# 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

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topKlöckner, 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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