A novel shock instability analysis model named cell–shock–cell system is presented. Shock-related nonunique numerical solutions of the Euler equation are presented in this system, which indicates that this simple system keeps the essential characteristics of numerical shock instability. The stability analysis of this system was conducted, and some important results were obtained. Carbuncle phenomena were shown to originate from multidimensional instability of the upstream shock cell. The numerical shock instability essentially starts from the grid face perpendicular to the shock rather than the grid parallel to it. The analytical eigenvalue analysis of the linearized equations showed that inappropriate pressure dissipation of Riemann solver at the vertical transverse face of a shock was responsible for the carbuncle phenomena and shock instability. Based on the mechanism that was identified, a fundamental cure principle was proposed. These new findings can serve as a basis for understanding the numerical shock instabilities presented in one-dimensional Riemann-solver-based numerical schemes as well as in designing shock-stable schemes.
Mechanism Study of Shock Instability in Riemann-Solver-Based Shock-Capturing Scheme
AIAA Journal ; 56 , 9 ; 3636-3651
2018-07-30
16 pages
Article (Journal)
Electronic Resource
English
General Procedure for Riemann Solver to Eliminate Carbuncle and Shock Instability
Online Contents | 2017
|General Procedure for Riemann Solver to Eliminate Carbuncle and Shock Instability
Online Contents | 2017
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