Global time-dependent simulations provide a means to investigate time-dependent dynamic evolution in accretion disks. This paper seeks to extend previous local simulations by beginning a systematic effort to develop fully global three-dimensional simulations. The nonlinear development of the magnetorotational instability is investigated using a time-explicit finite difference code written in cylindrical coordinates. The equations of ideal magnetohydrodynamics are solved with the assumption of an adiabatic equation of state. Both a Newtonian, and a pseudo-Newtonian potential are used. Two simplifications are also explored: a cylindrical gravitational potential (the ``cylindrical disk''), and axisymmetry. The results from those simulations are compared with fully three dimensional global simulations. The global simulations investigate initial equilibrium pressure supported accretion tori with two different initial field geometries: poloidal fields that are constant along initial equidensity surfaces, and toroidal fields with a constant ratio of gas to magnetic pressure. In both cases the magnetorotational instability rapidly develops, and the torus becomes turbulent. The resulting turbulence transports angular momentum, and the torus develops an angular momentum distribution that is near Keplerian.

37 pages, 14 figures