(Abridged) We perform high resolution 2D hydrodynamical simulations of face-on ram pressure stripping (RPS) of disk galaxies to compile a comprehensive parameter study varying galaxy properties (mass, vertical structure of the gas disk) and covering a large range of ICM conditions, reaching from high density environments like in cluster centres to low density environments typical for cluster outskirts or groups. We find that the ICM-ISM interaction proceeds in three phases: firstly the instantaneous stripping phase, secondly the dynamic intermediate phase, thirdly the quasi-stable continuous viscous stripping phase. The stripping efficiency depends slightly on the Mach number of the flow, however, the main parameter is the ram pressure. The stripping efficiency does not depend on the vertical structure and thickness of the gas disk. We discuss uncertainties in the classic estimate of the stripping radius of citet{gunn72}, and adapt the estimate used by cite{mori00} for spherical galaxies, (comparison of central pressure with ram pressure). We find that the latter estimate predicts the radius and mass of the gas disk remaining at the end of the second phase very well, and better than the citet{gunn72} criterion. From our simulations we conclude that gas disks of galaxies in high density environments are heavily truncated or even completely stripped, but also the gas disks of galaxies in low density environments are disturbed by the flow and back-falling material, so that they should also be pre-processed.
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