Imperial College London
Dr Matthew Eaton

DrMatthewEaton

Faculty of Engineering, Department of Mechanical Engineering

Reader
 
 
 
//

Contact

 

+44 (0)20 7594 7053m.eaton

 
 
//

Location

 

657City and Guilds BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Kophazi:2020:10.1016/j.anucene.2019.107049,
author = {Kophazi, J and Eaton, M and McClarren, R and Latimer, C},
doi = {10.1016/j.anucene.2019.107049},
journal = {Annals of Nuclear Energy},
pages = {1--16},
title = {A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation},
url = {http://dx.doi.org/10.1016/j.anucene.2019.107049},
volume = {136},
year = {2020}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper presents the application of isogeometric analysis (IGA) to the spatial discretisationof the multi-group, self-adjoint angular flux (SAAF) form of the neutron transport equation witha discrete ordinate (SN) angular discretisation. The IGA spatial discretisation is based uponnon-uniform rational B-spline (NURBS) basis functions for both the test and trial functions. Inaddition a source iteration compatible maximum principle is used to derive the IGA spatiallydiscretised SAAF equation. It is demonstrated that this maximum principle is mathematicallyequivalent to the weak form of the SAAF equation. The rate of convergence of the IGA spatial discretisation of the SAAF equation is analysed using a method of manufactured solutions(MMS) verification test case. The results of several nuclear reactor physics verification benchmark test cases are analysed. This analysis demonstrates that for higher-order basis functions,and for the same number of degrees of freedom, the FE based spatial discretisation methods arenumerically less accurate than IGA methods. The difference in numerical accuracy between theIGA and FE methods is shown to be because of the higher-order continuity of NURBS basisfunctions within a NURBS patch as well as the preservation of both the volume and surfacearea throughout the solution domain within the IGA spatial discretisation. Finally, the numericalresults of applying the IGA SAAF method to the OECD/NEA, seven-group, two-dimensionalC5G7 quarter core nuclear reactor physics verification benchmark test case are presented. Theresults, from this verification benchmark test case, are shown to be in good agreement with solutions of the first-order form as well as the second-order even-parity form of the neutron transportequation for the same order of discrete ordinate (SN) angular approximation.
AU  - Kophazi,J
AU  - Eaton,M
AU  - McClarren,R
AU  - Latimer,C
DO  - 10.1016/j.anucene.2019.107049
EP  - 16
PY  - 2020///
SN  - 0306-4549
SP  - 1
TI  - A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation
T2  - Annals of Nuclear Energy
UR  - http://dx.doi.org/10.1016/j.anucene.2019.107049
UR  - https://www.sciencedirect.com/science/article/pii/S0306454919305511?via%3Dihub
UR  - http://hdl.handle.net/10044/1/73656
VL  - 136
ER  -
Download