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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
Author Details
-
Implicit discontinuous Galerkin method on agglomerated high-order grids for 3D simulations
Qin, Wanglong | Lyu, Hongqiang | Wu, Yizhao | Zhou, Shijie | Chen, ZhengwuChinese Journal of Aeronautics, Vol. 29 (2016), Iss. 6 P.1496
https://doi.org/10.1016/j.cja.2016.10.004 [Citations: 2] -
Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
Bürger, Raimund | Kenettinkara, Sudarshan Kumar | Zorío, DavidComputers & Mathematics with Applications, Vol. 74 (2017), Iss. 6 P.1288
https://doi.org/10.1016/j.camwa.2017.06.019 [Citations: 9] -
Discontinuous Galerkin Methods for Compressible and Incompressible Flows on Space–Time Adaptive Meshes: Toward a Novel Family of Efficient Numerical Methods for Fluid Dynamics
Fambri, Francesco
Archives of Computational Methods in Engineering, Vol. 27 (2020), Iss. 1 P.199
https://doi.org/10.1007/s11831-018-09308-6 [Citations: 13] -
Semi-implicit discontinuous Galerkin methods for the incompressible Navier–Stokes equations on adaptive staggered Cartesian grids
Fambri, Francesco | Dumbser, MichaelComputer Methods in Applied Mechanics and Engineering, Vol. 324 (2017), Iss. P.170
https://doi.org/10.1016/j.cma.2017.06.003 [Citations: 34] -
Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Zanotti, Olindo | Fambri, Francesco | Dumbser, Michael | Hidalgo, ArturoComputers & Fluids, Vol. 118 (2015), Iss. P.204
https://doi.org/10.1016/j.compfluid.2015.06.020 [Citations: 118]