Discontinuous Galerkin Methods for Neutrino Radiation Transport

We are developing new computational methods for simulation of neutrino transport in core-collapse supernovae, which is challenging since neutrinos evolve from being diffusive in the proto-neutron star to nearly free streaming in the critical neutrino heating region. To this end, we consider conservative formulations of the Boltzmann equation,\footnote{Cardall, Endeve, \& Mezzacappa 2013, Phys. Rev. D {\bf 88}, 023011} and aim to develop robust, high-order accurate methods. Runge-Kutta discontinuous Galerkin (DG) methods,\footnote{Cockburn \& Shu 2001, J. Sci. Comput. {\bf 16}, 173-261} offer several attractive properties, including (i) high-order accuracy on a compact stencil and (ii) correct asymptotic behavior in the diffusion limit. We have recently developed a new DG method for the advection part for the transport solve,\footnote{Endeve, Hauck, Xing, \& Mezzacappa 2015 (arXiv:1410.7431)} which is high-order accurate and strictly preserves the physical bounds of the distribution function; i.e., $f\in[0,1]$. We summarize the main ingredients of our bound-preserving DG method and discuss ongoing work to include neutrino-matter interactions in the scheme.