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Radiation hydrodynamical transport of ionization fronts in the nextgeneration of cosmological reionization simulations holds the promise ofpredicting UV escape fractions from first principles as well as investigatingthe role of photoionization in feedback processes and structure formation. Wepresent a multistep integration scheme for radiative transfer and hydrodynamicsfor accurate propagation of I-fronts and ionized flows from a point source incosmological simulations. The algorithm is a photon-conserving method whichcorrectly tracks the position of I-fronts at much lower resolutions thannon-conservative techniques. The method applies direct hierarchical updates tothe ionic species, bypassing the need for the costly matrix solutions requiredby implicit methods while retaining sufficient accuracy to capture the trueevolution of the fronts. We review the physics of ionization fronts inpower-law density gradients, whose analytical solutions provide excellentvalidation tests for radiation coupling schemes. The advantages and potentialdrawbacks of direct and implicit schemes are also considered, with particularfocus on problem timestepping which if not properly implemented can lead tomorphologically plausible I-front behavior that nonetheless departs fromtheory. We also examine the effect of radiation pressure from very luminouscentral sources on the evolution of I-fronts and flows.

A Multistep Algorithm for the Radiation Hydrodynamical Transport of Cosmological Ionization Fronts and Ionized Flows