Volume 27, Issue 5
A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

Jian YuJan S. Hesthaven

Commun. Comput. Phys., 27 (2020), pp. 1309-1343.

Published online: 2020-03

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  • Abstract

Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on various approaches, such as slope limiting, (H)WENO reconstruction, a posteriori sub-cell limiting, and artificial viscosity, among which a subclass of artificial viscosity methods are compared in the present work. Four models are evaluated, including a dilation-based model, a highest modal decay model, an averaged modal decay model, and an entropy viscosity model. Performance for smooth, non-smooth and broadband problems are examined with typical one- and two-dimensional cases.

  • Keywords

High order methods, discontinuous Galerkin, shock capturing, artificial viscosity.

  • AMS Subject Headings

76M10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yuj@buaa.edu.cn (Jian Yu)

Jan.Hesthaven@epfl.ch (Jan S. Hesthaven)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1309, author = {Yu , Jian and Hesthaven , Jan S.}, title = {A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {5}, pages = {1309--1343}, abstract = {

Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on various approaches, such as slope limiting, (H)WENO reconstruction, a posteriori sub-cell limiting, and artificial viscosity, among which a subclass of artificial viscosity methods are compared in the present work. Four models are evaluated, including a dilation-based model, a highest modal decay model, an averaged modal decay model, and an entropy viscosity model. Performance for smooth, non-smooth and broadband problems are examined with typical one- and two-dimensional cases.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0118}, url = {http://global-sci.org/intro/article_detail/cicp/15772.html} }
TY - JOUR T1 - A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework AU - Yu , Jian AU - Hesthaven , Jan S. JO - Communications in Computational Physics VL - 5 SP - 1309 EP - 1343 PY - 2020 DA - 2020/03 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0118 UR - https://global-sci.org/intro/article_detail/cicp/15772.html KW - High order methods, discontinuous Galerkin, shock capturing, artificial viscosity. AB -

Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on various approaches, such as slope limiting, (H)WENO reconstruction, a posteriori sub-cell limiting, and artificial viscosity, among which a subclass of artificial viscosity methods are compared in the present work. Four models are evaluated, including a dilation-based model, a highest modal decay model, an averaged modal decay model, and an entropy viscosity model. Performance for smooth, non-smooth and broadband problems are examined with typical one- and two-dimensional cases.

Jian Yu & Jan S. Hesthaven. (2020). A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework. Communications in Computational Physics. 27 (5). 1309-1343. doi:10.4208/cicp.OA-2019-0118
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