Smoothed particle hydrodynamics with radiative transfer in the   flux-limited diffusion approximation
  We describe the implementation and testing of a smoothed particle hydrodynamics (SPH) code that solves the equations of radiation hydrodynamics in the flux-limited diffusion (FLD) approximation. The SPH equations of radiation hydrodynamics for an explicit integration scheme are derived and tested. We also discuss the implementation of an implicit numerical scheme for solving the radiation equations that allows the system to be evolved using timesteps much longer than the explicit radiation timestep. The code is tested on a variety of one-dimensional radiation hydrodynamics problems including radiation propagating in an optically thin medium, optically thick and thin shocks, subcritical and supercritical radiating shocks, and a radiation dominated shock. Many of the tests were also performed by Turner and Stone (2001) to test their implementation of a FLD module for the ZEUS-2D code. The SPH code performs at least as well as the ZEUS-2D code in these tests. 
Stuart C. Whitehouse and Matthew R. Bate