  Coupled radiative-hydrodynamics simulations of the epoch of reionization aim
to reproduce the propagation of ionization fronts during the transition before
the overlap of HII regions. Many of these simulations use moment-based methods
to track radiative transfer processes using explicit solvers and are therefore
subject to strict stability conditions regarding the speed of light, which
implies a great computational cost. It can be reduced by assuming a reduced
speed of light, and this approximation is now widely used to produce
large-scale simulations of reionization. We introduce a new method for
estimating and comparing the ionization front speeds based on maps of the
reionization redshifts. We applied it to a set of cosmological simulations of
the reionization using a set of reduced speeds of light, and measured the
evolution of the ionization front speeds during the reionization process. We
find that ionization fronts progress via a two-stage process, the first stage
at low velocity as the fronts emerge from high density regions and a second
later stage just before the overlap, during which front speeds increase close
to the speed of light. Using a set of small 8Mpc/h^3 simulations, we find that
a minimal velocity of 0.3c is able to model these two stages in this specific
context without significant impact. Values as low as 0.05c can model the first
low velocity stage, but limit the acceleration at later times. Lower values
modify the distribution of front speeds at all times. Using larger 64Mpc/h^3
volumes that better account for distant sources, we find that reduced speed of
light has a greater impact on reionization times and front speeds in underdense
regions that are reionized at late times. The same quantities measured in dense
regions with slow fronts are less sensitive to c values.
