Conclusions:
Theory of black hole accretion disks is based on a few analytic and semi-analytic models;
Shakura-Sunyaev (and Novikov-Thorne), slim disks, ADAFs, and Polish doughnuts.
The models are based on the "alpha" prescription for viscous stress. It is
still not clear whether the original alpha prescription is physically acceptable,
or whether its recently suggested modifications could be eventually made
physically acceptable.
Numerical simulations (MHD, 3D, time-dependent) in general agree with the analytic models. In some particular cases the agreement is excellent. Most recently, there were attempts to make the analytic models more physically realistic.
I know of no fundamental result in the black hole accretion disk theory which was found by numerical simulations alone, without a previous anticipation from analytic models.
