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.
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2017 25th International Conference on Nuclear Engineering
July 2–6, 2017
Shanghai, China
Conference Sponsors:
- Nuclear Engineering Division
ISBN:
978-0-7918-5781-6
PROCEEDINGS PAPER
A Comparative Study of 10 Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations Available to Purchase
Yining Zhang,
Yining Zhang
Harbin Institute of Technology, Harbin, China
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Haochun Zhang,
Haochun Zhang
Harbin Institute of Technology, Harbin, China
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Yang Su,
Yang Su
KTH Royal Institute of Technology, Stockholm, Sweden
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Guangbo Zhao
Guangbo Zhao
Harbin Institute of Technology, Harbin, China
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Yining Zhang
Harbin Institute of Technology, Harbin, China
Haochun Zhang
Harbin Institute of Technology, Harbin, China
Yang Su
KTH Royal Institute of Technology, Stockholm, Sweden
Guangbo Zhao
Harbin Institute of Technology, Harbin, China
Paper No:
ICONE25-67275, V003T02A049; 7 pages
Published Online:
October 17, 2017
Citation
Zhang, Y, Zhang, H, Su, Y, & Zhao, G. "A Comparative Study of 10 Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations." Proceedings of the 2017 25th International Conference on Nuclear Engineering. Volume 3: Nuclear Fuel and Material, Reactor Physics and Transport Theory; Innovative Nuclear Power Plant Design and New Technology Application. Shanghai, China. July 2–6, 2017. V003T02A049. ASME. https://doi.org/10.1115/ICONE25-67275
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