ISSN:
1436-5057
Keywords:
AMS Subject Classifications: 76E05, 65N25, 65N35.
;
Key Words: Orr-Sommerfeld equation, hydrodynamic stability, eigenvalue problem, spectral method.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract A spectral Galerkin discretization for calculating the eigenvalues of the Orr-Sommerfeld equation is presented. The matrices of the resulting generalized eigenvalue problem are sparse. A convergence analysis of the method is presented which indicates that a) no spurious eigenvalues occur and b) reliable results can only be expected under the assumption of scale resolution, i.e., that Re/p 2 is small; here Re is the Reynolds number and p is the spectral order. Numerical experiments support that the assumption of scale resolution is necessary in order to obtain reliable results. Exponential convergence of the method is shown theoretically and observed numerically.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s006070070014
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