Math. Model. Nat. Phenom.
Volume 6, Number 3, 2011Computational aerodynamics
|Page(s)||57 - 83|
|Published online||16 May 2011|
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
Courant Institute of Mathematical Sciences, New York
University, New York,
2 Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005
3 Division of Applied Mathematics, Brown University, Providence, RI 02912
⋆ Corresponding author. E-mail:
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.
Mathematics Subject Classification: 65N30 / 65N35 / 65N40 / 35F61
Key words: shock detection / Euler’s equations / discontinuous Galerkin / explicit time integration / shock capturing / artificial viscosity
© EDP Sciences, 2011
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