Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code.

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Title: Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code.
Authors: Satti, Hicham1 (AUTHOR) sattihicham@gmail.com, El Hajjaji, Otman1 (AUTHOR), Bardouni, Tarek El1 (AUTHOR), Ghalbzouri, Tarik El1 (AUTHOR)
Source: Nuclear Science & Engineering. Feb2025, Vol. 199 Issue 2, p280-294. 15p.
Subjects: Neutron diffusion, Mathematical transformations, Neutron flux, Moments method (Statistics), Benchmark problems (Computer science)
Abstract: This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code's reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode's methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode's adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode's prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns. [ABSTRACT FROM AUTHOR]
Copyright of Nuclear Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code.
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  Data: <searchLink fieldCode="JN" term="%22Nuclear+Science+%26+Engineering%22">Nuclear Science & Engineering</searchLink>. Feb2025, Vol. 199 Issue 2, p280-294. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Neutron+diffusion%22">Neutron diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Neutron+flux%22">Neutron flux</searchLink><br /><searchLink fieldCode="DE" term="%22Moments+method+%28Statistics%29%22">Moments method (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Benchmark+problems+%28Computer+science%29%22">Benchmark problems (Computer science)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code's reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode's methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode's adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode's prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Nuclear Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/00295639.2024.2357454
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 280
    Subjects:
      – SubjectFull: Neutron diffusion
        Type: general
      – SubjectFull: Mathematical transformations
        Type: general
      – SubjectFull: Neutron flux
        Type: general
      – SubjectFull: Moments method (Statistics)
        Type: general
      – SubjectFull: Benchmark problems (Computer science)
        Type: general
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      – TitleFull: Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code.
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            NameFull: Satti, Hicham
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            NameFull: El Hajjaji, Otman
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            NameFull: Bardouni, Tarek El
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            NameFull: Ghalbzouri, Tarik El
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              M: 02
              Text: Feb2025
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              Y: 2025
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