  We present numerical hydrodynamical models of the collision between the
galaxies IC 2163 and NGC 2207. These models extend the results of earlier work
where the galaxy discs were modeled one at a time. We confirm the general
result that the collision is primarily planar, that is, at moderate inclination
relative to the two discs, and prograde for IC 2163, but retrograde for NGC
2207. We list 34 specific morphological or kinematic features on a variety of
scales, found with multi-waveband observations, which we use to constrain the
models. The models are able to reproduce most of these features, with a
relative orbit in which the companion (IC 2163) disc first side-swipes the
primary (NGC 2207) disc on the west side, then moves around the edge of the
primary disc to the north and to its current position on the east side. The
models also provide evidence that the dark matter halo of NGC 2207 has only
moderate extent. For IC 2163, the prolonged prograde disturbance in the model
produces a tidal tail, and an oval or ocular waveform very much like the
observed ones, including some fine structure. The retrograde disturbance in the
model produces no strong waveforms within the primary galaxy. This suggests
that the prominent spiral waves in NGC 2207 were present before the collision,
and models with waves imposed in the initial conditions confirm that they would
not be disrupted by the collision. With an initial central hole in the gas disc
of the primary, and imposed spirals, the model also reproduces the broad ring
seen in HI observations. We believe that this is now one of the best modeled
systems of colliding galaxies. (Abridged)
