A vector spherical harmonic spectral code for linearised magnetohydrodynamics

Abstract

Linearised rotating magnetohydrodynamic stability code for the steady axisymmetric basic states of an electrically conducting fluid sphere is described. The code generates compact hybrid angular spectral forms of the magnetic induction, heat and Boussinesq Navier-Stokes equations, using toroidal and poloidal representations of the perturbation vector fields, and vector or scalar spherical harmonic expansions of all fields. The momentum equation may include inertial, Coriolis, buoyancy, viscous and magnetic Lorentz forces. Three subroutines evaluate the spectral interactions of products. There are only six radial functions, which are discretised using uniform second-order finite differences. The resulting large scale complex non-hermitian generalised eigen- and critical-value problems are solved using inverse and Newton-Raphson iteration methods, respectively. Test results are presented for several models.