Viscous shock capturing in a time-explicit discontinuous Galerkin method

A. Klöckner, T. Warburton, J. S. Hesthaven

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)57-83
Number of pages27
JournalMathematical Modelling of Natural Phenomena
Issue number3
StatePublished - Jan 2011
Externally publishedYes


  • Euler's equations
  • artificial viscosity
  • discontinuous Galerkin
  • explicit time integration
  • shock capturing
  • shock detection

ASJC Scopus subject areas

  • Modeling and Simulation


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