Simulations of X-ray clusters were conducted to study the formation and evolution of galaxy clusters in the Cold Dark Matter cosmogony. Clusters of various masses were selected from previous N-body models and resimulated at higher resolution using a combined N-body/Smooth Particle Hydrodynamics code. The effects of radiative cooling on the gas were neglected. The density profiles of clusters in equilibrium are similar for both gas and dark matter, showing no sign of a uniform density core and steepening gradually from the center outward. The standard β-model is a reasonable fit for most observable radii, but the slope parameter β_f increases with the outermost radius of the fit. Temperature profiles of different simulated clusters are similar, with temperature being almost uniform in regions emitting most X-ray flux but dropping at larger radii. The gas temperature and dark matter velocity dispersion in equilibrium clusters give values of β_T consistent with unity when using X-ray emission-weighted temperature. Larger values of β_T are found in merging objects where there is a transient boost in velocity dispersion. Thus, β_T > 1 may indicate merging in real clusters. The similar structure of clusters of differing mass results in scaling relations between X-ray and dynamical properties of clusters at any given redshift. These scalings are inconsistent with the observed slope of the luminosity-temperature relation or the observed sense of evolution of the cluster luminosity function. This suggests that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or substantial pre-heating at high redshift. The paper presents new N-body/hydrodynamic simulations to explore the simple nonradiative model, including the case where the gas is initially preheated. The simulations are similar to but have better spatial resolution than those presented by Evrard and Thomas and Couchman. The results show that the density profiles of clusters are well fit by the β-model, but the values of β_f depend on the range of radii used for the fit. The temperature profiles of the simulated clusters are similar to those of real clusters, with a near-isothermal region extending to r ~ 0.5r_200 and a gradual decline to about half the central value near r_200. The X-ray luminosity of the simulated clusters is consistent with the theoretical scaling relation, but the observed L_X-T relation is steeper than predicted. The "β-discrepancy" refers to a discrepancy when fitting cluster data to the β-model, which assumes spherical symmetry, hydrostatic equilibrium, and isotropic isothermal gas profiles. The simulations show that the product β_fT is the same for both gas and dark matter, and that the observed β_T values are consistent with the simulations. The results suggest that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or pre-heating at high redshift.Simulations of X-ray clusters were conducted to study the formation and evolution of galaxy clusters in the Cold Dark Matter cosmogony. Clusters of various masses were selected from previous N-body models and resimulated at higher resolution using a combined N-body/Smooth Particle Hydrodynamics code. The effects of radiative cooling on the gas were neglected. The density profiles of clusters in equilibrium are similar for both gas and dark matter, showing no sign of a uniform density core and steepening gradually from the center outward. The standard β-model is a reasonable fit for most observable radii, but the slope parameter β_f increases with the outermost radius of the fit. Temperature profiles of different simulated clusters are similar, with temperature being almost uniform in regions emitting most X-ray flux but dropping at larger radii. The gas temperature and dark matter velocity dispersion in equilibrium clusters give values of β_T consistent with unity when using X-ray emission-weighted temperature. Larger values of β_T are found in merging objects where there is a transient boost in velocity dispersion. Thus, β_T > 1 may indicate merging in real clusters. The similar structure of clusters of differing mass results in scaling relations between X-ray and dynamical properties of clusters at any given redshift. These scalings are inconsistent with the observed slope of the luminosity-temperature relation or the observed sense of evolution of the cluster luminosity function. This suggests that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or substantial pre-heating at high redshift. The paper presents new N-body/hydrodynamic simulations to explore the simple nonradiative model, including the case where the gas is initially preheated. The simulations are similar to but have better spatial resolution than those presented by Evrard and Thomas and Couchman. The results show that the density profiles of clusters are well fit by the β-model, but the values of β_f depend on the range of radii used for the fit. The temperature profiles of the simulated clusters are similar to those of real clusters, with a near-isothermal region extending to r ~ 0.5r_200 and a gradual decline to about half the central value near r_200. The X-ray luminosity of the simulated clusters is consistent with the theoretical scaling relation, but the observed L_X-T relation is steeper than predicted. The "β-discrepancy" refers to a discrepancy when fitting cluster data to the β-model, which assumes spherical symmetry, hydrostatic equilibrium, and isotropic isothermal gas profiles. The simulations show that the product β_fT is the same for both gas and dark matter, and that the observed β_T values are consistent with the simulations. The results suggest that the central properties of the intracluster medium are determined by non-gravitational processes such as radiative cooling or pre-heating at high redshift.