Volume 15, Issue 5
A Stability Analysis of Hybrid Schemes to Cure Shock Instability

Zhijun Shen, Wei Yan & Guangwei Yuan

Commun. Comput. Phys., 15 (2014), pp. 1320-1342.

Published online: 2014-05

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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.

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@Article{CiCP-15-1320, author = {}, title = {A Stability Analysis of Hybrid Schemes to Cure Shock Instability}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1320--1342}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210513.091013a}, url = {http://global-sci.org/intro/article_detail/cicp/7139.html} }
TY - JOUR T1 - A Stability Analysis of Hybrid Schemes to Cure Shock Instability JO - Communications in Computational Physics VL - 5 SP - 1320 EP - 1342 PY - 2014 DA - 2014/05 SN - 15 DO - http://dor.org/10.4208/cicp.210513.091013a UR - https://global-sci.org/intro/article_detail/cicp/7139.html KW - AB -

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.

Zhijun Shen, Wei Yan & Guangwei Yuan. (2020). A Stability Analysis of Hybrid Schemes to Cure Shock Instability. Communications in Computational Physics. 15 (5). 1320-1342. doi:10.4208/cicp.210513.091013a
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