none6si©: 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.We introduce arepo-rt, a novel radiation hydrodynamic (RHD) solver for the unstructured moving-mesh code arepo. Our method solves the moment-based radiative transfer equations using the M1 closure relation. We achieve second-order convergence by using a slope-limited linear spatial extrapolation and a first-order time prediction step to obtain the values of the primitive variables on both sides of the cell interface. A Harten–Lax–van Leer flux function, suitably modified for moving meshes, is then used to solve the Riemann problem at the interface. The implementation is fully conservative and compatible with the...