# NADA-FLD: A General Relativistic, Multi-dimensional Neutrino-hydrodynamics Code Employing Flux-limited Diffusion

## TL;DR

The paper introduces NADA-FLD, a new multi-dimensional neutrino-hydrodynamics code in general relativity using flux-limited diffusion, tested on supernova models and showing good agreement with existing codes.

## Contribution

NADA-FLD is a novel code that combines GR, multi-dimensional neutrino transport, and flux-limited diffusion with explicit schemes for lateral diffusion and advection.

## Key findings

- Good agreement with ALCAR code in Newtonian models
- Reproduces main effects of GR in supernova simulations
- Demonstrates stability and accuracy in toy-model tests

## Abstract

We present the new code NADA-FLD to solve multi-dimensional neutrino-hydrodynamics in full general relativity (GR) in spherical polar coordinates. The energy-dependent neutrino transport assumes the flux-limited diffusion (FLD) approximation and evolves the neutrino energy densities measured in the frame comoving with the fluid. Operator splitting is used to avoid multi-dimensional 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.