Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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An hp-angular adaptivity with the discrete ordinates method for Boltzmann transport equation

  • Ni Dai (School of Nuclear Science and Engineering, North China Electric Power University) ;
  • Bin Zhang (School of Nuclear Science and Engineering, North China Electric Power University) ;
  • Xinyu Wang (School of Nuclear Science and Engineering, North China Electric Power University) ;
  • Daogang Lu (School of Nuclear Science and Engineering, North China Electric Power University) ;
  • Yixue Chen (School of Nuclear Science and Engineering, North China Electric Power University)
  • Received : 2022.06.08
  • Accepted : 2022.10.19
  • Published : 2023.02.25
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Abstract

This paper describes an hp-angular adaptivity algorithm in the discrete ordinates method for Boltzmann transport applications with strong angular effects. This adaptivity uses discontinuous finite element quadrature sets with different degrees, which updates both angular mesh and the degree of the underlying discontinuous finite element basis functions, allowing different angular local refinement to be applied in space. The regular and goal-based error metrics are considered in this algorithm to locate some regions to be refined. A mapping algorithm derived by moment conservation is developed to pass the angular solution between spatial regions with different quadrature sets. The proposed method is applied to some test problems that demonstrate the ability of this hp-angular adaptivity to resolve complex fluxes with relatively few angular unknowns. Results illustrate that a reduction to approximately 1/50 in quadrature ordinates for a given accuracy compared with uniform angular discretization. This method therefore offers a highly efficient angular adaptivity for investigating difficult particle transport problems.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (11975097).

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