Numerical Solutions of Diffusion Equations in Multi-Dimensional Slab Geometry by Fourier Expansions

Solutions of multi-dimensional neutron diffusion equations in Cartesian coordinates are obtained in the form of regionwise multi-dimensional Fourier series. Equations for two- and three-dimensional problems are derived. A critical and a source problem in two dimensions, and a one-regional source pro...

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Bibliographic Details
Published inJournal of nuclear science and technology Vol. 12; no. 6; pp. 325 - 335
Main Authors OHTANI, Nobuo, JUNG, Jungchung, KOBAYASHI, Keisuke, NISHIHARA, Hiroshi
Format Journal Article
LanguageEnglish
Published Tokyo Taylor & Francis Group 01.06.1975
Taylor & Francis Ltd
Subjects
accuracy
boundary condition
critical problem
diffusion equation
Fourier series
multi-group
multi-region
neutron flux
numerical solution
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Summary:Solutions of multi-dimensional neutron diffusion equations in Cartesian coordinates are obtained in the form of regionwise multi-dimensional Fourier series. Equations for two- and three-dimensional problems are derived. A critical and a source problem in two dimensions, and a one-regional source problem in three dimensions are numerically studied. Two kinds of Fourier series are numerically examined from the viewpoint of rapidity of convergence of the series. To obtain the value of the flux more accurately, a method is presented which contributes to improvement of the flux profile.
ISSN:0022-3131
1881-1248
DOI:10.1080/18811248.1975.9733115