A symmetric interior-penalty discontinuous Galerkin isogeometric analysis spatial discretization of the self-adjoint angular flux form of the neutron transport equation
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Published version
Author(s)
Wilson, S
Eaton, M
Kophazi, J
Type
Journal Article
Abstract
This paper presents the first application of a symmetric interior-penalty discontinuous Galerkin isogeometric analysis (SIP-DG-IGA) spatial discretization to the self-adjoint angular flux (SAAF) form of the multi-group neutron transport equation. The penalty parameters are determined, for general element types, from a mathematically rigorous coercivity analysis of the bilinear form. The proposed scheme produces a compact spatial discretization stencil. It also yields symmetric positive-definite (SPD) matrices, which can be efficiently solved using pre-conditioned conjugate gradient (PCG) solution algorithms. The proposed discretization scheme is verified using the method of manufactured solutions (MMS) and several nuclear reactor physics benchmark verification test cases. For sufficiently smooth elliptic problems, the proposed spatial discretization can exploit higher-order continuity, or 𝑘-refinement, of the NURBS basis to consistently yield greater numerical accuracy per degree of freedom (DoF) than standard ℎ-refinement. Since this is a discontinuous scheme, it can also accurately model significant changes in the neutron scalar flux that may occur near the material interfaces of heterogeneous problems.
Date Issued
2024-12-01
Online Publication Date
2024-09-30T10:37:53Z
Date Acceptance
2024-09-19
ISSN
0045-7825
Publisher
Elsevier
Journal / Book Title
Computational Methods in Applied Mechanics and Engineering
Volume
432
Issue
Part B
Copyright Statement
© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
(http://creativecommons.org/licenses/by/4.0/).
License URI
Identifier
https://www.sciencedirect.com/science/article/pii/S0045782524006698?via%3Dihub
Publication Status
Published
Article Number
117414
Date Publish Online
2024-09-26