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research article

Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method

Kloeckner, A.
•
Warburton, T.
•
Hesthaven, Jan S.  
2011
Mathematical Modelling of Natural Phenomena

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 smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the detector's design and analyze its performance on a number of benchmark problems. We further explain the scaling and smoothing steps necessary to turn the output of the detector into a local, artificial viscosity. We close by providing an extensive array of numerical tests of the detector in use.

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Math. Model. Nat. Phenom. 2011 Klöckner.pdf

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http://purl.org/coar/version/c_970fb48d4fbd8a85

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