Bound-Preserving Discontinuous Galerkin Methods for Neutrino Transport

We aim to develop accurate and robust methods for simulation of multi-dimensional neutrino transport in nuclear astrophysics applications. Specifically, methods that work well in scattering and/or absorption dominated regimes, and in the streaming limit. Here we consider a multi-group two-moment model which evolves the spectral particle density $\mathcal{N}$ and flux $\boldsymbol{\mathcal{F}}$ --- angular moments of a phase space distribution function $f$. Since, by the Pauli exclusion principle, the neutrino distribution function is bounded ($f\in[0,1]$), a realizable set of moments ($\mathcal{N},\boldsymbol{\mathcal{F}}$) must also be bounded. Specifically, $\mathcal{N} \in [0,1]$ and $(1-\mathcal{N})\mathcal{N} - |\boldsymbol{\mathcal{F}}| \geq 0$. To achieve high-order accuracy, efficiency (i.e., large time step), and the bound-preserving property, an implicit-explicit (IMEX) discontinuous Galerkin (DG) method has been developed. Here we present details of the mathematical model, the numerical method, and a detailed comparison of several IMEX schemes on relevant test problems.