超声速粘性剪切流空间稳定性对称紧致差分数值分析

用一类高精度对称紧致差分格式数值离散一阶改型三维可压粘性扰动方程，对导出的非线性离散特征值问题采用二阶修正Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ边值迭代局部解法，实现了超声速剪切流的线性空间稳定性分析。基于对流Ｍ数、Ｒｅ数、速度比、密度比等参数研究，讨论了压缩性效应、粘性效应、超声速扰动快／慢模态等，结果显示超声速粘性剪切流的弱不稳定性同多种影响因素密切相关。

Numerical Analysis of Viscous Spatial Stability in Supersonic Shear Layers Using Symmetric Compact Difference Method

The first order modified form of three dimensional compressible viscous disturbance equations is discretized numerically through using a family of high accuracy symmetric compact difference schemes. A second order modified Newton Raphson (MNR) iteration local method is developed to solve the obtained non linear discretized eigenvalue problem. The linear spatial stability in supersonic shear layers is analyzed numerically. Based on parameterized study including convective Mach number, Reynolds number, velocity ratio, density ratio, and so on, the compressibility, viscosity, supersonic fast/slow modes etc are discussed. The results show that the weak viscous instabilities of supersonic shear layers are related to many factors.