  We present a model for the interaction between dust and radiation fields in
the radiation hydrodynamic code AREPO-RT, which solves the moment-based
radiative transfer equations on an unstructured moving mesh. Dust is directly
treated using live simulation particles, each of which represent a population
of grains that are coupled to hydrodynamic motion through a drag force. We
introduce methods to calculate radiation pressure on and photon absorption by
dust grains. By including a direct treatment of dust, we are able to calculate
dust opacities and update radiation fields self-consistently based on the local
dust distribution. This hybrid scheme coupling dust particles to an
unstructured mesh for radiation is validated using several test problems with
known analytic solutions, including dust driven via spherically-symmetric flux
from a constant luminosity source and photon absorption from radiation incident
on a thin layer of dust. Our methods are compatible with the multifrequency
scheme in AREPO-RT, which treats UV and optical photons as single-scattered and
IR photons as multi-scattered. At IR wavelengths, we model heating of and
thermal emission from dust. Dust and gas are not assumed to be in local
thermodynamic equilibrium but transfer energy through collisional exchange. We
estimate dust temperatures by balancing these dust-radiation and dust-gas
energy exchange rates. This framework for coupling dust and radiation can be
applied in future radiation hydrodynamic simulations of galaxy formation.
