高超声速数值激波失稳的网格依赖性

高超声速强激波的稳定捕捉仍极具挑战性。目前工程计算中普遍应用的数值格式在模拟多维强激波时通常会遭遇明显的激波不稳定现象，且数值格式的激波稳定性对计算网格表现出严重的依赖性。基于矩阵稳定性分析法，对比了具有不同耗散性质的数值格式稳定捕捉激波的能力，分析了空间二阶精度格式的激波稳定性及限制器对激波稳定性的影响。在此基础上，重点探究了计算网格对激波稳定性的影响规律，研究了网格长宽比和畸变角度对激波稳定性的影响。结果显示，在激波附近通过增大网格长宽比或改变网格畸变角度可有效改善激波捕捉的稳定性；相比于增大网格长宽比，改变网格畸变角度提升激波捕捉稳定性的效果更加明显。在此基础上，结合数值耗散分析对高马赫数下数值激波失稳现象的网格依赖性机制进行了探讨。

Grid dependence of hypersonic numerical shock instability

The stable capture of hypersonic strong shock waves is still extremely challenging. At present, the numerical scheme used in engineering calculations usually encounters obvious shock instability when simulating multi-dimensional strong shock waves. Moreover, the shock stability of the numerical scheme depends on the computational grid. Based on the method of matrix stability analysis, this paper compared the ability of numerical schemes with different dissipation properties to capture shock waves, and analysed the shock stability of spatial second-order precision schemes as well as the effect of different limiters. On this basis, this paper explored the influence of computing grid on shock stability, and the influence of aspect ratio and distortion angle of grid on shock wave stability was studied. The research results show that in the vicinity of the shock wave, increasing the grid aspect ratio or the grid distortion angle can effectively improve the stability of shock capture. Moreover, compared to increasing the grid aspect ratio, changing the grid distortion angle has a more obvious effect on improving the stability of shock capture. Numerical dissipation analysis is conducted, and the grid-dependent mechanism of numerical shock instability under high Mach number is discussed.