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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received November 11, 1998; revised March 1, 2000
Rights and permissions
About this article
Cite this article
Melenk, J., Kirchner, N. & Schwab, C. Spectral Galerkin Discretization for Hydrodynamic Stability Problems. Computing 65, 97–118 (2000). https://doi.org/10.1007/s006070070014
Issue Date:
DOI: https://doi.org/10.1007/s006070070014