  The overwhelming evidence that the core collapse supernova mechanism is
inherently multidimensional, the complexity of the physical processes involved,
and the increasing evidence from simulations that the explosion is marginal
presents great computational challenges for the realistic modeling of this
event, particularly in 3 spatial dimensions. We have developed a code which is
scalable to computations in 3 dimensions which couples PPM Lagrangian with
remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport
[2], with many improvements), and a nuclear network [3]. The neutrino transport
is performed in a ray-by-ray plus approximation wherein all the lateral effects
of neutrinos are included (e.g., pressure, velocity corrections, advection)
except the transport. A moving radial grid option permits the evolution to be
carried out from initial core collapse with only modest demands on the number
of radial zones. The inner part of the core is evolved after collapse along
with the rest of the core and mantle by subcycling the lateral evolution near
the center as demanded by the small Courant times. We present results of 2-D
simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M
progenitor. In each of these simulations we have discovered that once the
oxygen rich material reaches the shock there is a synergistic interplay between
the reduced ram pressure, the energy released by the burning of the shock
heated oxygen rich material, and the neutrino energy deposition which leads to
a revival of the shock and an explosion.
