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A comparative study of 10 different methods on numerical solving of point reactor neutron kinetics equations
KTH.
2017 (English)In: 2017 25th International Conference on Nuclear Engineering: Nuclear Fuel and Material, Reactor Physics and Transport Theory; Innovative Nuclear Power Plant Design and New Technology Application, ASME Press, 2017Conference paper, Published paper (Refereed)
Abstract [en]

Point reactor neutron kinetics equations describe the time dependent neutron density variation in a nuclear reactor core. These equations are widely applied to nuclear system numerical simulation and nuclear power plant operational control. This paper analyses the characteristics of 10 different basic or normal methods to solve the point reactor neutron kinetics equations. These methods are: explicit and implicit Euler method, explicit and implicit four order Runge-Kutta method, Taylor polynomial method, power series method, decoupling method, end point floating method, Hermite method, Gear method. Three different types of step reactivity values are introduced respectively at initial time when point reactor neutron kinetics equations are calculated using different methods, which are positive reactivity, negative reactivity and higher positive reactivity. The calculation results show that (i) minor relative error can be gain after three types of step reactivity are introduced, when explicit or implicit four order Runge-Kutta method, Taylor polynomial method, power series method, end point floating method or Hermite method is taken. These methods which are mentioned above are appropriate for solving point reactor neutron kinetics equations. (ii) the relative error of decoupling method is large, under the calculation condition of this paper. When a higher reactivity is introduced, the calculation of decoupling method cannot be convergence. (iii) after three types of step reactivity are introduced respectively, the relative error of implicit Euler method is higher than any other method except decoupling method. The third highest is Gear method. (iv) when the higher reactivity is introduced, the relative error of explicit and implicit Euler method are almost coincident, and higher than any other methods obviously. (v) 4 methods are suitable for solution on these given conditions, which are implicit Runge-Kutta method, Taylor polynomial method, power series method and end point floating method, considering both the accuracy and stiffness.

Place, publisher, year, edition, pages
ASME Press, 2017.
Keywords [en]
Numerical simulation, Point reactor neutron kinetics, Stiff problem
National Category
Energy Engineering
Identifiers
URN: urn:nbn:se:kth:diva-217598DOI: 10.1115/ICONE25-67275Scopus ID: 2-s2.0-85032478430ISBN: 9784888982566 OAI: oai:DiVA.org:kth-217598DiVA, id: diva2:1157159
Conference
2017 25th International Conference on Nuclear Engineering, ICONE 2017, Shanghai, China, 2 July 2017 through 6 July 2017
Note

QC 20171115

Available from: 2017-11-15 Created: 2017-11-15 Last updated: 2018-06-19Bibliographically approved

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Publisher's full textScopushttp://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2658607

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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Output format
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