Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Delta-form-based method of solving high order spatial discretization schemes for neutron transport

  • Zhou, Xiafeng (Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Zhong, Changming (Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Li, Fu (Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Institute of Nuclear and New Energy Technology, Tsinghua University)
  • Received : 2020.06.08
  • Accepted : 2020.12.29
  • Published : 2021.07.25
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Abstract

Delta-form-based methods for solving high order spatial discretization schemes are introduced into the reactor SN transport equation. Due to the nature of the delta-form, the final numerical accuracy only depends on the residuals on the right side of the discrete equations and have nothing to do with the parts on the left side. Therefore, various high order spatial discretization methods can be easily adopted for only the transport term on the right side of the discrete equations. Then the simplest step or other robust schemes can be adopted to discretize the increment on the left hand side to ensure the good iterative convergence. The delta-form framework makes the sweeping and iterative strategies of various high order spatial discretization methods be completely the same with those of the traditional SN codes, only by adding the residuals into the source terms. In this paper, the flux limiter method and weighted essentially non-oscillatory scheme are used for the verification purpose to only show the advantages of the introduction of delta-form-based solving methods and other high order spatial discretization methods can be also easily extended to solve the SN transport equations. Numerical solutions indicate the correctness and effectiveness of delta-form-based solving method.

Keywords

Acknowledgement

This research is supported by the National Natural Science Foundation of China (12005073), the National Key R&D Program of China (2018YFE0180900), Science and Technology on Reactor System Design Technology Laboratory Foundation Project (HT-KFKT-10-2018005), Key Laboratory Foundation Project of Advanced Reactor Engineering and Safety of Ministry of Education (ARES-2018-07).

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