Asymptotic $P_N$ Approximation in Radiative Transfer Problems

TL;DR

This paper evaluates the accuracy of the time-dependent asymptotic $P_N$ approximation in radiative transfer, demonstrating its effectiveness through benchmark testing and addressing closure equation challenges.

Contribution

It introduces a refined asymptotic $P_N$ approximation for radiative transfer, including closure adjustments for cases with particle emission rates exceeding one.

Findings

Excellent agreement with benchmark results

Accurate prediction of radiative heat-wave fronts

Effective handling of closure equations in complex scenarios

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