We present a new implementation of radiation hydrodynamics (RHD) in the adaptive mesh refinement (AMR) code RAMSES. The multi-group radiative transfer (RT) is performed on the AMR grid with a first-order Godunov method using the M1 closure for the Eddington tensor, and is coupled to the hydrodynamics via non-equilibrium thermochemistry of hydrogen and helium. This moment-based approach has the large advantage that the computational cost is independent of the number of radiative sources -it can even deal with continuous regions of emission such as bound-free emission from gas. As it is built directly into RAMSES, the RT takes natural advantage of the refinement and parallelization strategies already in place. Since we use an explicit advection solver for the radiative transport, the time step is restricted by the speed of light -a severe limitation that can be alleviated using the so-called "reduced speed of light" approximation. We propose a rigorous framework to assess the validity of this approximation in various conditions encountered in cosmology and galaxy formation. We finally perform with our newly developed code a complete suite of RHD tests, comparing our results to other RHD codes. The tests demonstrate that our code performs very well and is ideally suited for exploring the effect of radiation on current scenarios of structure and galaxy formation.It is highly desirable to follow self-consistently, with RHD simulations, the time-evolution and morphology of large-scale intergalactic medium (IGM) reionization and at the same time the smaller scale formation of the presumed sources of reionization; how galaxy formation is regulated by the ionizing radiation being released, how much of the radiation escapes from the galaxies to ionize the IGM, how first generation stars are formed in a metal-free environment and how radiative and supernovae feedback from those stars affect the inter-galactic medium. The galaxies and the IGM are indeed inter-connected via the ionizing radiation: the photons released from the galaxies affect the state of the surrounding gas via ionization and heating and may even prevent it from falling in or condensing into external gravitational potentials, especially small ones (e.g. Wise & Abel 2008; Ocvirk & Aubert 2011), which can then in turn significantly alter the ionization history. c 0000 RAS arXiv:1304.7126v2 [astro-ph.CO]
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