  A variety of approximate schemes for modelling the low-density Intergalactic
Medium (IGM) in the high-redshift Universe is compared to the results of a
large high-resolution hydro-dynamical simulation. These schemes use either an
analytical description of the dark matter distribution and the IGM or numerical
simulations of the DM distributions combined with different approximate
relations between dark matter field and the gas distribution. Schemes based on
a filtering of the dark matter distribution with a global Jeans scale result in
a rather poor description of the gas distribution. An adaptive filtering which
takes into account the density/temperature dependence of the Jeans scale is
required. A reasonable description of the gas distribution can be achieved
using a fit of the mean relation between the dark matter and gas densities in
the hydro-dynamical simulation to relate dark matter and gas distribution. In
the hydro-dynamical simulations deviations from this mean relation are
correlated with gradients in the dark matter peculiar velocity field indicative
of shocks in the gas component. A scheme which takes into account this
correlation results in a further improved gas distribution. Such adaptive
filtering schemes applied to dark matter simulations will be very well suited
for studies of statistical properties of the Lyalpha forest which investigate
the IGM and the underlying dark matter distribution and require a large dynamic
range and/or an extensive parameter study.
