The Ln/Ln0 Method for 1D Neutron Transport in a Slab Medium

B. D. Ganapol

doi:10.1080/23324309.2022.2111443

The Ln/Ln0 Method for 1D Neutron Transport in a Slab Medium

B. D. Ganapol

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A new, highly precise benchmark for the monoenergetic 1 D neutron transport equation with isotropic scattering, based on Case’s singular eigenfunctions, is presented. Because of the nature of singular distributions, Case’s analytical solution notoriously resists straightforward numerical computation. To overcome this difficulty, two complementary Lagrange interpolation schemes are constructed to achieve extreme precision (∼8 to 10 places) for number of secondaries in the range 0.001 < c < 0.99999 and slab thicknesses in the range 1 < Δ <100.

Original language	English (US)
Pages (from-to)	239-264
Number of pages	26
Journal	Journal of Computational and Theoretical Transport
Volume	51
Issue number	5
DOIs	https://doi.org/10.1080/23324309.2022.2111443
State	Published - 2022
Externally published	Yes

Keywords

extreme precision
Gauss quadrature
Lagrange interpolation
Neutron transport
slab

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Transportation
General Physics and Astronomy
Applied Mathematics

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10.1080/23324309.2022.2111443

Cite this

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title = "The Ln/Ln0 Method for 1D Neutron Transport in a Slab Medium",

abstract = "A new, highly precise benchmark for the monoenergetic 1 D neutron transport equation with isotropic scattering, based on Case{\textquoteright}s singular eigenfunctions, is presented. Because of the nature of singular distributions, Case{\textquoteright}s analytical solution notoriously resists straightforward numerical computation. To overcome this difficulty, two complementary Lagrange interpolation schemes are constructed to achieve extreme precision (∼8 to 10 places) for number of secondaries in the range 0.001 < c < 0.99999 and slab thicknesses in the range 1 < Δ <100.",

keywords = "extreme precision, Gauss quadrature, Lagrange interpolation, Neutron transport, slab",

author = "Ganapol, {B. D.}",

note = "Funding Information: The author acknowledges the two reviewers for their interest and pointing out some typos and omissions. In particular, reviewer one, who re-derived every single equation and found more than a few incorrect expressions. His/her effort is certainly worthy of a beer or two if we find ourselves in the same place in the future and they are willing to admit to the review. Publisher Copyright: {\textcopyright} 2022 Taylor & Francis Group, LLC.",

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AU - Ganapol, B. D.

N1 - Funding Information: The author acknowledges the two reviewers for their interest and pointing out some typos and omissions. In particular, reviewer one, who re-derived every single equation and found more than a few incorrect expressions. His/her effort is certainly worthy of a beer or two if we find ourselves in the same place in the future and they are willing to admit to the review. Publisher Copyright: © 2022 Taylor & Francis Group, LLC.

PY - 2022

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N2 - A new, highly precise benchmark for the monoenergetic 1 D neutron transport equation with isotropic scattering, based on Case’s singular eigenfunctions, is presented. Because of the nature of singular distributions, Case’s analytical solution notoriously resists straightforward numerical computation. To overcome this difficulty, two complementary Lagrange interpolation schemes are constructed to achieve extreme precision (∼8 to 10 places) for number of secondaries in the range 0.001 < c < 0.99999 and slab thicknesses in the range 1 < Δ <100.

AB - A new, highly precise benchmark for the monoenergetic 1 D neutron transport equation with isotropic scattering, based on Case’s singular eigenfunctions, is presented. Because of the nature of singular distributions, Case’s analytical solution notoriously resists straightforward numerical computation. To overcome this difficulty, two complementary Lagrange interpolation schemes are constructed to achieve extreme precision (∼8 to 10 places) for number of secondaries in the range 0.001 < c < 0.99999 and slab thicknesses in the range 1 < Δ <100.

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The Ln/Ln0 Method for 1D Neutron Transport in a Slab Medium

Abstract

Keywords

ASJC Scopus subject areas

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