Asymptotic P_N Approximation in Radiative Transfer Problems

Abstract

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 (${\omega }_{\text{eff}}$) 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.

Keywords:

• Radiative transfer
• asymptotic P₁ approximation
• Su–Olson benchmark

Additional information

Funding

We acknowledge the support of the PAZY Foundation under Grant No. 61139927.