  We describe and test an updated version of radiation-hydrodynamics (RHD) in
the RAMSES code, that includes three new features: i) radiation pressure on
gas, ii) accurate treatment of radiation diffusion in an unresolved optically
thick medium, and iii) relativistic corrections that account for Doppler
effects and work done by the radiation to first order in v/c. We validate the
implementation in a series of tests, which include a morphological assessment
of the M1 closure for the Eddington tensor in an astronomically relevant
setting, dust absorption in a optically semi-thick medium, direct pressure on
gas from ionising radiation, convergence of our radiation diffusion scheme
towards resolved optical depths, correct diffusion of a radiation flash and a
constant luminosity radiation, and finally, an experiment from Davis et al. of
the competition between gravity and radiation pressure in a dusty atmosphere,
and the formation of radiative Rayleigh-Taylor instabilities. With the new
features, RAMSES-RT can be used for state-of-the-art simulations of radiation
feedback from first principles, on galactic and cosmological scales, including
not only direct radiation pressure from ionising photons, but also indirect
pressure via dust from multi-scattered IR photons reprocessed from
higher-energy radiation, both in the optically thin and thick limits.
