Kloeckner, A.
Warburton, T.
Hesthaven, Jan S.
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
Mathematical Modelling of Natural Phenomena
0973-5348
10.1051/mmnp/20116303
6
3
57-83
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.
shock detection;
Euler's equations;
discontinuous Galerkin;
explicit time integration;
shock capturing;
artificial viscosity;
EDP SCIENCES S A
2011
http://infoscience.epfl.ch/record/190465/files/Math.%20Model.%20Nat.%20Phenom.%202011%20Kl%C3%B6ckner.pdf;