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Open AccessArticle

A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

1
Department of Atomic and Heat- and -Power Engineering, Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia
2
Faculty of Nuclear Engineering, Shahid Beheshti University of Iran, P.O. Box 1983963113 Tehran, Iran
*
Author to whom correspondence should be addressed.
Energies 2020, 13(20), 5424; https://doi.org/10.3390/en13205424
Received: 30 August 2020 / Revised: 9 October 2020 / Accepted: 15 October 2020 / Published: 17 October 2020
(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)
The application of continuous and discontinuous approaches of the finite element method (FEM) to the neutron transport equation (NTE) has been investigated. A comparative algorithm for analyzing the capability of various types of numerical solutions to the NTE based on variational formulation and discontinuous finite element method (DFEM) has been developed. The developed module is coupled to the program discontinuous finite element method for neutron (DISFENT). Each variational principle (VP) is applied to an example with drastic changes in the distribution of neutron flux density, and the obtained results of the continuous and discontinuous finite element (DFE) have been compared. The comparison between the level of accuracy of each approach using new module of DISFENT program has been performed based on the fine mesh solutions of the multi-PN (MPN) approximation. The obtained results of conjoint principles (CPs) have been demonstrated to be very accurate in comparison to other VPs. The reduction in the number of required meshes for solving the problem is considered as the main advantage of this principle. Finally, the spatial additivity to the context of the spherical harmonics has been implemented to the CP, to avoid from computational error accumulation. View Full-Text
Keywords: neutron transport equation; comprehensive comparative analysis; continuous finite element; discontinuous finite element; conjoint variational principle; spatially adaptive approach neutron transport equation; comprehensive comparative analysis; continuous finite element; discontinuous finite element; conjoint variational principle; spatially adaptive approach
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Sadeghi, K.; Ghazaie, S.H.; Sokolova, E.; Zolfaghari, A.; Abbasi, M.R. A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches. Energies 2020, 13, 5424.

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