  In recent years a number of authors have introduced methods to model the
effects of radiation pressure feedback on flows of interstellar and
intergalactic gas, and have posited that the forces exerted by stars' radiation
output represents an important feedback mechanism capable of halting accretion
and thereby regulating star formation. However, numerical simulations have
reached widely varying conclusions about the effectiveness of this feedback. In
this paper I show that much of the divergence in the literature is a result of
failure to obey an important resolution criterion: whether radiation feedback
is able to reverse an accretion flow is determined on scales comparable to the
dust destruction radius, which is $\lesssim 1000$ AU even for the most luminous
stellar sources. Simulations that fail to resolve this scale can produce
unphysical results, in many cases leading to a dramatic overestimate of the
effectiveness of radiation feedback. Most published simulations of radiation
feedback on molecular cloud and galactic scales fail to satisfy this condition.
I show how the problem can be circumvented by introducing a new subgrid model
that explicitly accounts for momentum balance on unresolved scales, making it
possible to simulate dusty accretion flows safely even at low resolution.
