Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation
File(s)
Accepted version
Published version
Author(s)
Owens, AR
Welch, JA
Kophazi, J
Eaton, MD
Type
Journal Article
Abstract
In this paper two discontinuous Galerkin isogeometric analysis methods are developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation. The discontinuous Galerkin projection approach was taken on both an element level and the patch level for a given Non-Uniform Rational B-Spline (NURBS) patch. This paper describes the detailed dispersion analysis that has been used to analyse the numerical stability of both of these schemes. The convergence of the schemes for both smooth and non-smooth solutions was also investigated using the method of manufactured solutions (MMS) for multidimensional problems and a 1D semi-analytical benchmark whose solution contains a strongly discontinuous first derivative. This paper also investigates the challenges posed by strongly curved boundaries at both the NURBS element and patch level with several algorithms developed to deal with such cases. Finally numerical results are presented both for a simple pincell test problem as
well as the C5G7 quarter core MOX/UOX small Light Water Reactor (LWR) benchmark problem. These numerical results produced by the isogeometric analysis (IGA) methods are compared and contrasted against linear and quadratic discontinuous Galerkin finite element (DGFEM) SN based methods.
well as the C5G7 quarter core MOX/UOX small Light Water Reactor (LWR) benchmark problem. These numerical results produced by the isogeometric analysis (IGA) methods are compared and contrasted against linear and quadratic discontinuous Galerkin finite element (DGFEM) SN based methods.
Editor(s)
Strain, JA
Date Issued
2016-06-15
Date Acceptance
2016-03-27
Citation
Journal of Computational Physics, 2016, 315 (1), pp.501-535
ISSN
0021-9991
Publisher
Elsevier
Start Page
501
End Page
535
Journal / Book Title
Journal of Computational Physics
Volume
315
Issue
1
Copyright Statement
© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC
BY license (http://creativecommons.org/licenses/by/4.0/).
BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Identifier
PII: S0021-9991(16)30025-0
Grant Number
EP/J002011/1
EP/K503733/1
Subjects
Isogeometric
Neutron Transport
Hyperbolic Equations
Discontinuous Galerkin
Discrete Ordinates
Reactor Physics
Publication Status
Published
Date Publish Online
2016-03-31