On numerical instabilities of Godunov-type schemes for strong shocks

被引:43
|
作者
Xie, Wenjia [1 ]
Li, Wei [2 ]
Li, Hua [1 ]
Tian, Zhengyu [1 ]
Pan, Sha [1 ]
机构
[1] Natl Univ Def Technol, Coll Aerosp Sci & Engn, Changsha 410073, Hunan, Peoples R China
[2] China Aerodynam Res & Dev Ctr, Computat Aerodynam Res Inst, Mianyang, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Godunov-type schemes; Carbuncle; Riemann solver; Shock instability; Finite volume; Hypersonic; HYPERBOLIC CONSERVATION-LAWS; APPROXIMATE RIEMANN SOLVERS; CARBUNCLE PHENOMENON; COMPUTATIONAL PHYSICS; DIFFERENCE-SCHEMES; STABILITY ANALYSIS; GAS-DYNAMICS; FLUX; AUSM; DISSIPATION;
D O I
10.1016/j.jcp.2017.08.063
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:607 / 637
页数:31
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