## A spectral Galerkin method for the coupled Orr-Sommerfeld and induction equations for free-surface MHD

- Dimitrios Giannakis, Paul F. Fischer, Robert Rosner
- J. Comput. Physics
- 2009

Highly Influenced

@article{Melenk2000SpectralGD, title={Spectral Galerkin Discretization for Hydrodynamic Stability Problems}, author={Jens Markus Melenk and N. P. Kirchner and Christoph Schwab}, journal={Computing}, year={2000}, volume={65}, pages={97-118} }

- Published 2000 in Computing
DOI:10.1007/s006070070014

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… CONTINUE READING