  We present a new radiative transfer method (SPH-M1RT) that is coupled
dynamically with smoothed particle hydrodynamics (SPH). We implement it in the
(tasked-based parallel) SWIFT galaxy simulation code but it can be
straightforwardly implemented to other SPH codes. Our moment-based method
simultaneously solves the radiation energy and flux equations in SPH, making it
adaptive in space and time. We modify the M1 closure relation to stabilize
radiation fronts in the optically thin limit which performs well even in the
case of head-on beam collisions. We also introduce anisotropic artificial
viscosity and high-order artificial diffusion schemes, which allow the code to
handle radiation transport accurately in both the optically thin and optically
thick regimes. Non-equilibrium thermochemistry is solved using a semi-implicit
subcycling technique. The computational cost of our method is independent of
the number of sources and can be lowered using the reduced speed of light
approximation. We demonstrate the robustness of our method by applying it to a
set of standard tests from the cosmological radiative transfer comparison
project of Iliev et al. The SPH-M1RT scheme is well-suited for modelling
situations in which numerous sources emit ionising radiation, such as
cosmological simulations of galaxy formation or simulations of the interstellar
medium.
