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Goal-Based Error Estimation, Functional Correction, h, p and hp Adaptivity of the 1-D Diamond Difference Discrete Ordinate Method
File(s)
Author(s)
Jeffers, RS
Kophazi, J
Eaton, MD
Févotte, F
Hülsemann, F
Type
Journal Article
Abstract
This paper uses local dual weighted residual (DWR) error indicators to flag cells for goal-based refinement in a 1-D diamond difference (DD) discretisation of the discrete ordinate (SN) neutron transport equations. Goal-orientated adaptive mesh refinement (GO-AMR) aims to produce a mesh that is optimal for a given goal or QoI (Quantity of Interest). h, p and hp refinement is implemented and applied to various test cases. A merit function is derived for the combined hp algorithm and is calculated for each refinement option within each flagged cell. The refinement option with the highest merit function is chosen for a given flagged cell. This paper also investigates the use of the DWR error estimation as a correction term for the originally calculated QoI. If error correction and GO-AMR are combined the DWR error indicators do not always give an optimal mesh for the corrected value of the QoI. Therefore, refinement indicators based on the error in the error correction term are used and tested in this work.
Date Issued
2018-01-18
Date Acceptance
2017-11-20
Citation
Journal of Computational and Theoretical Transport, 2018, 46 (6-7), pp.427-458
URI
DOI
ISSN
2332-4309
Publisher
Taylor & Francis
Start Page
427
End Page
458
Journal / Book Title
Journal of Computational and Theoretical Transport
Volume
46
Issue
6-7
Copyright Statement
© 2018 Taylor & Francis Group, LLC
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Publication Status
Published
Date Publish Online
2018-01-18