  We present a method for including steady-state gas flows in the plasma
physics code Cloudy, which was previously restricted to modeling static
configurations. The numerical algorithms are described in detail, together with
an example application to plane-parallel ionization-bounded HII regions. As
well as providing the foundation for future applications to more complex flows,
we find the following specific results regarding the effect of advection upon
ionization fronts in HII regions:
  1. Significant direct effects of advection on the global emission properties
occur only when the ionization parameter is lower than is typical for HII
regions.
  2. The overheating of partially ionized gas in the front is not large, even
for supersonic (R-type) fronts.
  3. The most significant morphological signature of advective fronts is an
electron density spike that occurs at the ionization front. Observational
evidence for such a spike is found in images of the Orion bar.
  4. Plane-parallel, weak-D fronts are found to show at best a shallow
correlation between mean velocity and ionization potential for optical emission
lines even when the flow velocity closely approaches the ionized sound speed.
