The Diffusion-Synthetic Acceleration of Transport Iterations, with Application to a Radiation Hydrodynamics Problem

TLDR: In this article, the authors describe new numerical methods for solving time-dependent radiative transfer problems in emitting media and discuss three aspects of the solution method: the time dependence, the intimate coupling between the radiation field and the medium, and the iteration acceleration of the equation of transfer.

Abstract: Publisher Summary Radiation hydrodynamics treats the interactions of thermal radiation with matter. Thermal radiation is taken to mean electromagnetic radiation of atomic origin, obtained from the processes of scattering, absorption, and thermal emission. The radiation field is described by an equation of transfer, which is a Boltzmann transport equation for photons. From a computational viewpoint, time-dependent radiative transfer problems in emitting media are difficult to solve. In general, their solution involves an equation with seven independent variables for the radiation field, along with the additional equations describing the mass, momentum, and energy balance of the underlying medium. This chapter describes new numerical methods for solving such problems. It also discusses three aspects of the solution method: the time dependence, the intimate coupling between the radiation field and the medium, and the iteration acceleration of the equation of transfer. The time dependence is treated implicitly, that is, the equation of transfer is written in terms of the dependent variables evaluated at the advanced time.