Discontinuous Galerkin Methods for the Two-Moment Model of Radiation Transport

We are developing computational methods for simulation of radiation transport in astrophysical systems (e.g., neutrino transport in core-collapse supernovae). Here we consider the two-moment model of radiation transport, where the energy density $E$ and flux $\boldsymbol{F}$ --- angular moments of a phase space distribution function --- approximates the radiation field in a computationally tractable manner. We aim to develop multi-dimensional methods that are (i) high-order accurate for computational efficiency, and (ii) robust in the sense that the solution remains in the realizable set $R=\{ (E,\boldsymbol{F}) ~ | ~ E\ge0 ~ \mbox{and} ~ E-|\boldsymbol{F}|\ge0\}$ (i.e., $E$ and $\boldsymbol{F}$ are consistent with moments of an underlying distribution). Our approach is based on the Runge-Kutta discontinuous Galerkin method\footnote{Cockburn \& Shu 2001, J. Sci. Comput. {\bf 16}, 173-261}, which has many attractive properties, including high-order accuracy on a compact stencil. We present the physical model and numerical method, and show results from a multi-dimensional implementation. Tests show that the method is high-order accurate and strictly preserves realizability of the moments.