Finite element method for neutron diffusion problems in hexagonal geometry

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The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described ... continued below

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Pages: 311

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Wei, T.Y.C. & Hansen, K.F. June 1, 1975.

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Description

The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes. (auth)

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Pages: 311

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  • Other Information: Thesis. Orig. Receipt Date: 30-JUN-76

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  • Report No.: COO--2262-7
  • Grant Number: AT(11-1)-2262
  • DOI: 10.2172/4112659 | External Link
  • Office of Scientific & Technical Information Report Number: 4112659
  • Archival Resource Key: ark:/67531/metadc866649

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Office of Scientific & Technical Information Technical Reports

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  • June 1, 1975

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  • Sept. 16, 2016, 12:32 a.m.

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Wei, T.Y.C. & Hansen, K.F. Finite element method for neutron diffusion problems in hexagonal geometry, thesis or dissertation, June 1, 1975; United States. (digital.library.unt.edu/ark:/67531/metadc866649/: accessed October 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.