A Stability Analysis of Hybrid Schemes to Cure Shock Instability (Communications in Computational Physics, 2014)
The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining highresolution flux with more dissipative solver is an attractive attempt to cure this kindof non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-DEuler 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 onsuch analysis, some hybrid schemes are compared to illustrate different mechanisms incontrolling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability sourceis more stable than other hybrid schemes.