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Research Papers

A Comparative Study of Ten Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations

[+] Author and Article Information
Yining Zhang

School of Energy Science and Engineering,
Harbin Institute of Technology,
Dongli Building #546,
Harbin 150001, China
e-mail: zhangmdc@163.com

Haochun Zhang

Mem. ASME
School of Energy Science and Engineering,
Harbin Institute of Technology,
Dongli Building #546,
Harbin 150001, China
e-mail: zhc5@vip.163.com

Kexin Wang

School of Energy Science and Engineering,
Harbin Institute of Technology,
Dongli Building #546,
Harbin 150001, China
e-mail: 13039968005@163.com

1Corresponding author.

Manuscript received August 30, 2017; final manuscript received November 28, 2017; published online March 5, 2018. Assoc. Editor: Leon Cizelj.

ASME J of Nuclear Rad Sci 4(2), 021004 (Mar 05, 2018) (7 pages) Paper No: NERS-17-1102; doi: 10.1115/1.4038772 History: Received August 30, 2017; Revised November 28, 2017

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 analyzes the characteristics of ten different basic or normal methods to solve the point reactor neutron kinetics equations. The accuracy after introducing different kinds of reactivity, stiffness of methods, and computational efficiency are analyzed. The calculation results show that: considering both the accuracy and stiffness, implicit Runge–Kutta method and Hermite method are more suitable for solution on these given conditions. The explicit Euler method is the fastest, while the power series method spends the most computational time.

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References

Ray, S. S. , 2012, “ An Explicit Finite Difference Scheme for Numerical Solution of Fractional Neutron Point Kinetic Equation,” Ann. Nucl. Energy, 41(41), pp. 61–66.
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Figures

Grahic Jump Location
Fig. 6

Computational efficiency of different numerical methods

Grahic Jump Location
Fig. 1

Relative error of neutron density after introducing the positive reactivity ρ = 0.003 (h = 0.0001 s)

Grahic Jump Location
Fig. 2

Relative error of neutron density after introducing the negative reactivity ρ = −0.007 (h = 0.0001 s)

Grahic Jump Location
Fig. 3

Relative error of neutron density after introducing the higher reactivity ρ = 0.007 (h = 0.0001 s)

Grahic Jump Location
Fig. 4

Relative error of neutron density after introducing the negative reactivity ρ = −0.007 (h = 0.01 s)

Grahic Jump Location
Fig. 5

Relative error on different time-step h after introducing the positive reactivity ρ = 0.003

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