  This paper presents a hybrid Godunov method for three-dimensional radiation
hydrodynamics. The multidimensional technique outlined in this paper is an
extension of the one-dimensional method that was developed by Sekora & Stone
2009, 2010. The earlier one-dimensional technique was shown to preserve certain
asymptotic limits and be uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the
algorithmic details for constructing a multidimensional method. A future paper
will present numerical tests that demonstrate the robustness of the
computational technique across a wide-range of parameter space.
