Academic Journal

SN Method for Solving Transport Source Problems With Anisotropic Scattering.

Bibliographic Details
Title: SN Method for Solving Transport Source Problems With Anisotropic Scattering.
Authors: Morató, S., Miró, R., Bernal, Á., Roman, J. E., Verdú, G., Habib, Mohammad Rezwan
Source: Science & Technology of Nuclear Installations; 7/19/2026, Vol. 2026, p1-11, 11p
Subject Terms: Neutron transport theory, Neutron scattering, Software libraries (Computer programming), Finite difference method, Neutron temperature, Sparse matrices
Abstract: A discrete ordinates (SN) method has been applied to the solution of the steady‐state multigroup neutron transport equation in Cartesian geometry. Angular and spatial discretization were performed using the (SN) scheme and the finite difference method, respectively, with isotropic and anisotropic scattering treated up to arbitrary order. The algorithms were implemented in a FORTRAN code named n‐DOTEC. The contribution of this work lies in the development and verification of a computational framework for one‐ and two‐dimensional fixed‐source transport problems, capable of handling multiple energy groups and anisotropic scattering expansions of arbitrary order, and using PETSc together with MUMPS for the solution of the resulting sparse linear systems. In the two‐dimensional case, the code includes a product quadrature (PQ) developed by the authors, based on Gauss‐Legendre quadrature for both polar and azimuthal angles, with point weights defined as the product of the corresponding one‐dimensional weights. The code was validated against several one‐dimensional benchmarks and a two‐dimensional benchmark problem. Test cases include fixed‐source problems with vacuum and reflective boundary conditions under demanding configurations that require high‐order (SN) to achieve accuracy. The numerical results demonstrate good agreement with analytical solutions and reference codes such as DANTSYS and PARTISN. Reported mean relative errors were below 1% for most cases, and as low as 0.0005% for a two‐group anisotropic scattering benchmark, confirming the robustness of the implementation. The method efficiently computes flux distributions for any number of energy groups, and its simple formulation makes it a reliable tool for transport calculations. In addition, n‐DOTEC has potential applications in generating variance‐reduction parameters, such as weight windows, for Monte Carlo simulations. [ABSTRACT FROM AUTHOR]
Copyright of Science & Technology of Nuclear Installations is the property of Wiley-Blackwell 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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  Label: Title
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  Data: S<subscript>N</subscript> Method for Solving Transport Source Problems With Anisotropic Scattering.
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  Data: <searchLink fieldCode="AR" term="%22Morató%2C+S%2E%22">Morató, S.</searchLink><br /><searchLink fieldCode="AR" term="%22Miró%2C+R%2E%22">Miró, R.</searchLink><br /><searchLink fieldCode="AR" term="%22Bernal%2C+Á%2E%22">Bernal, Á.</searchLink><br /><searchLink fieldCode="AR" term="%22Roman%2C+J%2E+E%2E%22">Roman, J. E.</searchLink><br /><searchLink fieldCode="AR" term="%22Verdú%2C+G%2E%22">Verdú, G.</searchLink><br /><searchLink fieldCode="AR" term="%22Habib%2C+Mohammad+Rezwan%22">Habib, Mohammad Rezwan</searchLink>
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  Data: Science & Technology of Nuclear Installations; 7/19/2026, Vol. 2026, p1-11, 11p
– Name: Subject
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  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Neutron+transport+theory%22">Neutron transport theory</searchLink><br /><searchLink fieldCode="DE" term="%22Neutron+scattering%22">Neutron scattering</searchLink><br /><searchLink fieldCode="DE" term="%22Software+libraries+%28Computer+programming%29%22">Software libraries (Computer programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Neutron+temperature%22">Neutron temperature</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A discrete ordinates (SN) method has been applied to the solution of the steady‐state multigroup neutron transport equation in Cartesian geometry. Angular and spatial discretization were performed using the (SN) scheme and the finite difference method, respectively, with isotropic and anisotropic scattering treated up to arbitrary order. The algorithms were implemented in a FORTRAN code named n‐DOTEC. The contribution of this work lies in the development and verification of a computational framework for one‐ and two‐dimensional fixed‐source transport problems, capable of handling multiple energy groups and anisotropic scattering expansions of arbitrary order, and using PETSc together with MUMPS for the solution of the resulting sparse linear systems. In the two‐dimensional case, the code includes a product quadrature (PQ) developed by the authors, based on Gauss‐Legendre quadrature for both polar and azimuthal angles, with point weights defined as the product of the corresponding one‐dimensional weights. The code was validated against several one‐dimensional benchmarks and a two‐dimensional benchmark problem. Test cases include fixed‐source problems with vacuum and reflective boundary conditions under demanding configurations that require high‐order (SN) to achieve accuracy. The numerical results demonstrate good agreement with analytical solutions and reference codes such as DANTSYS and PARTISN. Reported mean relative errors were below 1% for most cases, and as low as 0.0005% for a two‐group anisotropic scattering benchmark, confirming the robustness of the implementation. The method efficiently computes flux distributions for any number of energy groups, and its simple formulation makes it a reliable tool for transport calculations. In addition, n‐DOTEC has potential applications in generating variance‐reduction parameters, such as weight windows, for Monte Carlo simulations. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Science & Technology of Nuclear Installations is the property of Wiley-Blackwell 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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      – Type: doi
        Value: 10.1155/stni/4816167
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      – Code: eng
        Text: English
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        PageCount: 11
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    Subjects:
      – SubjectFull: Neutron transport theory
        Type: general
      – SubjectFull: Neutron scattering
        Type: general
      – SubjectFull: Software libraries (Computer programming)
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      – SubjectFull: Finite difference method
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      – SubjectFull: Neutron temperature
        Type: general
      – SubjectFull: Sparse matrices
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      – TitleFull: SN Method for Solving Transport Source Problems With Anisotropic Scattering.
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            NameFull: Morató, S.
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            – D: 19
              M: 07
              Text: 7/19/2026
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              Y: 2026
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