Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method

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

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 3, page 57-83
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Klöckner, A., Warburton, T., and Hesthaven, J. S.. "Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method." Mathematical Modelling of Natural Phenomena 6.3 (2011): 57-83. <http://eudml.org/doc/222355>.

@article{Klöckner2011,
abstract = {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. },
author = {Klöckner, A., Warburton, T., Hesthaven, J. S.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {shock detection; Euler’s equations; discontinuous Galerkin; explicit time integration; shock capturing; artificial viscosity; Euler's equations},
language = {eng},
month = {5},
number = {3},
pages = {57-83},
publisher = {EDP Sciences},
title = {Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method},
url = {http://eudml.org/doc/222355},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Klöckner, A.
AU - Warburton, T.
AU - Hesthaven, J. S.
TI - Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/5//
PB - EDP Sciences
VL - 6
IS - 3
SP - 57
EP - 83
AB - 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.
LA - eng
KW - shock detection; Euler’s equations; discontinuous Galerkin; explicit time integration; shock capturing; artificial viscosity; Euler's equations
UR - http://eudml.org/doc/222355
ER -

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