  The final stages of cosmic reionisation (EndEoR) are expected to be strongly
regulated by the residual neutral hydrogen in the already ionised regions of
the Universe. Its presence limits the mean distance that ionising photons can
travel and hence, the extent of the regions that sources of ionising photons
can affect. The structures containing most of this residual neutral hydrogen
are typically unresolved in large-scale simulations of reionisation. Here, we
investigate and compare a range of approaches for including the effect of these
small-scale absorbers, also known as Lyman limit systems (LLS), in such
simulations. We evaluate the impact of these different approaches on the
reionisation history, the evolution of the ultraviolet background, and its
fluctuations. We also compare to observational results on the distribution of
Lyman-$\alpha$ opacity towards the EndEoR and the measured mean free path of
ionising photons. We further consider their effect on the 21-cm power spectrum.
We find that although each of the different approaches can match some of the
observed probes of the final stages of reionisation, only the use of a
redshift-dependent and position-dependent LLS model is able to reproduce all of
them. We therefore recommend that large-scale reionisation simulations, which
aim to describe both the state of the ionised and neutral intergalactic medium
use such an approach, although the other, simpler approaches are applicable
depending on the science goal of the simulation.
