We study the process of a galaxy moving through the intracluster gas in a cluster of galaxies, using two-dimensional hydrodynamic simulations at high resolution. We find that ram pressure stripping occurs in the form of individual events which are separated by a few times 10(7) yr. In addition, we find that the galaxy accretes gas from the downstream side into the core. This accretion process exhibits a radial ''pumping'' mode, similar to the one found previously in simulations of wind accretion onto compact objects. The flow is found to exhibit a complex shock structure around the core. Some implications of our results for the understanding of a few recent observations are discussed.