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The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann

Abstract

In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation which involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expanding in orthogonal polynomials the angular flux of neutrons leaking from the medium and making no assumption about the angular flux within the medium, very good approximations to several classical plane geometry problems, i.e. the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method can be extended to other geometries. (authors) [French] On etablit une nouvelle methode d'approximation pour l'equation de Boltzmann en partant d'une forme particuliere de cette equation qui n'implique que le flux angulaire a la frontiere du milieu et ou les variables d'espace n'apparaissent pas explicitement. Par un developpement en polynomes orthogonaux du flux angulaire sortant du milieu et sans faire d'hypothese sur le flux angulaire a l'interieur du milieu, on obtient de tres bonnes approximations pour plusieurs problemes classiques en geometrie plane: l'albedo et le facteur de transmission des plaques, la longueur d'extrapolation du probleme de  More>>
Authors:
Benoist, P; Kavenoky, A [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Jan 15, 1968
Product Type:
Technical Report
Report Number:
CEA-R-3170
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALBEDO; BOLTZMANN STATISTICS; MILNE PROBLEM; NEUTRON SPECTRA; POLYNOMIALS; STATISTICAL MECHANICS
OSTI ID:
20818100
Research Organizations:
Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires, Departement des etudes de piles, service de physique mathematique
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR05R3170118229
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
49 pages
Announcement Date:
Dec 30, 2006

Citation Formats

Benoist, P, and Kavenoky, A. The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann. France: N. p., 1968. Web.
Benoist, P, & Kavenoky, A. The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann. France.
Benoist, P, and Kavenoky, A. 1968. "The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann." France.
@misc{etde_20818100,
title = {The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann}
author = {Benoist, P, and Kavenoky, A}
abstractNote = {In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation which involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expanding in orthogonal polynomials the angular flux of neutrons leaking from the medium and making no assumption about the angular flux within the medium, very good approximations to several classical plane geometry problems, i.e. the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method can be extended to other geometries. (authors) [French] On etablit une nouvelle methode d'approximation pour l'equation de Boltzmann en partant d'une forme particuliere de cette equation qui n'implique que le flux angulaire a la frontiere du milieu et ou les variables d'espace n'apparaissent pas explicitement. Par un developpement en polynomes orthogonaux du flux angulaire sortant du milieu et sans faire d'hypothese sur le flux angulaire a l'interieur du milieu, on obtient de tres bonnes approximations pour plusieurs problemes classiques en geometrie plane: l'albedo et le facteur de transmission des plaques, la longueur d'extrapolation du probleme de Milne, le spectre des neutrons reflechis par un milieu semi-infini ralentisseur. La methode se generalise a d'autres geometries. (auteurs)}
place = {France}
year = {1968}
month = {Jan}
}