A numerical method for three-dimensional simulations of collapsing, isothermal, magnetic gas clouds

In this paper a numerical method for the investigation of collapsing gas clouds will be described. The method is based on the particle method SPH (Smooth Particle Hydrodynamics). Different forms of the magnetic force terms are discussed and one form, that which conserves linear and angular momentum exactly, is shown to be unstable. A simple technique which removes the instability is described. The method is applied here to Alfvén waves, shock waves, magnetic polytropes and to equilibrium models of isothermal gas clouds.