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An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation
File(s)
Author(s)
Owens, A
Welch, J
Kophazi, J
Eaton, M
Type
Journal Article
Abstract
In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements.
Date Issued
2017-02-04
Date Acceptance
2017-01-30
Citation
Computer Methods in Applied Mechanics and Engineering, 2017, 318, pp.215-241
URI
DOI
ISSN
0045-7825
Publisher
Elsevier
Start Page
215
End Page
241
Journal / Book Title
Computer Methods in Applied Mechanics and Engineering
Volume
318
Copyright Statement
© 2017 The Authors. Published by Elsevier B.V. Accepted manuscript published online distributed under a Creative Commons License (https://creativecommons.org/licenses/by/4.0/)
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/J002011/1
Subjects
Applied Mathematics
01 Mathematical Sciences
09 Engineering
Publication Status
Published