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

@article{Giannakis2009ASG,
title={A spectral Galerkin method for the coupled Orr-Sommerfeld and induction equations for free-surface MHD},
author={Dimitrios Giannakis and Paul F. Fischer and Robert Rosner},
journal={J. Comput. Physics},
year={2009},
volume={228},
pages={1188-1233}
}

We develop and test spectral Galerkin schemes to solve the coupled Orr–Sommerfeld (OS) and induction equations for parallel, incompressible MHD in free-surface and fixed-boundary geometries. The schemes’ discrete bases consist of Legendre internal shape functions, supplemented with nodal shape functions for the weak imposition of the stress and insulating boundary conditions. The orthogonality properties of the basis polynomials solve the matrixcoefficient growth problem, and eigenvalue… CONTINUE READING