Assessment of shock capturing schemes for discontinuous Galerkin method

doi:10.1007/s10483-014-1875-7

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (11): 1361-1374.doi: https://doi.org/10.1007/s10483-014-1875-7

Assessment of shock capturing schemes for discontinuous Galerkin method

于剑, 阎超, 赵瑞

School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China

收稿日期:2014-02-27 修回日期:2014-05-06 出版日期:2014-11-01 发布日期:2014-11-01
通讯作者: Jian YU, Professor, Ph.D., E-mail: yujian@ase.buaa.edu.cn E-mail:yujian@ase.buaa.edu.cn
基金资助:
Research supported by the National Basic Research Program of China (No. 2009CB724104)

Assessment of shock capturing schemes for discontinuous Galerkin method

Jian YU, Chao YAN, Rui ZHAO

School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China

Received:2014-02-27 Revised:2014-05-06 Online:2014-11-01 Published:2014-11-01
Supported by:
Research supported by the National Basic Research Program of China (No. 2009CB724104)

摘要/Abstract

摘要： This paper carries out systematical investigations on the performance of several typical shock-capturing schemes for the discontinuous Galerkin (DG) method, including the total variation bounded (TVB) limiter and three artificial diffusivity schemes (the basis function-based (BF) scheme, the face residual-based (FR) scheme, and the element residual-based (ER) scheme). Shock-dominated flows (the Sod problem, the Shu- Osher problem, the double Mach reflection problem, and the transonic NACA0012 flow) are considered, addressing the issues of accuracy, non-oscillatory property, dependence on user-specified constants, resolution of discontinuities, and capability for steady solutions. Numerical results indicate that the TVB limiter is more efficient and robust, while the artificial diffusivity schemes are able to preserve small-scale flow structures better. In high order cases, the artificial diffusivity schemes have demonstrated superior performance over the TVB limiter.

关键词: shock capturing, total variation bounded (TVB), discontinuous Galerkin (DG), limiter, artificial diffusivity

Abstract: This paper carries out systematical investigations on the performance of several typical shock-capturing schemes for the discontinuous Galerkin (DG) method, including the total variation bounded (TVB) limiter and three artificial diffusivity schemes (the basis function-based (BF) scheme, the face residual-based (FR) scheme, and the element residual-based (ER) scheme). Shock-dominated flows (the Sod problem, the Shu- Osher problem, the double Mach reflection problem, and the transonic NACA0012 flow) are considered, addressing the issues of accuracy, non-oscillatory property, dependence on user-specified constants, resolution of discontinuities, and capability for steady solutions. Numerical results indicate that the TVB limiter is more efficient and robust, while the artificial diffusivity schemes are able to preserve small-scale flow structures better. In high order cases, the artificial diffusivity schemes have demonstrated superior performance over the TVB limiter.

Key words: discontinuous Galerkin (DG), artificial diffusivity, total variation bounded (TVB), limiter, shock capturing

中图分类号:

O357.3

于剑;阎超;赵瑞. Assessment of shock capturing schemes for discontinuous Galerkin method[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1361-1374.

Jian YU;Chao YAN;Rui ZHAO. Assessment of shock capturing schemes for discontinuous Galerkin method[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1361-1374.

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Assessment of shock capturing schemes for discontinuous Galerkin method

Assessment of shock capturing schemes for discontinuous Galerkin method

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