A Straightforward $hp$-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods
Year: 2014
Author: Hongqiang Lu, Qiang Sun
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m-s1
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 135–144
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: $hp$-adaptivity shock capturing discontinuous Galerkin.
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