A discontinuous Bubnov-Galerkin spectral element spatial discretisation of the first-order form of the neutron transport equation using a discrete ordinate angular discretisation with multidimensional anisotropic dispersion and dissipation analysis
File(s)
Published version
Author(s)
Type
Journal Article
Abstract
In this paper, the discontinuous Bubnov-Galerkin spectral element method (DBG-SEM) has been used to
spatially discretise the first order form of the neutron transport (FONT) equation. A discrete ordinate (SN)
approximation is also used to discretise the angular variables and the multigroup approximation has been
used to discretise the energy variable. The DBG-SEM has been compared against the discontinuous Bubnov
Galerkin finite element method (DBG-FEM) using two benchmark verification test cases. This is the first
time that a detailed comparison of DBG-SEM and DBG-FEM has been completed in the context of the FONT
equation. The method of manufactured solutions (MMS) has been used to investigate the convergence rate of
the proposed discretisation schemes. This demonstrates that both the DBG-SEM and DBG-FEM yield the same
rate of convergence with increasing polynomial order. Both the DBG-SEM and DBG-FEM were used to solve
the OECD/NEA two-dimensional (2D) C5G7 nuclear reactor physics benchmark verification test case. Again
both methods yield a similar level of numerical accuracy using both straight-sided and curvilinear elements.
This analysis of the local element matrix condition number demonstrates that the DBG-SEM yields a lower
condition number than the DBG-FEM. Finally, multidimensional anisotropic dispersion and dissipation analysis (MA-DDA) was utilised to understand the dispersion and dissipation errors of the DBG-SEM and DBG-FEM. This is the first time that DDA has been utilised for analysing the dispersive and dissipative properties of
spatial discretisation methods for the FONT equation in multidimensions. This analysis demonstrated that the
DBG-SEM and DBG-FEM have similar dispersion and dissipative behaviour when exact element integration was
used, which is an expected result.
spatially discretise the first order form of the neutron transport (FONT) equation. A discrete ordinate (SN)
approximation is also used to discretise the angular variables and the multigroup approximation has been
used to discretise the energy variable. The DBG-SEM has been compared against the discontinuous Bubnov
Galerkin finite element method (DBG-FEM) using two benchmark verification test cases. This is the first
time that a detailed comparison of DBG-SEM and DBG-FEM has been completed in the context of the FONT
equation. The method of manufactured solutions (MMS) has been used to investigate the convergence rate of
the proposed discretisation schemes. This demonstrates that both the DBG-SEM and DBG-FEM yield the same
rate of convergence with increasing polynomial order. Both the DBG-SEM and DBG-FEM were used to solve
the OECD/NEA two-dimensional (2D) C5G7 nuclear reactor physics benchmark verification test case. Again
both methods yield a similar level of numerical accuracy using both straight-sided and curvilinear elements.
This analysis of the local element matrix condition number demonstrates that the DBG-SEM yields a lower
condition number than the DBG-FEM. Finally, multidimensional anisotropic dispersion and dissipation analysis (MA-DDA) was utilised to understand the dispersion and dissipation errors of the DBG-SEM and DBG-FEM. This is the first time that DDA has been utilised for analysing the dispersive and dissipative properties of
spatial discretisation methods for the FONT equation in multidimensions. This analysis demonstrated that the
DBG-SEM and DBG-FEM have similar dispersion and dissipative behaviour when exact element integration was
used, which is an expected result.
Date Issued
2026-12-01
Date Acceptance
2026-07-03
Citation
Annals of Nuclear Energy, 2026, 239
ISSN
0306-4549
Publisher
Elsevier BV
Journal / Book Title
Annals of Nuclear Energy
Volume
239
Copyright Statement
© 2026 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
112630
Date Publish Online
2026-07-24