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We present a set of new numerical methods that are relevant to calculatingradiation pressure terms in hydrodynamics calculations, with a particular focuson massive star formation. The radiation force is determined from a Monte Carloestimator and enables a complete treatment of the detailed microphysics,including polychromatic radiation and anisotropic scattering, in both thefree-streaming and optically-thick limits. Since the new method iscomputationally demanding we have developed two new methods that speed up thealgorithm. The first is a photon packet splitting algorithm that enablesefficient treatment of the Monte Carlo process in very optically thick regions.The second is a parallelisation method that distributes the Monte Carloworkload over many instances of the hydrodynamic domain, resulting in excellentscaling of the radiation step. We also describe the implementation of a sinkparticle method that enables us to follow the accretion onto, and the growthof, the protostars. We detail the results of extensive testing and benchmarkingof the new algorithms.

Radiation-hydrodynamical simulations of massive star formation using Monte Carlo radiative transfer: I. Algorithms and numerical methods