Subgroup and resonance spectrum expansion self-shielding methods using a discontinuous Bubnov-Galerkin isogeometric analysis discrete ordinate discretization of the neutron transport equation
Author(s)
Type
Journal Article
Abstract
In this paper, a discontinuous Bubnov-Galerkin isogeometric analysis discrete ordinate (DBG-IGA-SN) form of the subgroup projection and resonance spectrum expansion (RSE) methods within the DRAGON5 code is presented. The DBG-IGA-SN method uses non-uniform rational B-spline (NURBS) basis functions to spatially discretize the neutron transport equation. The NURBS basis functions, which are used to represent both the solution field and the geometry, are able to exactly represent pin cell geometries even on the coarsest spatial representation. This is not possible with traditional Lagrangian finite elements.
This is the first instance of a DBG-IGA-SN discretization of the RSE method. We compared the numerical accuracy of the DBG-IGA-SN method to the existing collision probability (CP) method within DRAGON5 against Serpent and CP ultrafine-group reference solutions for a series of uranium-oxide and mixed-oxide Rowlands pins. In DRAGON5, the CP method is frequently used for resonance self-shielding calculations. We use it in this work as a deterministic method standard for comparison to assess DBG-IGA-SN performance.
We found that our implementation of the DBG-IGA-SN method achieved similar numerical accuracy compared to the CP method overall. The infinite multiplication factor errors were no greater than 107 pcm for the uranium-oxide cases and 152 pcm for the mixed-oxide cases with a Serpent reference, with a variation of about 10 pcm between DBG-IGA-SN and CP. For the CP ultrafine-group method reference cases, the infinite multiplication factor errors did not surpass 108 pcm and 127 pcm for the uranium-oxide and mixed-oxide cases, respectively.
In addition, DBG-IGA-SN had lower infinite multiplication factor numerical errors than CP in all cases, in one case by 21 pcm. We also found that the RSE method had higher errors in the multiplication factors and reaction rates than the subgroup projection method for both the uranium-oxide and mixed-oxide cases when using the CP ultrafine-group method reference.
Future work will investigate the relative performance of the DBG-IGA-SN for larger, more complex cases, where strengths of the method, such as its scalability and ability to model exact geometries and anisotropic scatter, may make it desirable for production resonance self-shielding calculations.
This is the first instance of a DBG-IGA-SN discretization of the RSE method. We compared the numerical accuracy of the DBG-IGA-SN method to the existing collision probability (CP) method within DRAGON5 against Serpent and CP ultrafine-group reference solutions for a series of uranium-oxide and mixed-oxide Rowlands pins. In DRAGON5, the CP method is frequently used for resonance self-shielding calculations. We use it in this work as a deterministic method standard for comparison to assess DBG-IGA-SN performance.
We found that our implementation of the DBG-IGA-SN method achieved similar numerical accuracy compared to the CP method overall. The infinite multiplication factor errors were no greater than 107 pcm for the uranium-oxide cases and 152 pcm for the mixed-oxide cases with a Serpent reference, with a variation of about 10 pcm between DBG-IGA-SN and CP. For the CP ultrafine-group method reference cases, the infinite multiplication factor errors did not surpass 108 pcm and 127 pcm for the uranium-oxide and mixed-oxide cases, respectively.
In addition, DBG-IGA-SN had lower infinite multiplication factor numerical errors than CP in all cases, in one case by 21 pcm. We also found that the RSE method had higher errors in the multiplication factors and reaction rates than the subgroup projection method for both the uranium-oxide and mixed-oxide cases when using the CP ultrafine-group method reference.
Future work will investigate the relative performance of the DBG-IGA-SN for larger, more complex cases, where strengths of the method, such as its scalability and ability to model exact geometries and anisotropic scatter, may make it desirable for production resonance self-shielding calculations.
Date Issued
2026-03-09
Date Acceptance
2025-12-25
Citation
Nuclear Science and Engineering, 2026
ISSN
0029-5639
Publisher
Taylor and Francis Group
Journal / Book Title
Nuclear Science and Engineering
Copyright Statement
© 2026 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
License URL
Publication Status
Published online
Date Publish Online
2026-03-09