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{Gordon:2021:10.1016/j.anucene.2021.108161,
author = {Gordon, T and Cooling, CM and Williams, MMR and Eaton, M},
doi = {10.1016/j.anucene.2021.108161},
journal = {Annals of Nuclear Energy},
pages = {1--27},
title = {Numerical comparison of mathematical and computational models for the simulation of stochastic neutron kinetics problems},
url = {http://dx.doi.org/10.1016/j.anucene.2021.108161},
volume = {157},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper concerns numerical comparisons between five mathematical models capable of modelling the stochastic behaviour ofneutrons in low extraneous (extrinsic or fixed) neutron source applications. These models include analog Monte-Carlo (AMC),forward probability balance equations (FPB), generating function form of the forward probability balance equations (FGF), generatingfunction form of the backward probability balance equations (P´al-Bell), and an Itˆo calculus model using both an explicit andimplicit Euler-Maruyama discretization scheme. Results such as the survival probability, extinction probability, neutron populationmean and standard deviation, and neutron population cumulative distribution function have all been compared. The least computationallydemanding mathematical model has been found to be the use of the P´al-Bell equations which on average take four ordersof magnitude less time to compute than the other methods in this study. The accuracy of the AMC and FPB models have beenfound to be strongly linked to the computational e ciency of the models. The computational e ciency of the models decreasesignificantly as the maximum allowable neutron population is approached. The Itˆo calculus methods, utilising explicit and implicitEuler-Maruyama discretization schemes, have been found to be unsuitable for modelling very low neutron populations. However,improved results, using the Itˆo calculus methods, have been achieved for systems containing a greater number of neutrons.
AU  - Gordon,T
AU  - Cooling,CM
AU  - Williams,MMR
AU  - Eaton,M
DO  - 10.1016/j.anucene.2021.108161
EP  - 27
PY  - 2021///
SN  - 0306-4549
SP  - 1
TI  - Numerical comparison of mathematical and computational models for the simulation of stochastic neutron kinetics problems
T2  - Annals of Nuclear Energy
UR  - http://dx.doi.org/10.1016/j.anucene.2021.108161
UR  - https://www.sciencedirect.com/science/article/pii/S0306454921000372?via%3Dihub
UR  - http://hdl.handle.net/10044/1/85688
VL  - 157
ER  -
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