  Two different computational approaches to the magnetorotational instability
(MRI) are pursued: the shearing box approach which is suited for local
simulations and the embedding box approach whereby a Taylor Couette flow is
embedded in a box so that numerical problems with the coordinate singularity
are avoided. New shearing box simulations are presented and differences between
regular and hyperviscosity are discussed. Preliminary simulations of spherical
nonlinear Taylor Couette flow in an embedding box are presented and the effects
of an axial field on the background flow are studied.
