  We present results from a series of cosmological SPH (smoothed particle
hydrodynamics) simulations coupled with the P3M
(Particle-Particle-Particle-Mesh) solver for the gravitational force. The
simulations are designed to predict the statistical properties of X-ray
clusters of galaxies as well as to study the formation of galaxies. We have
seven simulation runs with different assumptions on the thermal state of the
intracluster gas. Following the recent work by Pearce et al., we modify our SPH
algorithm so as to phenomenologically incorporate the galaxy formation by
decoupling the cooled gas particles from the hot gas particles. All the
simulations employ 128^3 particles both for dark matter and for gas components,
and thus constitute the largest systematic catalogues of simulated clusters in
the SPH method performed so far. These enable us to compare the analytical
predictions on statistical properties of X-ray clusters against our direct
simulation results in an unbiased manner. We find that the luminosities of the
simulated clusters are quite sensitive to the thermal history and also to the
numerical resolution of the simulations, and thus are not reliable. On the
other hand, the mass-temperature relation for the simulated clusters is fairly
insensitive to the assumptions of the thermal state of the intracluster gas,
robust against the numerical resolution, and in fact agrees well with the
analytic prediction. Therefore the prediction for the X-ray temperature
function of clusters on the basis of the Press-Schechter mass function and the
virial equilibrium is fairly reliable.
