ABSTRACT
The full frequency-dependent radiative transfer problem in more than one space dimension has to be solved as a function of up to six variables plus the time. It is not even close to being feasible to solve the complete problem in full generality numerically. Nevertheless, there are numerous astrophysical problems that require solving the equations of hydrodynamics coupled with the equation of radiation transfer. The equations of radiation hydrodynamics are given in Section 9.4. A commonly used technique is to average over frequency and to solve the equations in the flux-limited diffusion approximation (Section 1.6.4). In Section 9.4, this method is discussed for the particular case of hydrodynamics in two space dimensions. The same method is easily extended to three dimensions. Even though the time-dependent solution of these equations does not give information as a function of frequency, it is possible to get approximate emergent spectra at particular times in the evolution, by means of the technique of Section 9.1. This procedure is discussed in Section 9.5. The final section gives an example of a full three-dimensional calculation of hydrodynamics plus radiation transport, and how the results can be compared with observations.
