Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Variational nodal methods for neutron transport: 40 years in review

  • Zhang, Tengfei (School of Mechanical Engineering, Shanghai Jiao Tong University) ;
  • Li, Zhipeng (CAEP Software Centre for High Performance Numerical Simulation)
  • Received : 2022.02.05
  • Accepted : 2022.04.18
  • Published : 2022.09.25
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Abstract

The variational nodal method for solving the neutron transport equation has evolved over 40 years. Based on a functional form of the Boltzmann neutron transport equation, the method now comprises a complete set of variants that can be employed for different problems. This paper presents an extensive review of the development of the variational nodal method. The emphasis is on summarizing the whole theoretical system rather than validating the methodologies. The paper covers the variational nodal formulation of the Boltzmann neutron transport equation, the Ritz procedure for various application purposes, the derivation of boundary conditions, the extension for adjoint and perturbation calculations, and treatments for anisotropic scattering sources. Acceleration approaches for constructing response matrices and solving the resulting system of algebraic equations are also presented.

Keywords

Acknowledgement

This research was supported by the National Natural Science Foundation of China (NSFC) [12175138, 11805122].

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