  Modeling core-collapse supernovae (CCSNe) with neutrino transport in three
dimensions (3D) requires tremendous computing resources and some level of
approximation. We present a first comparison study of CCSNe in 3D with
different physics approximations and hydrodynamics codes. We aim to assess the
impact of the hydrodynamics code, approximations for the neutrino and gravity
treatments, and rotation on the simulation of CCSNe in 3D. We use four
different hydrodynamics codes in this work (ELEPHANT, FLASH, fGR1, and SPHYNX)
in combination with two different neutrino treatments, the isotropic diffusion
source approximation (IDSA) and two-moment M1, and three different gravity
treatments: Newtonian, 1D General Relativity (GR) correction, and full GR).
Additional parameters discussed in this study are the inclusion of
neutrino-electron scattering via a parametrized deleptonization (PD) and the
influence of rotation. The four codes compared in this work include Eulerian
and fully Lagrangian (smoothed particle hydrodynamics) codes for the first
time. They show agreement in the overall evolution of the collapse phase and
early post-bounce within the range of 10% (20% in some cases). The comparison
of the different neutrino treatments highlights the need to further investigate
the antineutrino luminosities in IDSA, which tend to be relatively high. We
also demonstrate the requirement for a more detailed heavy-lepton neutrino
leakage. When comparing with a full GR code, including an M1 transport method,
we confirm the influence of neutrino-electron scattering during the collapse
phase, which is adequately captured by the PD scheme. Also, the effective GR
potential reproduces the overall dynamic evolution correctly in all Newtonian
codes. Additionally, we verify that rotation aids the shock expansion and
estimate the overall angular momentum losses for each code in rotating
scenarios.
