  Observations are providing increasingly detailed quantitative information
about the accretion flows that power such high energy systems as X-ray binaries
and active galactic nuclei. Analytic models of such systems must rely on
assumptions such as regular flow geometry and a simple, parameterized stress.
Global numerical simulations offer a way to investigate the basic physical
dynamics of accretion flows without these assumptions. For black hole accretion
studies one solves the equations of general relativistic magnetohydrodynamics.
Magnetic fields are of fundamental importance to the structure and evolution of
accretion disks because magnetic turbulence is the source of the anomalous
stress that drives accretion. We have developed a three-dimensional general
relativistic magnetohydrodynamic simulation code to evolve time-dependent
accretion systems self-consistently. Recent global simulations of black hole
accretion disks suggest that the generic structure of the accretion flow is
usefully divided into five regimes: the main disk, the inner disk, the corona,
the evacuated funnel, and the funnel wall jet. The properties of each of these
regions are summarized.
