A Multistep Algorithm for the Radiation Hydrodynamical Transport of   Cosmological Ionization Fronts and Ionized Flows
  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. 
Daniel J. Whalen, Michael L. Norman