Global MHD Simulations of Cylindrical Keplerian Disks
  This paper presents a series of global three dimensional accretion disk simulations carried out in the cylindrical limit in which the vertical component of the gravitational field is neglected. The simulations use a cylindrical pseudo-Newtonian potential to model the main dynamical properties of the Schwarzschild metric. The disks are initially constant density with a Keplerian angular momentum distribution and contain a weak toroidal or vertical field. These simulations reaffirm many of the conclusions of previous local simulations. The magnetorotational instability grows rapidly and produces MHD turbulence with a significant Maxwell stress which drives accretion. Tightly-wrapped low-$m$ spiral waves are prominent. In some simulations radial variations in Maxwell stress concentrate gas into rings, creating substantial spatial inhomogeneities. There is a nonzero stress at the marginally stable orbit which produces a small decline in specific angular momentum inside the last stable orbit. Detailed comparisons between simulations are used to examine the effects of computational domain and equation of state. Simulations that begin with vertical fields have greater field amplification and higher ratios of stress to magnetic pressure compared with those beginning with toroidal fields. In contrast to MHD, hydrodynamics alone neither creates nor sustains turbulence. 
John F. Hawley (U. Virginia)