  The two-moment method is widely used to approximate the full neutrino
transport equation in core-collapse supernova (CCSN) simulations, and different
closures lead to subtle differences in the simulation results. In this paper,
we compare the effects of closure choices on various physical quantities in 1D
and 2D time-dependent CCSN simulations with our multi-group radiation
hydrodynamics code Fornax. We find that choices of the 3rd-order closure
relations influence the time-dependent simulations only slightly. Choices of
the 2nd-order closure relation have larger consequences than choices of the
3rd-order closure do, but these are still small compared to the remaining
variations due to ambiguities in some physical inputs such as the nuclear
equation of state. We also find that deviations in Eddington factors are not
monotonically related to deviations in physical quantities, which means that
simply comparing the Eddington factors does not inform one concerning which
closure is better.
