Numerical analysis
A Fast and Accurate Numerical Method for Radiative Transfer in the Atmosphere
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1179-1189.

To solve the radiative transfer equations for the atmosphere, we turn to an equivalent integral equation which has no numerically singular terms. An iterative scheme is proposed for its solution and convergence is proved.

The side effect of this proof is an existence result for the radiative transfer equations, in one spatial variable, with frequency dependent absorption and scattering coefficients.

A numerical study is given with some comments on the effect of greenhouse gases on the temperature in the atmosphere.

Pour résoudre les équations du transfert radiatif pour l’atmosphère nous nous tournons vers une formulation intégrale équivalente qui a l’avantage de ne pas contenir de fonction singulière. Une méthode itérative est proposée pour sa résolution et un résultat de convergence est donné.

En corollaire un résultat d’existence et d’unicité est prouvé pour les équations du transfert radiatif, 1D en espace, sous des hypothèses assez générales sur les coefficients d’absorption et de scattering et leurs dépendances en fréquence.

Une étude numérique termine cette étude ainsi que quelques commentaires sur l’effet des gaz à effet de serre sur la temperature de l’atmosphère.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.239
Classification: 00X99, 85AXX, 65M12
Pironneau, Olivier 1

1 LJLL, Boite 187, Sorbonne Université, 75005 Paris, France.
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Pironneau, Olivier. A Fast and Accurate Numerical Method for Radiative Transfer in the Atmosphere. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1179-1189. doi : 10.5802/crmath.239. http://www.numdam.org/articles/10.5802/crmath.239/

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