Nonlinear Iterative Method for Solving SP<sub>3</sub> Equation

Pan Qingquan; Lu Haoliang; Cai Li; Li Dongsheng; Wang Kan

doi:10.13832/j.jnpe.2017.03.0038

Volume 38 Issue 3

Feb. 2025

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Pan Qingquan, Lu Haoliang, Cai Li, Li Dongsheng, Wang Kan. Nonlinear Iterative Method for Solving SP3 Equation[J]. Nuclear Power Engineering, 2017, 38(3): 38-42. doi: 10.13832/j.jnpe.2017.03.0038

Citation:

Pan Qingquan, Lu Haoliang, Cai Li, Li Dongsheng, Wang Kan. Nonlinear Iterative Method for Solving SP₃ Equation[J]. Nuclear Power Engineering, 2017, 38(3): 38-42. doi: 10.13832/j.jnpe.2017.03.0038

Pan Qingquan, Lu Haoliang, Cai Li, Li Dongsheng, Wang Kan. Nonlinear Iterative Method for Solving SP3 Equation[J]. Nuclear Power Engineering, 2017, 38(3): 38-42. doi: 10.13832/j.jnpe.2017.03.0038

Citation:

Pan Qingquan, Lu Haoliang, Cai Li, Li Dongsheng, Wang Kan. Nonlinear Iterative Method for Solving SP₃ Equation[J]. Nuclear Power Engineering, 2017, 38(3): 38-42. doi: 10.13832/j.jnpe.2017.03.0038

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Nonlinear Iterative Method for Solving SP₃ Equation

doi: 10.13832/j.jnpe.2017.03.0038

1. Department of Engineering Physics, Tsinghua University, Beijing, 100084, China;
2. China Nuclear Power Technology Research Institute, Shenzhen, Guangdong, 518031, China

Received Date: 2016-08-15
Rev Recd Date: 2017-03-02

Available Online: 2025-02-09

Abstract

Abstract

The SP₃ equation is an approximation of the 3^rd-order spherical harmonic method.Relative to the diffusion theory,it has higher accuracy for calculation.Adopting the nonlinear iterative method to solve the SP₃ equation,and putting forward the coupling relationship with Angular discrete,the problems of the complexity about the coupling relationship in the vacuum-boundary and the numerical instability during correction for 2^nd-order flux are successfully solved.A code named NLSP₃ for solving the SP3 equation with nonlinear iterative method was developed.Through the calculation of the benchmark problems,the feasibility of the algorithm is proved.
- Semi-analytical nodal,
- Nonlinear iteration,
- Simplified spherical harmonic,
- Numerical instability