粘性可压混合层时间稳定性对称紧致差分求解

Numerical solution for the viscous temporal stability ofcompressible mixing layers with symmetric compact difference schemes

基于可压扰动方程组的一阶改型 ,将高精度对称紧致格式引入边值法数值线性稳定性分析。对所获非线性离散特征值问题给出了一个通用形式二阶迭代局部算法 ,实现了时间模式和空间模式的统一求解 ,并将扰动特征值及其特征函数同时得到。据此分析了可压平面自由混合层时间稳定性 ,涉及二维 /三维扰动波、粘性 /无粘扰动波、第一 /第二模态、特征函数、伪特征值谱等。研究表明 ,压缩性效应和粘性效应对最不稳定扰动波数和增长率呈相似的减抑作用 ;在 Mc=1附近 ,从高波数段开始 。

Based on the first-order form of compressible stability equations, a family of symmetric compacted difference schemes with high precision is employed for the boundary value problem in numerical stability analysis. A generalized form of the second order local iteration method is given for the obtained nonlinear discretized eigenvalue problem, hence both temporal and spatial stability can be observed similarly, and disturbance eigenmodes and their eigenfunctions are gained simultaneously. The temporal stability for compressible plane free mixing layers is investigated, including two and three dimensional waves, viscous inviscid waves, first and second modes, eigenfunctions, pseudo-eigenvalue spectra and so on. The results show that the viscosity as well as compressibility may reduce the wavenumber and growth rate of the unstable waves. Furthermore, near Mc=1, the viscosity may accelerate the change of two dimensional most unstable waves from the first mode to the second mode at high wavenumber.