A time-stepping dynamically-consistent spherical-shell dynamo code

Abstract

A pseudo-spectral dynamo code, developed as a computational laboratory, is described. The magnetic, heat and Boussinesq Navier-Stokes equations, with inertia, non-linear advection, buoyancy with asymmetric gravity, Coriolis, viscous and Lorentz forces, are solved numerically in a rotating conducting fluid shell. The convection is thermally driven by prescribed boundary temperatures. The equations are discretised using toroidal-poloidal fields, Chebychev collocation in radius and spherical harmonic expansion in angles. Derivatives are performed spectrally. Products are evaluated in physical space for efficiency. Fields are transformed between physical and spectral spaces by fast Fourier and Gauss-Legendre methods. Linear terms are time-stepped implicitly and product terms explicitly using an Adams predictor/corrector. Results are presented for two benchmark models.