Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes
File(s)
Accepted version
Author(s)
Type
Journal Article
Abstract
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, keff, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for keff with directional dependence. General error estimators are derived for any given functional of the flux and applied to keff to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The keff goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Date Issued
2013
Citation
Journal of Computational Physics, 2013, 242, pp.726-762
ISSN
0021-9991
Publisher
Elsevier
Start Page
726
End Page
762
Journal / Book Title
Journal of Computational Physics
Volume
242
Copyright Statement
Copyright © 2013 Elsevier Inc. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, 242, 2013. DOI:10.1016/j.jcp.2012.12.035.
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000319049800037&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Neutron transport
Anisotropic mesh adaptivity
Goal-based mesh refinement
A posteriori error analysis
Neutron multiplication factor
Publication Status
Published