A Two-moment Neutrino Transport Scheme for the CHIMERA Supernova Code

Abstract We introduce our two-moment scheme, referred to as A-M1 (analytic closure-M1), to solve the neutrino Boltzmann transport equation with the aim of using it to replace the flux-limited diffusion (FLD) scheme currently utilized in C himera . We first present the A-M1 equations and the numerical method used for solving them. We then present the results of several numerical experiments that were conducted to test the ability of the scheme to perform some basic tasks that are encountered in simulating core-collapse supernovae. The first two were simply to test the ability of the code to ensure conservation of and to respect the fermionic character of neutrinos. More challenging tests were the ability of the code to match analytic solutions in the realms of both diffusion and free streaming. Finally, the ability of the code to match the analytic solution of the homogeneous sphere problem was tested. By separating a diffusive and a free-streaming regime by a density discontinuity, this test mimics the configuration of a supernova core consisting of a dense proto–neutron star below and a rarefied heating region above separated by a steepening density cliff. While the Eddington factor was prescribed in the two preceding tests, a number of analytic Eddington factors were tested in the latter test. A future paper will describe the performance of the A-M1 code on nonstatic backgrounds and will present detailed comparisons of core-collapse simulations performed with the A-M1 scheme versus the current FLD scheme.