  We have chosen a reduced set of 18 ionization rate equations (for ions of H,
C, N, O, S and Ne), which allow us to obtain a moderately accurate estimate of
the non-equilibrium radiative cooling function. We evaluate the accuracy of
this approach by comparing our cooling function with previous calculations,
computed with a more extended set of ions, for the case of gas that cools from
a high temperature at constant density. We also compute steady, plane shock
models, which we find to compare well with models calculated with much more
detailed microphysics. Using our reduced set of rate equations, we present a
simulation of a radiative bow shock formed by a supersonic, plane stream
impinging on a rigid sphere. The parameters for the calculation are chosen as
to approximately represent typical values found for Herbig-Haro objects, and to
give a cooling distance to bow shock radius ratio of 1/10. This simulation is
done with an adaptive grid code, which allows a reasonably high resolution
(with greater than or equal to 25 points) of the standoff distance between the
bow shock and the rigid obstacle. Contrary to the standard expectation, we find
that the bow shock standoff distance in the stagnation region is considerably
shorter than the cooling distance behind a plane-parallel shock. Also, the
centrifugal pressure is found to play an important role in determining the
structure of the recombin- ation region. This appears to partially invalidate
previous bow shock models based on a ``quasi-1D'' approach, at least for the
particular parameters chosen for the present simulation. Finally, we present
tabulations of the cooling rates that have been used (for the different
species), in order to facilitate the inclusion of this treatment in other
gasdynamic codes.
