Co-moving frame radiative transfer in spherical media with arbitrary   velocity fields
  Recently, with the advances in computational speed and availability there has been a growth in the number and resolution of fully 3-D hydrodynamical simulations. However, all of these simulations are purely hydrodynamical and there has been little attempt to include the effects of radiative transfer except in a purely phenomenological manner because the computational cost is too large even for modern supercomputers. While there has been an effort to develop 3-D Monte Carlo radiative transfer codes, most of these have been for static atmospheres or have employed the Sobolev approximation, which limits their applicability to studying purely geometric effects such as macroscopic mixing. Also the computational requirements of Monte Carlo methods are such that it is difficult to couple with 3-D hydrodynamics. Here, we present an algorithm for calculating 1-D spherical radiative transfer in the presence of non-monotonic velocity fields in the co-moving frame. Non-monotonic velocity flows will occur in convective, and Raleigh--Taylor unstable flows, in flows with multiple shocks, and in pulsationally unstable stars such as Mira and Cepheids. This is a first step to developing fully 3-D radiative transfer than can be coupled with hydrodynamics. We present the computational method and the results of some test calculations. 
E. Baron and Peter H. Hauschildt