Shearing and embedding box simulations of the magnetorotational instability

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.