Towards General Relativistic Boltzmann Transport for Binary Neutron Star Mergers

We present a new neutrino transport code for binary neutron star
merger simulations for the numerical relativity code AthenaK. We use
finite element and spectral approaches to handle the angular dependence
while energy discretization is handled using a finite volume scheme. We
employ an asymptotic-preserving discontinuous Galerkin (DG) method for the
spatial discretization to ensure correct behavior in the
diffusion-dominated regime. A semi-implicit time stepping scheme is used
to handle the stiff and non-stiff sources correctly. In the first part of
the talk we describe the two approaches for angular discretization: the
finite-element method in angle (FEMN) and filtered spherical harmonics
(FPN) with an emphasis on positivity preservation for multi-energy
schemes. We also describe a strategy to obtain the two moments method (M1)
from the formulated equations. We then compare the efficacy of the three
approaches using various toy problems in the presence of a moving medium
and general relativity.