The Petschek model of magnetic field line reconnection is generalized for magnetopause-like conditions to enable a comparison of data and theory. The two-dimensional, compressible MHD model considered reveals four discontinuities which are necessary to match the different magnetic fields and plasma parameters inside and outside the magnetopause. The magnetosheath plasma is accelerated and deflected by a large-amplitude Alfv¿n (rotational) wave and either a slow shock or a slow rarefaction wave (slow expansion fan). Another slow shock focuses the plasma flow from the magnetospheric side. A contact discontinuity inside the boundary layer separates the plasma flows from magnetosheath and magnetosphere. Using realistic magnetopause parameters, the results are illustrated by numerical examples and discussed in connection with geophysical observations.