Finite Element Method with Spectral Green's Function in Slab Geometry for Neutron Diffusion in Multiplying Media and One Energy Group

Authors

  • Rogério Vinícius Matos Rocha State University of Santa Cruz
  • Dany Sanchez Dominguez State University of Santa Cruz
  • Susana Marrero Iglesias State University of Santa Cruz
  • Ricardo Carvalho de Barros State University of Rio de Janeiro

DOI:

https://doi.org/10.5540/tema.2016.017.02.0173

Keywords:

Eigenvalue problems, Neutron diffusion equation, Spectral Green's Function.

Abstract

The physical phenomenon of neutrons transport associated with eigenvalue problems appears in the criticality calculations of nuclear reactors and can be treated as a diffusion process. This paper presents a new method to solve eigenvalue problems of neutron diffusion in slab geometry and one energy group. This formulation combines the Finite Element Method, considered an intermediate mesh method, with the Spectral Green's Function Method, which is free of truncation errors, and it is considered a coarse mesh method. The novelty of this formulation is to approach the spatial moments of the neutron flux distribution by the first-order polynomials obtained from the spectral analysis of diffusion equation. The approximations provided by the new formulation allow obtaining accurate results in coarse mesh calculations. To validate the method, we compare the results obtained with the methods described in the literature, specifically the Diamond Difference method. The accuracy and the computational performance of the proposed formulation were characterized by solving benchmarks problems with a high degree of heterogeneity.

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Published

2016-09-04

How to Cite

Rocha, R. V. M., Dominguez, D. S., Iglesias, S. M., & Barros, R. C. de. (2016). Finite Element Method with Spectral Green’s Function in Slab Geometry for Neutron Diffusion in Multiplying Media and One Energy Group. Trends in Computational and Applied Mathematics, 17(2), 173. https://doi.org/10.5540/tema.2016.017.02.0173

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Original Article