  We introduce a new set of large scale, high resolution hydrodynamical
simulations of the intergalactic medium: the Sherwood simulation suite. These
are performed in volumes 10^3-160^3 h^-3 comoving Mpc^{3}, span almost four
orders of magnitude in mass resolution with up to 17.2 billion particles, and
employ a variety of physics variations including warm dark matter and galactic
outflows. We undertake a detailed comparison of the simulations to high
resolution, high signal-to-noise observations of the Lyman-alpha forest over
the redshift range 2 < z < 5. The simulations are in very good agreement with
the observational data, lending further support to the paradigm that the
Lyman-alpha forest is a natural consequence of the web-like distribution of
matter arising in LCDM cosmological models. Only a small number of minor
discrepancies remain with respect to the observational data. Saturated
Lyman-alpha absorption lines with column densities N_HI > 10^14.5 cm^-2 at 2 <
z < 2.5 are underpredicted in the models. An uncertain correction for continuum
placement bias is required to match the distribution and power spectrum of the
transmitted flux, particularly at z > 4. Finally, the temperature of
intergalactic gas in the simulations may be slightly too low at z=2.7 and a
flatter temperature-density relation is required at z=2.4, consistent with the
expected effects of non-equilibrium ionisation during He-II reionisation.
