We present a sub-grid model that emulates the magnetic dynamo operating in magnetized accretion disks .
We have implemented this model in the general relativisic radiation magnetohydrodynamic ( GRRMHD ) code KORAL , using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo .
With the inclusion of this dynamo , we are able to run 2D axisymmetric GRRMHD simulations of accretion disks for arbitrarily long times .
The simulated disks exhibit sustained turbulence , with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies .
Using this dynamo code , we present a set of long-duration global simulations of super-Eddington , optically-thick disks around non-spinning and spinning black holes .
Super-Eddington disks around non-rotating black holes exhibit a surprisingly large efficiency , \eta \approx 0.04 , independent of the accretion rate , where we measure efficiency in terms of the total energy output , both radiation and mechanical , flowing out to infinity .
Super-Eddington disks around spinning black holes are even more efficient , and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism .
All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis .
We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates ( \dot { M } \lesssim 2 \dot { M } _ { Edd } ) .
None of these models reached a steady state .
Instead , the disks collapsed as a result of runaway cooling , presumably because of a thermal instability .