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arXiv · 2011.01543

Asymptotic $P_N$ Approximation in Radiative Transfer Problems

Re'em Harel·Stanislav Burov·Shay I. Heizler
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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.

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Re'em Harel, Stanislav Burov, Shay I. Heizler. 2020-11-03. Asymptotic $P_N$ Approximation in Radiative Transfer Problems. https://doi.org/10.1080/23324309.2020.1845738

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