Volume 6, Issue 1
A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

Hongqiang Lu & Qiang Sun

Adv. Appl. Math. Mech., 6 (2014), pp. 135-144.

Published online: 2014-06

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  • Abstract

In this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforward hp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

  • Keywords

hp-adaptivity shock capturing discontinuous Galerkin

  • AMS Subject Headings

35L67 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-135, author = {Hongqiang Lu and Qiang Sun}, title = {A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {1}, pages = {135--144}, abstract = {

In this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforward hp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m-s1}, url = {http://global-sci.org/intro/article_detail/aamm/9.html} }
TY - JOUR T1 - A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods AU - Hongqiang Lu & Qiang Sun JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 135 EP - 144 PY - 2014 DA - 2014/06 SN - 6 DO - http://dor.org/10.4208/aamm.2013.m-s1 UR - https://global-sci.org/intro/aamm/9.html KW - hp-adaptivity KW - shock capturing KW - discontinuous Galerkin AB -

In this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforward hp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

Hongqiang Lu & Qiang Sun. (1970). A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods. Advances in Applied Mathematics and Mechanics. 6 (1). 135-144. doi:10.4208/aamm.2013.m-s1
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