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

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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)

Abstract

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

2010 MSC Number:

O357.3

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

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Assessment of shock capturing schemes for discontinuous Galerkin method

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