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A Stability Analysis of Hybrid Schemes to Cure Shock Instability

A Stability Analysis of Hybrid Schemes to Cure Shock Instability
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Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.210513.091013a

Communications in Computational Physics, Vol. 15 (2014), Iss. 5 : pp. 1320–1342

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:   

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