Neutrino Transport

The flow of matter in a core collapse supernova poses some unique challenges that are not present in many other terrestrial and astrophysical problems. The matter is degenerate, and described by a complex equation of state for hot, dense matter at both super- and sub-nuclear densities. Even though hydrodynamic models of relativistic heavy ion collisions involve matter at several times the nuclear saturation density, the range of densities---over ten orders of magnitude---in the core of a collapsed star provides an added degree of complexity to the supernova problem.

There are a variety of schemes for the numerical solution of neutrino transport and neutrino radiation hydrodynamics problems. Each scheme, in turn, gives rise to a different system of linear or nonlinear algebraic equations to be solved. In this proposal, we will consider robust schemes based on a fully implicit finite differencing of the neutrino transport and neutrino radiation hydrodynamics equations. Schemes of this type are advantageous in that time scales associated with neutrino emission, absorption, and transport are typically orders of magnitude smaller than time scales associated with the hydrodynamic flow, and particularly advantageous in situations in which the fluid and neutrino radiation field are in equilibrium. The schemes we will consider are accurate, stable, and robust in these situations, and should find wide applicability in a number of disciplines.