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Title: A Finite Subelement Generalization of the Variational Nodal Method

Abstract

The variational nodal method is generalized by dividing each spatial node into a number of triangular finite elements designated as subelements. The finite subelement trial functions allow for explicit geometry representations within each node, thus eliminating the need for nodal homogenization. The method is implemented within the Argonne National Laboratory code VARIANT and applied to two-dimensional multigroup problems.Eigenvalue and pin-power results are presented for a four-assembly Organization for Economic Cooperation and Development/Nuclear Energy Agency benchmark problem containing enriched UO{sub 2} and mixed oxide fuel pins. Our seven-group model combines spherical or simplified spherical harmonic approximations in angle with isoparametric linear or quadratic subelement basis functions, thus eliminating the need for fuel-coolant homogenization. Comparisons with reference seven-group Monte Carlo solutions indicate that in the absence of pin-cell homogenization, high-order angular approximations are required to obtain accurate eigenvalues, while the results are substantially less sensitive to the refinement of the finite subelement grids.

Authors:
 [1];  [2];  [3];  [4];  [4]
  1. University of Missouri- Rolla (United States)
  2. University of Missouri-Rolla (United States)
  3. Northwestern University (United States)
  4. Argonne National Laboratory (United States)
Publication Date:
OSTI Identifier:
20804852
Resource Type:
Journal Article
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 144; Journal Issue: 1; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0029-5639
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; APPROXIMATIONS; BENCHMARKS; COOLANTS; EIGENVALUES; FUNCTIONS; GEOMETRY; MATHEMATICAL SOLUTIONS; MIXED OXIDE FUELS; MONTE CARLO METHOD; SPHERICAL CONFIGURATION; TWO-DIMENSIONAL CALCULATIONS; URANIUM DIOXIDE; VARIATIONAL METHODS

Citation Formats

Smith, M A, Tsoulfanidis, N, Lewis, E E, Palmiotti, G, and Taiwo, T A. A Finite Subelement Generalization of the Variational Nodal Method. United States: N. p., 2003. Web. doi:10.13182/NSE144-36.
Smith, M A, Tsoulfanidis, N, Lewis, E E, Palmiotti, G, & Taiwo, T A. A Finite Subelement Generalization of the Variational Nodal Method. United States. https://doi.org/10.13182/NSE144-36
Smith, M A, Tsoulfanidis, N, Lewis, E E, Palmiotti, G, and Taiwo, T A. 2003. "A Finite Subelement Generalization of the Variational Nodal Method". United States. https://doi.org/10.13182/NSE144-36.
@article{osti_20804852,
title = {A Finite Subelement Generalization of the Variational Nodal Method},
author = {Smith, M A and Tsoulfanidis, N and Lewis, E E and Palmiotti, G and Taiwo, T A},
abstractNote = {The variational nodal method is generalized by dividing each spatial node into a number of triangular finite elements designated as subelements. The finite subelement trial functions allow for explicit geometry representations within each node, thus eliminating the need for nodal homogenization. The method is implemented within the Argonne National Laboratory code VARIANT and applied to two-dimensional multigroup problems.Eigenvalue and pin-power results are presented for a four-assembly Organization for Economic Cooperation and Development/Nuclear Energy Agency benchmark problem containing enriched UO{sub 2} and mixed oxide fuel pins. Our seven-group model combines spherical or simplified spherical harmonic approximations in angle with isoparametric linear or quadratic subelement basis functions, thus eliminating the need for fuel-coolant homogenization. Comparisons with reference seven-group Monte Carlo solutions indicate that in the absence of pin-cell homogenization, high-order angular approximations are required to obtain accurate eigenvalues, while the results are substantially less sensitive to the refinement of the finite subelement grids.},
doi = {10.13182/NSE144-36},
url = {https://www.osti.gov/biblio/20804852}, journal = {Nuclear Science and Engineering},
issn = {0029-5639},
number = 1,
volume = 144,
place = {United States},
year = {Thu May 15 00:00:00 EDT 2003},
month = {Thu May 15 00:00:00 EDT 2003}
}