling of Natural Phenomena (1)

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Viscous Shock Capturing in a Time-Explicit DiscontinuousGalerkin Method
A. Klöckner, T. Warburton, J. S. Hesthaven
Journal:

Mathematical Modelling of Natural Phenomena / Volume 6 / Issue 3 / 2011

Published online by Cambridge University Press:

16 May 2011, pp. 57-83

Print publication:

2011
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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.