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arXiv · 2208.06410

Radiative Transfer For Variable 3D Atmospheres

Francois Golse·Frederic Hecht·Olivier Pironneau·Pierre-Henri Tournier·Didier Smets
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Abstract

To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is a very fast: 50K physical points, all directions of radiation and 680 frequencies require less than 5 minutes on an Apple M1 Laptop. The method is capable of handling variable absorptioN and scattering functionS of spatial positions and frequencies. The implementation is done using htool, a matrix compression library interfaced with the PDE solver freefem++. Applications to the temperature in the French Chamonix valley is presented at different hours of the day with and without snow / clouds and with a variable absorption taken from the Gemini measurements. The result is precise enough to assert temperature differences due to increased absorption in the vibrational frequency subrange of greenhouse gasses.

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Francois Golse, Frederic Hecht, Olivier Pironneau, Pierre-Henri Tournier, Didier Smets. 2022-08-11. Radiative Transfer For Variable 3D Atmospheres. https://doi.org/10.1016/j.jcp.2022.111864

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