NADA-FLD: a general relativistic, multidimensional neutrino-hydrodynamics code employing flux-limited diffusion

We present the new code NADA-FLD to solve multidimensional neutrino-hydrodynamics in full general relativity (GR) in spherical polar coordinates. The energy-dependent neutrino transport assumes the flux-limited diffusion approximation and evolves the neutrino energy densities measured in the frame comoving with the fluid. Operator splitting is used to avoid multidimensional coupling of grid cells in implicit integration steps involving matrix inversions. Terms describing lateral diffusion and advection are integrated explicitly using the Allen-Cheng or the Runge-Kutta-Legendre method, which remain stable even in the optically thin regime. We discuss several toy-model problems in one and two dimensions to test the basic functionality and individual components of the transport scheme. We also perform fully dynamic core-collapse supernova (CCSN) simulations in spherical symmetry. For a Newtonian model, we find good agreement with the M1 code ALCAR, and for a GR model, we reproduce the main effects of GR in CCSNe already found by previous works.