### 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 F_{N} solution directly on the integro-dijferential equation satisfied by the pseudo problem. Through appropriate projections, a straightforward F_{N} formulation results in singular integral equations for both the flux and current. Enhanced by convergence acceleration, the F_{N} 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 F_{N} theory.

Original language | English (US) |
---|---|

Pages (from-to) | 169-181 |

Number of pages | 13 |

Journal | Nuclear Science and Engineering |

Volume | 159 |

Issue number | 2 |

State | Published - Jun 2008 |

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### ASJC Scopus subject areas

- Nuclear Energy and Engineering

### Cite this

**A neutron transport benchmark in one-dimensional cylindrical geometry : Revisited.** / Ganapol, Barry D.

Research output: Contribution to journal › Article

*Nuclear Science and Engineering*, vol. 159, no. 2, pp. 169-181.

}

TY - JOUR

T1 - A neutron transport benchmark in one-dimensional cylindrical geometry

T2 - Revisited

AU - Ganapol, Barry D

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=45749121451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45749121451&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:45749121451

VL - 159

SP - 169

EP - 181

JO - Nuclear Science and Engineering

JF - Nuclear Science and Engineering

SN - 0029-5639

IS - 2

ER -