ar X iv : a st ro - p h / 06 07 28 1 v 1 12 J ul 2 00 6 A Numerical Algorithm for Modeling Multigroup Neutrino - Radiation Hydrodynamics in Two Spatial Dimensions

It is now generally agreed that multidimensional, multigroup, radiation hydrodynamics is an indispensable element of any realistic model of stellar-core collapse, core-collapse supernovae, and proto-neutron star instabilities. We have developed a new, two-dimensional, multigroup algorithm that can model neutrino-radiation-hydrodynamic flows in core-collapse supernovae. Our algorithm uses an approach that is similar to the ZEUS family of algorithms, originally developed by Stone and Norman. However, we extend that previous work in three significant ways: First, we incorporate multispecies, multigroup, radiation hydrodynamics in a flux-limited-diffusion approximation. Our approach is capable of modeling pair-coupled neutrino-radiation hydrodynamics, and includes effects of Pauli blocking in the collision integrals. Blocking gives rise to nonlinearities in the discretized radiation-transport equations , which we evolve implicitly in time. We employ parallelized Newton-Krylov methods to obtain a solution of these nonlinear, implicit equations. Our second major extension to the ZEUS algorithm is inclusion of an electron conservation equation, which describes evolution of electron-number density in the hydrodynamic flow. This permits following the effects of deleptonization in a stellar core. In our third extension, we have modified the hydrodynamics algorithm to accommodate realistic, complex equations of state, including those having non-convex behavior. In this paper, we present a description of our complete algorithm, giving detail sufficient to allow others to implement, reproduce, and extend our work. Finite-differencing details are presented in appendices. We also discuss implementation of this algorithm on state-of-the-art, parallel-computing architectures. Finally, we present results of verification tests that demonstrate the numerical accuracy of this algorithm on diverse hydrodynamic, gravitational, radiation-transport, and radiation-hydrodynamic sample problems. We believe our methods to be of general use in a variety of model settings where radiation transport or radiation hydrodynamics is important. Extension of this work to three spatial dimensions is straightforward.