a1 Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
a2 Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005
a3 Division of Applied Mathematics, Brown University, Providence, RI 02912
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.
(Online publication May 16 2011)
Mathematics Subject Classification: