  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
($\omega_{\mathrm{eff}}$) 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.

Computational Physics;Statistical Mechanics;Plasma Physics