We introduce CRASH-AMR, a new version of the cosmological radiative transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately ionization and temperature patterns in high-density regions. We have tested CRASH-AMR by simulating the evolution of an ionized region produced by a single source embedded in gas at constant density, as well as by a more realistic configuration of multiple

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... es in an inhomogeneous density field. While we find an excellent agreement with the previous version of CRASH when the adaptive mesh refinement (AMR) feature is disabled, showing that no numerical artefact has been introduced in CRASH-AMR, when additional refinement levels are used the code can simulate more accurately the physics of ionized gas in high-density regions. This result has been attained at no computational loss, as RT simulations on AMR grids with maximum resolution equivalent to that of a uniform Cartesian grid can be run with a gain of up to 60 per cent in computational time.