Imperial College London
Dr Matthew Eaton

DrMatthewEaton

Faculty of Engineering, Department of Mechanical Engineering

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+44 (0)20 7594 7053m.eaton

 
 
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Location

 

657City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Latimer:2020:10.1016/j.pnucene.2019.103238,
author = {Latimer, C and Kópházi, J and Eaton, MD and McClarren, RG},
doi = {10.1016/j.pnucene.2019.103238},
journal = {Progress in Nuclear Energy},
pages = {1--15},
title = {A geometry conforming, isogeometric, weighted least squares (WLS) method for the neutron transport equation with discrete ordinate (SN) angular discretisation},
url = {http://dx.doi.org/10.1016/j.pnucene.2019.103238},
volume = {121},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper presents the application of isogeometric analysis (IGA) to the spatial discretisation of the multi-group, source iteration compatible, weighted least squares (WLS) form of the neutron transport equation with a discrete ordinate (S) angular discretisation. The WLS equation is an elliptic, second-order form of the neutron transport equation that can be applied to neutron transport problems on computational domains where there are void regions present. However, the WLS equation only maintains conservation of neutrons in void regions in the fine mesh limit. The IGA spatial discretisation is based up non-uniform rational B-splines (NURBS) basis functions for both the test and trial functions. In addition a methodology for selecting the magnitude of the weighting function for void and near-void problems is presented. This methodology is based upon solving the first-order neutron transport equation over a coarse spatial mesh. The results of several nuclear reactor physics verification benchmark test cases are analysed. The results from these verification benchmarks demonstrate two key aspects. The first is that the magnitude of the error in the solution due to approximation of the geometry is greater than or equal to the magnitude of the error in the solution due to lack of conservation of neutrons. The second is the effect of the weighting factor on the solution which is investigated for a boiling water reactor (BWR) lattice that contains a burnable poison pincell. It is demonstrated that the smaller the area this weighting factor is active over the closer the WLS solution is to that produced by solving the self adjoint angular flux (SAAF) equation. Finally, the methodology for determining the magnitude of the weighting factor is shown to produce a suitable weighting factor for nuclear reactor physics problems containing void regions. The more refined the coarse solution of the first-order transport equation, the more suitable the weighting factor.
AU  - Latimer,C
AU  - Kópházi,J
AU  - Eaton,MD
AU  - McClarren,RG
DO  - 10.1016/j.pnucene.2019.103238
EP  - 15
PY  - 2020///
SN  - 0149-1970
SP  - 1
TI  - A geometry conforming, isogeometric, weighted least squares (WLS) method for the neutron transport equation with discrete ordinate (SN) angular discretisation
T2  - Progress in Nuclear Energy
UR  - http://dx.doi.org/10.1016/j.pnucene.2019.103238
UR  - https://www.sciencedirect.com/science/article/pii/S0149197019303439?via%3Dihub
UR  - http://hdl.handle.net/10044/1/76608
VL  - 121
ER  -
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