  Results from hydrodynamical SPH simulations of galaxy clusters are used to
investigate the dependence of the final cluster X-ray properties on the
numerical resolution and the assumed models for the physical gas processes. Two
different spatially flat cosmological models have been considered: a
low-density cold dark matter universe with a vacuum energy density Omega_L=0.7
(LCDM) and a cold+hot dark matter model (CHDM). These simulations first include
radiative cooling and then also conversion of cold gas particles into stars.
When cold gas particles are allowed to convert into stars the final gas
profiles show a well defined core radius and the temperature profiles are
nearly flat. For the most massive test cluster in the LCDM model, these
simulations show a prominent cooling flow in the cluster core. This cluster was
analyzed in detail, running simulations with different star formation methods
and increasing numerical resolution. A comparison between different runs shows
that the results of simulations, based on star formation methods in which gas
conversion into stars is controlled by an efficiency parameter c_star, are
sensitive to the numerical resolution of the simulation. In this respect star
formation methods based instead on a local density threshold, as in Navarro and
White (1993), are shown to give more stable results. Final X-ray luminosities
are found to be numerically stable, with uncertainties of a factor two.
