  Density inhomogeneity in the intergalactic medium (IGM) can boost the
recombination rate of ionized gas substantially, affecting the growth of HII
regions during reionization. Previous attempts to quantify this effect
typically failed to resolve down to the Jeans scale in the pre-ionization IGM,
which is important in establishing this effect, along with the hydrodynamical
back-reaction of reionization on it. Towards that end, we perform a set of
fully-coupled, radiation-hydrodynamics simulations from cosmological initial
conditions, extending the mass resolution of previous work to the scale of
minihalos. Pre-reionization structure is evolved until a redshift $z_i$ at
which the ionizing radiation from external sources arrives to sweep an R-type
ionization front supersonically across the volume in a few Myr, until it is
trapped on the surfaces of minihalos and converted to D-type, after which the
minihalo gas is removed by photoevaporative winds. Small-scale density
structures during this time lead to a high ($>$10) clumping factor for ionized
gas, which hugely boosts the recombination rate until the structures are
disrupted by the hydrodynamic feedback after $\sim 10-100~\rm{Myr}$. For
incoming stellar radiation with intensity $J_{21}$ in a $200~h^{-1}~\rm{kpc}$
box with the mean density contrast $\bar\delta$, the number of extra
recombinations per H atom, on top of what is expected from homogeneously
distributed gas, is given by
$0.32[J_{21}]^{0.12}[(1+z_i)/11]^{-1.7}[1+\bar\delta]^{2.5}$. In models in
which most of the volume is ionized toward the end of reionization, this can
add more than one recombination per H atom to the ionizing photon budget to
achieve reionization.
