增强高超声速化学反应流数值计算的稳定性方法

针对高超声速化学反应流数值模拟中包含源项对角化雅可比矩阵的数值格式稳定性很差的问题，在对采用上下对称的高斯-赛德尔(LU-SGS)格式的离散方程进行线性稳定性分析的基础上，提出一种依据流动状态对流场的块网格进行局部加密的方法，以增强流场数值计算稳定性。在高超声速流场中，对包含激波后亚声速高温区域的块网格给予加密，而其他区域中的块网格可以适当进行网格粗化或保持不变。算例结果表明，相比于初始网格，局部加密后的改进网格并不会产生过多的网格量，而且能够采用较大的柯朗-弗里德里奇-列维（CFL）数以达到数值求解过程中稳定计算和快速收敛的目的。

A Method for Improving the Stability of Numerical Calculation in Hypersonic Chemically Reacting Flows

In numerical simulations of hypersonic flows with chemical reactions, the stability of the numerical scheme including the diagonalized Jacobian of chemical source becomes terrible. In this paper, according to the linear stability analysis of the discrete equation with the lower-upper symmetric Gauss-Seidel (LU-SGS) scheme, a local block grid refinement method is suggested based on the flow conditions for improving the stability. In the hypersonic chemically reacting flows, the refinement should be carried out for the block grid in the areas of subsonic state and high temperature behind the shock wave, and the block grid in other areas may be coarsened or invariable. The numerical results demonstrate that the improved grid has a stable computation and rapid convergence with a larger Courant-Friedrichs-Lewy (CFL) number, but cannot produce overmuch grid cells compared with initial grid.