Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model

Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function...

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Bibliographic Details
Published in:Journal of computational and theoretical transport 2021-11, Vol.50 (6-7), p.583-597
Main Author: McClarren, Ryan G.
Format: Article
Language:English
Subjects:
benchmark solutions
Diffusion
Exact solutions
Fourier transforms
Mathematical models
multigroup model
Numerical integration
radiative transfe
Radiative transfer
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Summary:Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.
ISSN:2332-4309
2332-4325
DOI:10.1080/23324309.2022.2032757