TY - JOUR
T1 - A Stability Analysis of Hybrid Schemes to Cure Shock Instability
AU - Zhijun Shen, Wei Yan & Guangwei Yuan
JO - Communications in Computational Physics
VL - 5
SP - 1320
EP - 1342
PY - 2014
DA - 2014/05
SN - 15
DO - http://doi.org/10.4208/cicp.210513.091013a
UR - https://global-sci.org/intro/article_detail/cicp/7139.html
KW - 
AB - <p style="text-align: justify;">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 <em>Roe</em> with <em>HLL</em> 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.</p>