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Method of Manufactured Solutions for the Neutron Kinetics Equations.

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Title: Method of Manufactured Solutions for the Neutron Kinetics Equations.
Authors: Dawn, William C.1 (AUTHOR) william.dawn@studsvik.com
Source: Nuclear Science & Engineering. Aug2026, Vol. 200 Issue 8, p1784-1797. 14p.
Subject Terms: *Neutron diffusion, *Analytical solutions, *Delayed neutrons, *Nuclear engineering
Abstract: Although it is commonplace to solve the space-time kinetics form of the neutron diffusion equation and the delayed neutron precursor equations, accurate benchmark solutions for such problems are lacking. In this work, an analytic solution to the neutron kinetics equations is provided via the Method of Manufactured Solutions. The form of the solution is a manufactured neutron flux and a prescribed absorption cross section $\Sigma_a(x,t)$ Σ a (x , t). For the first time, an exact solution for the neutron flux as a function of space and time is provided in a form that can be used to verify existing neutron kinetics methods. Then, this solution is used to verify the neutron kinetics methods in the LMFR Utility for Physics Informed Nuclear Engineering (LUPINE) to demonstrate how this solution can be used for practical verification and quantifying the order of convergence of existing neutron kinetics methods. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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  Availability: 0
Header DbId: enr
DbLabel: Energy & Power Source
An: 194842687
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Method of Manufactured Solutions for the Neutron Kinetics Equations.
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  Data: <searchLink fieldCode="AR" term="%22Dawn%2C+William+C%2E%22">Dawn, William C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> william.dawn@studsvik.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Nuclear+Science+%26+Engineering%22">Nuclear Science & Engineering</searchLink>. Aug2026, Vol. 200 Issue 8, p1784-1797. 14p.
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– Name: Abstract
  Label: Abstract
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  Data: Although it is commonplace to solve the space-time kinetics form of the neutron diffusion equation and the delayed neutron precursor equations, accurate benchmark solutions for such problems are lacking. In this work, an analytic solution to the neutron kinetics equations is provided via the Method of Manufactured Solutions. The form of the solution is a manufactured neutron flux and a prescribed absorption cross section $\Sigma_a(x,t)$ Σ a (x , t). For the first time, an exact solution for the neutron flux as a function of space and time is provided in a form that can be used to verify existing neutron kinetics methods. Then, this solution is used to verify the neutron kinetics methods in the LMFR Utility for Physics Informed Nuclear Engineering (LUPINE) to demonstrate how this solution can be used for practical verification and quantifying the order of convergence of existing neutron kinetics methods. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=enr&AN=194842687
RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/00295639.2025.2551471
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 1784
    Subjects:
      – SubjectFull: Neutron diffusion
        Type: general
      – SubjectFull: Analytical solutions
        Type: general
      – SubjectFull: Delayed neutrons
        Type: general
      – SubjectFull: Nuclear engineering
        Type: general
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      – TitleFull: Method of Manufactured Solutions for the Neutron Kinetics Equations.
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            NameFull: Dawn, William C.
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            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 200
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              Value: 8
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            – TitleFull: Nuclear Science & Engineering
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