Numerical shock instability is a complexity which may occur in supersonic simulations. Riemann solver is usually the crucial factor that affects both the computation accuracy and numerical shock stability. In this paper, several classical Riemann solvers are discussed, and the intrinsic mechanism of shock instability is especially concerned. It can be found that the momentum perturbation traversing shock wave is a major reason that invokes instability. Furthermore, slope limiters used to depress oscillation across shock wave is also a key factor for computation stability. Several slope limiters can cause significant numerical errors near shock waves, and make the computation fail to converge. Extra dissipation of Riemann solvers and slope limiters can be helpful to eliminate instability, but reduces the computation accuracy. Therefore, to properly introduce numerical dissipation is critical for numerical computations. Here, pressure based shock indicator is used to show the position of shock wave and tunes the numerical dissipation. Overall, the presented methods are showing satisfactory results in both the accuracy and stability.

翻译：数值激波不稳定性是超声速模拟中可能出现的一种复杂现象。黎曼求解器通常是影响计算精度和数值激波稳定性的关键因素。本文讨论了几种经典黎曼求解器，并特别关注激波不稳定性的内在机制。研究发现，穿过激波的动量扰动是引发不稳定的主要原因。此外，用于抑制激波振荡的斜率限制器也是影响计算稳定性的关键因素。某些斜率限制器会在激波附近引起显著数值误差，导致计算无法收敛。增加黎曼求解器和斜率限制器的额外耗散有助于消除不稳定性，但会降低计算精度。因此，合理引入数值耗散对数值计算至关重要。本文采用基于压力的激波指示器来显示激波位置并调节数值耗散。总体而言，所提出的方法在精度和稳定性方面均获得了令人满意的结果。