  In preparation for an experimental study of magnetorotational instability
(MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamic
simulations of the nonlinear evolution of MRI in the experimental geometry. The
simulations adopt initially uniform vertical magnetic fields, conducting radial
boundaries, and periodic vertical boundary conditions. No-slip conditions are
imposed at the cylinders. Our linear growth rates compare well with existing
local and global linear analyses. The MRI saturates nonlinearly with horizontal
magnetic fields comparable to the initial axial field. The rate of angular
momentum transport increases modestly but significantly over the initial state.
For modest fluid and magnetic Reynolds numbers Re, Rm between 100 and 1000, the
final state is laminar reduced mean shear except near the radial boundaries,
and with poloidal circulation scaling as the square root of resistivity, in
partial agreement with the analysis of Knobloch and Julien. A sequence of
simulations at Rm=20 and 100 < Re < 25,600 enables extrapolation to the
experimental regime (Rm ~ 20, Re ~ 10^7), albeit with unrealistic boundary
conditions. MRI should increase the experimentally measured torque
substantially over its initial purely hydrodynamic value.
