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We have developed a two-level hierarchical three-dimensional numerical code designed to simulate the formation of large scale structure in an expanding universe with Newtonian gravity and radiative cooling. The basis of this code is a standard particle-mesh algorithm used to evolve the dark matter and ZEUS-3D, an ideal nonrelativistic MHD fluid solver, to evolve the baryonic matter self-consistently with the evolving dark matter potential. We apply this code to resolve X-ray clusters in a cold dark matter universe. The evolving structure within the larger periodically identified box provides an adequate sampling of long wavelength perturbations to model tidal effects on matter falling into the cluster. A smaller more refined grid is constructed within the larger cube centered on a single rich cluster, increasing the dynamical range in length and mass scales and allowing us to resolve the cluster core. We performed a sequence of runs at consistently higher spatial grid resolutions and grid refinement factors to test the convergence of various physical parameters used to characterize such clusters, including the integrated X-ray luminosity and $\beta$-model fits.
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