  Ascertaining the core-collapse supernova mechanism is a complex, and yet
unsolved, problem dependent on the interaction of general relativity,
hydrodynamics, neutrino transport, neutrino-matter interactions, and nuclear
equations of state and reaction kinetics. Ab initio modeling of core-collapse
supernovae and their nucleosynthetic outcomes requires care in the coupling and
approximations of the physical components. We have built our multi-physics
CHIMERA code for supernova modeling in 1-, 2-, and 3-D, using ray-by-ray
neutrino transport, approximate general relativity, and detailed neutrino and
nuclear physics. We discuss some early results from our current series of
exploding 2D simulations and our work to perform computationally tractable
simulations in 3D using the "Yin-Yang" grid.
