A Numerical Scheme for Multi-fluid Magnetohydrodynamics

This paper describes a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution equation for the magnetic field that can be solved using an implicit scheme. This avoids the severe restriction on the stable timestep that would otherwise arise at high resolution, or when the Hall effect is large. Numerical tests show that the scheme can accurately model steady multi-fluid shock structures both with and without sub-shocks. Although the emphasis is on shocks in molecular clouds, a multi-dimensional version of this code could be applied to any Astrophysical flow in which ambi-polar diffusion or the Hall effect, or both play a significant role.