Photon Conserving Radiative Transfer around Point Sources in multi-dimensional Numerical Cosmology

Many questions in physical cosmology regarding the thermal and ionization history of the intergalactic medium are now successfully studied with the help of cosmological hydrodynamical simulations. Here we present a numerical method that solves the radiative transfer around point sources within a three dimensional cartesian grid. The method is energy conserving independently of resolution: this ensures the correct propagation speeds of ionization fronts. We describe the details of the algorithm, and compute as first numerical application the ionized region surrounding a mini-quasar in a cosmological density field at z=7.