  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.
