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A Stability Analysis of Hybrid Schemes to Cure Shock Instability

Published online by Cambridge University Press:  03 June 2015

Zhijun Shen ,
Wei Yan  and
Guangwei Yuan
Zhijun Shen*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China Center for Applied Physics and Technology, HEDPS, Peking University, Beijing 100871, China
Wei Yan*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China
Guangwei Yuan*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China
*
Corresponding author.Email:shen_zhijun@iapcm.ac.cn
Email:wyanmath01@sina.com
Email:yuan_guangwei@iapcm.ac.cn
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Abstract

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes. By combining the Roe with HLL flux in different directions and different flux components, we give an interesting explanation to the linear numerical instability. Based on such analysis, some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

Keywords

35L6565M0876M1276L05Godunov methodsnumerical shock instabilityhybrid scheme
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1320 - 1342
Copyright
Copyright © Global Science Press Limited 2014

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