Towards Robust Methods for Relativistic Neutrino Transport*

We develop 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, efficient, and robust, and consider a multi-group two-moment model in the so-called $\mathcal{O}(v/c)$ limit to account for neutrinos interacting with a moving fluid.
In this model, the 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.
Building on our previous work\footnote{Endeve et al. 2015, JCP, {287}, 151-183; Chu et al. 2018, arXiv:1809.06949}, 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 fermion distribution (satisfying $0\le f \le1$).
The set of realizable solutions is convex (albeit more complex than in the non-relativistic case), which allows us to develop the methods within a familiar framework.
We present the physical model, discuss the numerical method, and show preliminary results.