  Radiation hydrodynamical transport of ionization fronts in the next
generation of cosmological reionization simulations holds the promise of
predicting UV escape fractions from first principles as well as investigating
the role of photoionization in feedback processes and structure formation. We
present a multistep integration scheme for radiative transfer and hydrodynamics
for accurate propagation of I-fronts and ionized flows from a point source in
cosmological simulations. The algorithm is a photon-conserving method which
correctly tracks the position of I-fronts at much lower resolutions than
non-conservative techniques. The method applies direct hierarchical updates to
the ionic species, bypassing the need for the costly matrix solutions required
by implicit methods while retaining sufficient accuracy to capture the true
evolution of the fronts. We review the physics of ionization fronts in
power-law density gradients, whose analytical solutions provide excellent
validation tests for radiation coupling schemes. The advantages and potential
drawbacks of direct and implicit schemes are also considered, with particular
focus on problem timestepping which if not properly implemented can lead to
morphologically plausible I-front behavior that nonetheless departs from
theory. We also examine the effect of radiation pressure from very luminous
central sources on the evolution of I-fronts and flows.
