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孙德军, 童秉纲, 尹协远. 0rr-Sommerfeld方程数值解法中的复广义矩阵特征值问题[J]. 力学学报, 1995, 27(5): 631-635. DOI: 10.6052/0459-1879-1995-5-1995-477
引用本文: 孙德军, 童秉纲, 尹协远. 0rr-Sommerfeld方程数值解法中的复广义矩阵特征值问题[J]. 力学学报, 1995, 27(5): 631-635. DOI: 10.6052/0459-1879-1995-5-1995-477
THE COMPLEX GENERALIZED MATRIX EIGENVALUE PROBLEM IN NUMERICAL SOLVER FOR ORR-SOMMERFELD EQUATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(5): 631-635. DOI: 10.6052/0459-1879-1995-5-1995-477
Citation: THE COMPLEX GENERALIZED MATRIX EIGENVALUE PROBLEM IN NUMERICAL SOLVER FOR ORR-SOMMERFELD EQUATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(5): 631-635. DOI: 10.6052/0459-1879-1995-5-1995-477

0rr-Sommerfeld方程数值解法中的复广义矩阵特征值问题

THE COMPLEX GENERALIZED MATRIX EIGENVALUE PROBLEM IN NUMERICAL SOLVER FOR ORR-SOMMERFELD EQUATION

  • 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。

     

    Abstract: 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 eigenvaluepr...

     

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