  We have developed a time-dependent, multi-energy-group, and multi-angle
(S$_n$) Boltzmann transport scheme for radiation hydrodynamics simulations, in
one and two spatial dimensions. The implicit transport is coupled to both 1D
(spherically-symmetric) and 2D (axially-symmetric) versions of the explicit
Newtonian hydrodynamics code VULCAN. The 2D variant, VULCAN/2D, can be operated
in general structured or unstructured grids and though the code can address
many problems in astrophysics it was constructed specifically to study the
core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the
radiation/hydrodynamic evolution of differentially rotating bodies. We
summarize the equations solved and methods incorporated into the algorithm and
present results of a time-dependent 2D test calculation. A more complete
description of the algorithm is postponed to another paper. We highlight a 2D
test run that follows for 22 milliseconds the immediate post-bounce evolution
of a collapsed core. We present the relationship between the anisotropies of
the overturning matter field and the distribution of the corresponding flux
vectors, as a function of energy group. This is the first 2D multi-group,
multi-angle, time-dependent radiation/hydro calculation ever performed in core
collapse studies. Though the transport module of the code is not gray and does
not use flux limiters (however, there is a flux-limited variant of VULCAN/2D),
it still does not include energy redistribution and most velocity-dependent
terms.
