A Discontinuous Galerkin Method for Spectral Neutrino Transport

We are developing methods for simulation of multi-dimensional neutrino transport in nuclear astrophysics applications (e.g., core-collapse supernovae and binary neutron star mergers). We aim to develop methods that are accurate and robust. Here we consider a multi-group two-moment model, where the spectral particle density $\mathcal{N}$ and flux $\boldsymbol{\mathcal{F}}$ -- angular moments of a phase space distribution function $f$ -- approximates the radiation field in a computationally tractable manner. Our approach is based on the Runge-Kutta discontinuous Galerkin method\footnote{Cockburn \& Shu 2001, J. Sci. Comput. {\bf 16}, 173-261}. Building on our previous work\footnote{Endeve et al. 2015, JCP, {287}, 151-183}, we are developing a method that maintains realizable solutions in the sense that $\mathcal{N}$ and $\boldsymbol{\mathcal{F}}$ remains consistent with moments of an underlying Fermi-Dirac distribution (satisfying $0\le f \le1$). We present details of the physical model, the numerical method, and show preliminary numerical results.