摘要
Orr-Sommerfeld方程的求解通常可以化为一个复广义矩阵特征值问题AX=ωBX。本文用酉变换分别约化A,B为上Hessenberg阵和上三角阵,然后利用Muller求根方法可以求出其全部特征值,其中特征多项式的值由Hyman方法给出。当仅需要判断有无不稳定模态时,利用一个简单的矩阵变换将其化为强特征值的求解问题,从而可使用最简单的幂迭代,Chebyshev配置点法算例表明两种算法均快速有效。
The problem of solving Orr-Sommerfeld equation can usually be transformedinto a complex generalized matrix eigenvalue problem AX=ωBX。 This paper reduces A,Bto upper Hessenberg matrix and upper triangular matrix respectively by U-transformation,then uses Muller′s rootfinding method to obtain all eigenvalues,where the value of charac-teristic polynomial is given by Hyman′s indirect method.When only a judgement of whetherany mode is unstable is needee,the problem can be transformed into a dominant eigenvalueproblem by a simple matrix transformation, so the simplest power iterative method can beapplied,Example of Chebyshev collocation method shows that the two methods above areboth fast and effceint.
出处
《力学学报》
EI
CSCD
北大核心
1995年第5期631-635,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
关键词
稳定性
广义
特征值问题
矩阵
O-S方程
Orr-Sommerfeld equation, stability,generalized eigenvalue problem, Muller’smethod