Comptes Rendus
An approximate solution to the integral radiative transfer equation in an optically thick slab
[Solution approchée de l'équation de transfert intégrale dans une couche optiquement épaisse]
Comptes Rendus. Mécanique, Volume 331 (2003) no. 12, pp. 823-828.

On s'intéresse à la résolution de la forme intégrale de l'équation de transfert dans une atmosphère d'épaisseur optique τ0⪢1. Nous proposons une méthode ramenant ce problème au même problème posé dans une atmosphère d'épaisseur optique τ1τ0. Une majoration de l'erreur est donnée.

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ0⪢1. We propose a method transforming this problem in the same problem posed in an atmosphere with optical thickness τ1τ0. An error over- estimation is derived.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2003.09.007
Keywords: Waves, Radiative transfer equation, Optical thickness
Mot clés : Ondes, Équation de transfert, Épaisseur optique
Andrey Amosov 1 ; Grigori Panasenko 2 ; Bernard Rutily 3

1 Department of Mathematical Modelling, Moscow Power Engineering Institute, Krasnokazarmennaja 14, 111250 Moscow, Russia
2 Équipe d'analyse numérique, Université Jean Monnet, 23, rue P. Michelon, 42023 Saint-Etienne, France
3 Observatoire de Lyon 9, avenue Charles André, 69561 Saint-Genis-Laval cedex, France
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     title = {An approximate solution to the integral radiative transfer equation in an optically thick slab},
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Andrey Amosov; Grigori Panasenko; Bernard Rutily. An approximate solution to the integral radiative transfer equation in an optically thick slab. Comptes Rendus. Mécanique, Volume 331 (2003) no. 12, pp. 823-828. doi : 10.1016/j.crme.2003.09.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.09.007/

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[2] I.W. Busbridge The Mathematics of Radiative Transfer, University Press, Cambridge, 1960

[3] V. Kourganoff Basic Methods in Transfer Problems, Dover, New York, 1963

[4] V.V. Sobolev A Treatise on Radiative Transfer, Van Nostrand, Pricenton, NJ, 1963

[5] K.M. Case; P.F. Zweifel Linear Transport Theory, Addison-Wesley, Reading, MA, 1967

[6] K.M. Case; E. de Hoffman; G.P. Plachek Introduction to the Theory of Neutron Diffusion, Los Alamos Scientific Laboratory, US Goverment Printing Office, Washington, DC, 1953

[7] V.V. Ivanov Radiative Transfer and Spectra of Celestial Bodies, Transfer of Radiation in Spectral Lines, 385, Nauka, Moscow, 1969 (Traduction révisée, National Bureau of Standards Special Publication, 1973, US Government Printing Office, Washington, DC)

[8] G.P. Panasenko; B. Rutily; O. Titaud Asymptotic analysis of integral equations for great interval and its application to stellar radiative transfer, C. R. Mecanique, Volume 330 (2002), pp. 735-740

[9] A.A. Amosov; G.P. Panasenko; B. Rutily An approximate solution to the integral radiative transfer equation in an optically thick slab, 7th International Conference on Integral Methods in Science and Engineering, Saint-Etienne, France, 2002, pp. 12-13

[10] M.A. Heaslet; E.E. Warming Radiative source-function predictions for finite and semi-infinite non-conservative atmospheres, Astrophys. Space Sci., Volume 1 (1968), pp. 460-490

[11] T. Viik On an exact solution of the Ambartsumian equation, Tartu Astr. Obs. Publ., Volume 44 (1976), pp. 47-57

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