Asymptotic P_N Approximation in Radiative Transfer Problems

We study the validity of the time-dependent asymptotic P_N approximation in radiative transfer of photons. The time-dependent asymptotic P_N is an approximation which uses the standard P_N equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic P_N approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision ((Formula presented.)) can be larger than one due to inner or outer radiation sources and the coefficients of the closure must be extended for these cases. Our approximation is tested against a well-known radiative transfer benchmark. It yields excellent results, with almost correct particle velocity that controls the radiative heat-wave fronts.