Research Papers

The Differences Between the Two Forms of Semi-Analytical Nodal Methods on Solving the Third-Order Simplified Spherical Harmonics Method Equations1

[+] Author and Article Information
Pan Qingquan

Department of Engineering Physics,
Tsinghua University,
Room 901,
Beijing 100083, China
e-mail: 291618467@qq.com

Lu Haoliang

China Nuclear Power Tech Research Institute,
Technology Building,
Futian District,
Shenzhen 518000, Guangdong Province, China
e-mail: luhaol@cgnpc.com.cn

Li Dongsheng

China Nuclear Power Tech Research Institute,
Technology Building,
Futian District,
Shenzhen 518000, Guangdong Province, China
e-mail: lidongsheng@cgnpc.com.cn

Wang Kan

Department of Engineering Physics,
Tsinghua University,
Room 901,
Beijing 100083, China
e-mail: wangkan@mail.tsinghua.edu.cn

Manuscript received August 18, 2017; final manuscript received October 11, 2017; published online March 5, 2018. Assoc. Editor: Juan-Luis Francois.

ASME J of Nuclear Rad Sci 4(2), 021008 (Mar 05, 2018) (6 pages) Paper No: NERS-17-1079; doi: 10.1115/1.4038653 History: Received August 18, 2017; Revised October 11, 2017

Solving the third-order simplified spherical harmonics method (SP3) equations is one of the key points in the development of advanced reactor calculation methods and has been widely concerned. The semi-analytical nodal method (SANM), based on transverse-integrated diffusion equation, has the advantages of high accuracy and convenience for multigroup calculation. Due to its advantages, the method is expected to be used in solving the SP3 equations. However, the traditional SANM is not rigorous since the expansion process does not take the special modality of the SP3 equations and their analytical solutions into consideration. There are two modalities of the SP3 equations, so there are two traditional SANM forms on solving the SP3 equations, and the differences between the two forms will be very important in further research on the SANM. A code is developed to solve the SP3 equations under the two different forms. After the calculation of the same benchmark, the difference between the two forms on solving the SP3 equations is found. According to the results, and in view of the special modality of the SP3 equations, points on a more rigorous SANM for solving the SP3 equations are discussed.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


McClarren, R. G. , 2011, “ Theoretical Aspects of the Simplified Pn Equation,” Transp. Theory Stat. Physics, 39(2–4), pp. 73–109.
Yu, L. L. , 2014, “In-Depth Investigation and Further Development of Homogenization Method and Discontinuity Factor Theory,” Ph.D. thesis, Shanghai Jiaotong University, Shangai, China. http://www.lib.sjtu.edu.cn/
Xie, Z. S. , 1997, Numerical Calculation of Nuclear Reactor Physics, Atomic Energy Press, Beijing, China, Chap. 5.
Zimin, V. G. , Ninokata, H. , and Pogosbekyan, L. R. , 1998, “ Polynomial and Semi-Analytic Nodal Method for Nonlinear Iteration Procedure,” International Conference on Physics of Nuclear Science and Technology (PHYSOR-98), Long Island, NY, Oct. 5–8, pp. 994–1002.
Zimin, V. G. , and Ninokata, H. , 1998, “ Nodal Neutron Kinetics Model Based on Nonlinear Iteration Procedure for LWR Analysis,” Ann. Nucl. Energy, 25(8), pp. 507–515. [CrossRef]
Pan, Q. Q. , Lu, H. L. , Li, D. S. , and Wang, K. , 2017, “ Study on Semi-Analytical Nodal Method for Solving SP3 Equation,” ASME Paper No. ICONE25-67597.
Brantley Patric, S. , and Larsen, E. W. , 2000, “ The Simplified P3 Approximation,” Nucl. Sci. Eng., 134(1), pp. 1–21. [CrossRef]
Takeda, T. , and Ikeda, H. , 1991, “3-D Neutron Transport Benchmarks,” OECD/NEA Committee on Reactor Physics (NEACRP), Osaka University, Osaka, Japan, Technical Report No. NEACRP-L-330. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/22/085/22085401.pdf
Gelbard, E. M. , 1960, “Application of Spherical Harmonics Method to Reactor Problems,” Bettis Atomic Power Laboratory, West Mifflin, PA, Technical Report No. WAPD-BT-20.
Chao, Y. A. , 2016, “ A New SPN Theory Formulation With Self-Consistent Physical Assumptions on Angular Flux,” Ann. Nucl. Energy, 87(Pt. 2), pp. 137–144. [CrossRef]
Chao, Y. A. , 2016, “ A New and Rigorous SPN Theory for Piecewise Homogeneous Regions,” Ann. Nucl. Energy, 96, pp. 112–125. [CrossRef]
Kim, Y. I. , Kim, Y. J. , and Kim, S. J. , 1999, “ A Semi-Analytic Multigroup Nodal Method,” Ann. Nucl. Energy, 26(8), pp. 699–707. [CrossRef]
Fu, X. D. , and Cao, N. Z. , 2002, “ Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations,” J. Nucl. Sci. Technol., 39(10), pp. 1015–1025. [CrossRef]
Smith, K. S. , 1983, “ Nodal Method Storage Reduction by Nonlinear Iteration,” Trans. Am. Nucl. Soc, 44, pp. 265–266. https://inis.iaea.org/search/search.aspx?orig_q=RN:15010017
Pan, Q. Q. , Lu, H. L. , Li, D. S. , and Wang, K. , 2017, “ A New Nonlinear Iterative Method for SPN Theory,” Ann. Nucl. Energy, 110C, pp. 920–927. [CrossRef]


Grahic Jump Location
Fig. 1

The NLSP3 calculation frame

Grahic Jump Location
Fig. 2

The geometrical structure of the mono-energetic eigenvalue problem

Grahic Jump Location
Fig. 3

Structure of 3D-TAKEDA




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In