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A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

Published online by Cambridge University Press:  03 June 2015

Hongqiang Lu  and
Qiang Sun
Hongqiang Lu*
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Qiang Sun
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
* Corresponding author. Email: hongqiang.lu@nuaa.edu.cn
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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

35L6765M60hp-adaptivityshock capturingdiscontinuous Galerkin
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 1 , February 2014 , pp. 135 - 144
Copyright
Copyright © Global-Science Press 2014

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