Self-Similar Radiation-Hydrodynamics Solutions in the Equilibrium Diffusion Limit

This work presents semi-analytical solutions to a radiation-hydrodynamics problems of a radiation source driving an initially cold medium. Our solutions are in the equilibrium diffusion limit, include material motion and allow for radiation-dominated situations where the radiation energy is comparable to (or greater than) the material internal energy density. As such, this work is a generalization of the classical Marshak wave problem that assumes no material motion and that the radiation energy is negligible. Including radiation energy density in the model serves to slow down the wave propagation. The solutions provide insight into the impact of radiation energy and material motion, as well as present a novel verification test for radiation transport packages. As a verification test, the solution exercises the radiation-matter coupling terms and their v/c treatment without needing a hydrodynamics solve. An example comparison between the self-similar solution and a numerical code is given. Tables of the self-similar solutions are also provided