Supercomputer simulations have been used in conjunction with analytic
studies to investigate the central issue of astrophysical accretion-di
sk dynamics: the nature of the angular momentum transport. Simulations
provide the means to investigate and experiment with candidate mechan
isms, including global hydrodynamic instabilities, spiral shock waves,
and local magnetohydrodynamic (MHD) instabilities. Simulations have d
emonstrated that accretion disks are generally MHD turbulent. These re
sults suggest that the fundamental physical mechanism for angular mome
ntum transport in accretion disks has now been identified.