Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 6, Issue 3, Pages 57-83Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/20116303
Keywords
shock detection; Euler's equations; discontinuous Galerkin; explicit time integration; shock capturing; artificial viscosity
Categories
Funding
- AFOSR [FA9550-05-1-0473]
- National Science Foundation [DMS 0810187]
- NSF
- Department of Energy (DOE) [DEFG0288ER25053]
- AFOSR through AFOSR/NSSEFF [FA9550-07-1-0422, FA9550-10-1-0180]
- Direct For Mathematical & Physical Scien [0810187] Funding Source: National Science Foundation
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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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