A neutron transport benchmark in one-dimensional cylindrical geometry: Revisited

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Abstract

A new benchmark for monoenergetic neutron transport in one-dimensional cylindrical geometry is presented. In the past, several accurate benchmarks (i.e., numerical solutions) in cylindrical geometry, based on the singular eigenfunction expansion of the solution to the corresponding pseudoproblem, have appeared in the literature. In the new formulation, called the direct F N method in cylindricalgeometry, we base the FN solution directly on the integro-dijferential equation satisfied by the pseudo problem. Through appropriate projections, a straightforward FN formulation results in singular integral equations for both the flux and current. Enhanced by convergence acceleration, the FN approximation accurately reproduces published benchmark solutions for both fixed sources and criticality. Thus, we have developed an entirely pedagogical self-contained and highly accurate benchmark based on an alternative application of FN theory.

Original languageEnglish (US)
Pages (from-to)169-181
Number of pages13
JournalNuclear Science and Engineering
Volume159
Issue number2
DOIs
StatePublished - Jun 2008

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ASJC Scopus subject areas

  • Nuclear Energy and Engineering

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