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Enhanced finite difference scheme for the neutron diffusion equation using the importance function

Vagheian, M ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1016/j.anucene.2016.06.031
  3. Publisher: Elsevier Ltd , 2016
  4. Abstract:
  5. Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient. © 2016 Elsevier Ltd
  6. Keywords:
  7. Adjoint calculations ; Box scheme ; Enhanced finite difference method ; Neutron importance function ; Boiling water reactors ; Diffusion ; Eigenvalues and eigenfunctions ; Mesh generation ; Neutron flux ; Neutrons ; Partial differential equations ; Adjoints ; Bench-mark problems ; Box schemes ; Effective multiplication factor ; Finite difference scheme ; Finitedifference methods (FDM) ; Importance functions ; Neutron diffusion equations ; Finite difference method
  8. Source: Annals of Nuclear Energy ; Volume 96 , 2016 , Pages 412-421 ; 03064549 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0306454916304716