A finite subelement generalization of the variational nodal method

M. A. Smith*, N. Tsoulfanidis, E. E. Lewis, G. Palmiotti, T. A. Taiwo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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 UO2 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.

Original languageEnglish (US)
Pages (from-to)36-46
Number of pages11
JournalNuclear Science and Engineering
Issue number1
StatePublished - May 2003

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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