  In this paper we report on recent upgrades to our general relativistic
radiation magnetohydrodynamics code, Cosmos++, including the development of a
new primitive inversion scheme and a hybrid implicit-explicit solver with a
more general closure relation for the radiation equations. The new hybrid
solver helps stabilize the treatment of the radiation source terms, while the
new closure allows for a much broader range of optical depths to be considered.
These changes allow us to expand by orders of magnitude the range of
temperatures, opacities, and mass accretion rates, and move a step closer
toward our goal of performing global simulations of
radiation-pressure-dominated black hole accretion disks. In this work we test
and validate the new method against an array of problems. We also demonstrate
its ability to handle super-Eddington, quasi-spherical accretion. Even with
just a single proof-of-principle simulation, we already see tantalizing hints
of the interesting phenomenology associated with the coupling of radiation and
gas in super-Eddington accretion flows.
