Abstract. In this paper we describe a numerical method designed for modelling different kinds of astrophysical flows in three dimensions. Our method is a standard explicit finite difference method employing the local shearingbox technique. To model the features of astrophysical systems, which are usually compressible, magnetised and turbulent, it is desirable to have high spatial resolution and large domain size to model as many features as possible, on various scales, within a particular system. In addition, the time-scales involved are usually wideranging also requiring significant amounts of CPU time. These two limits (resolution and time-scales) enforce huge limits on computational capabilities. The model we have developed therefore uses parallel algorithms to increase the performance of standard serial methods. The aim of this paper is to report the numerical methods we use and the techniques invoked for parallelising the code. The justification of these methods is given by the extensive tests presented herein.

Abstract. The Accretion-Ejection Instability (AEI) described by Tagger & Pellat (1999, hereafter TP99) is explored numerically using a global 2d model of the inner region of a magnetised accretion disk. The disk is initially currentless but threaded by a vertical magnetic field created by external currents, and frozen in the flow. In agreement with the theory a spiral instability, similar in many ways to those observed in self-gravitating disks, develops when the magnetic field is, within a factor of a few, at equipartition with the disk thermal pressure. Perturbations in the flow build up currents and create a perturbed magnetic field within the disk. The present non-linear simulations give good evidence that such an instability can occur in the inner region of accretion disks, and generate accretion of gas and vertical magnetic flux toward the central object, if the equilibrium radial profiles of density and magnetic flux exceed a critical threshold.