A fast and accurate method of radiation hydrodynamics calculation in spherical symmetry

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower, but more generally applicable method to describe realistic problems. We perform various test calculations including a simplified protostellar collapse simulation. We also discuss possible future improvements.