An implicit FE-time solver for axisymmetric magnetic dynamo equations

Abstract

Magnetic fields are an essential element in investigations for the behaviour of interstellar matter, molecular clouds, galactic disks, accretion disks for stellar and collapsed objects as well as for the collimation and propagation of galactic and extragalactic jets. The time-evolution of magnetic fields in such turbulent media follows from the mean-field electrodynamics which includes the effects of advection, shear, rotation, helicity and diffusivity of the underlying fluid. Under axisymmetry, the induction equation splits into a coupled system of diffusion-type equations for the magnetic flux function ψ ( t, R, z) and the poloidal current stream-function T ( t, R, z). For this non-linearly coupled system, a fully implicit time-solver has been developed based on the methods of finite elements. This code can easily be implemented on any modern RISC workstation. With this code, magnetic fields in galactic disks evolving on the Hubble time can be followed up. Similarly, the time-evolution of magnetic fields in accretion disks around stellar and compact objects can be simulated for a few hundred Keplerian revolution times.