Mechanism-Derived Shock Instability Elimination for Riemann-Solver-Based Shock-Capturing Scheme

In our study series, the first paper found that the negative pressure dissipation of density flux at the vertical transverse face of a shock leads to shock instability. Here, we present a general eliminating method derived by this mechanism. This method, named transverse pressure dissipation modification, explicitly adds additional flux dissipation at the vertical transverse face of a shock. The stability of the modified scheme was analyzed by a linear stability method, and completely negative values of maximum real part eigenvalues of the linearized system were realized, which indicates the effectiveness of this method. This method was verified and compared in detail with the existing elimination method for typical cases via structured/unstructured mesh and two-dimensional and three-dimensional configurations. Transverse pressure dissipation modification can be connected to any Riemann solver, and the combined scheme is numerically shock stable and contact preserving.