### Abstract

Solutions of the one-group neutron transport equation are provided for point-beam and finite isotropic line sources in a homogeneous 3-D infinite medium with isotropic scattering. The solution is obtained via Fourier transforms and analytical/numerical inversions. The transport equation is cast into a 2-D equivalent form, which can ultimately be put in terms of a 1-D problem, thereby providing analytical leverage. The inversions use standard numerical techniques such as Gauss-Legendre quadrature and summation of infinite series. Even though the solution obtained here uses equivalent forms in fewer dimensions, it does represent a true 3-D analytical benchmark which is useful for both code verification and educational enrichment.

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

Pages (from-to) | 89-111 |

Number of pages | 23 |

Journal | Transport Theory and Statistical Physics |

Volume | 24 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1995 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Transportation

### Cite this

*Transport Theory and Statistical Physics*,

*24*(1-3), 89-111. https://doi.org/10.1080/00411459508205121

**A 3-D neutron transport benchmark solution.** / Ganapol, Barry D; Kornreich, D. E.

Research output: Contribution to journal › Article

*Transport Theory and Statistical Physics*, vol. 24, no. 1-3, pp. 89-111. https://doi.org/10.1080/00411459508205121

}

TY - JOUR

T1 - A 3-D neutron transport benchmark solution

AU - Ganapol, Barry D

AU - Kornreich, D. E.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Solutions of the one-group neutron transport equation are provided for point-beam and finite isotropic line sources in a homogeneous 3-D infinite medium with isotropic scattering. The solution is obtained via Fourier transforms and analytical/numerical inversions. The transport equation is cast into a 2-D equivalent form, which can ultimately be put in terms of a 1-D problem, thereby providing analytical leverage. The inversions use standard numerical techniques such as Gauss-Legendre quadrature and summation of infinite series. Even though the solution obtained here uses equivalent forms in fewer dimensions, it does represent a true 3-D analytical benchmark which is useful for both code verification and educational enrichment.

AB - Solutions of the one-group neutron transport equation are provided for point-beam and finite isotropic line sources in a homogeneous 3-D infinite medium with isotropic scattering. The solution is obtained via Fourier transforms and analytical/numerical inversions. The transport equation is cast into a 2-D equivalent form, which can ultimately be put in terms of a 1-D problem, thereby providing analytical leverage. The inversions use standard numerical techniques such as Gauss-Legendre quadrature and summation of infinite series. Even though the solution obtained here uses equivalent forms in fewer dimensions, it does represent a true 3-D analytical benchmark which is useful for both code verification and educational enrichment.

UR - http://www.scopus.com/inward/record.url?scp=21844524674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844524674&partnerID=8YFLogxK

U2 - 10.1080/00411459508205121

DO - 10.1080/00411459508205121

M3 - Article

VL - 24

SP - 89

EP - 111

JO - Journal of Computational and Theoretical Transport

JF - Journal of Computational and Theoretical Transport

SN - 2332-4309

IS - 1-3

ER -