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.
Highlights
Population growth and economic development require the continuous increase of electricity generation capacity
The formulation proposed in this work combines the linear approximation of Finite Element Method (FEM) method with a quasi-analytic approach of Spectral Green’s Function Nodal Methods (SGF) to solve neutron diffusion eigenvalue problems in slab geometry and one energy group
We presented in this work a hybrid formulation to solve the one-dimensional neutron diffusion equation in multiplying media and one energy group
Summary
Population growth and economic development require the continuous increase of electricity generation capacity. 174 FEM-SGF FOR NEUTRON DIFFUSION IN MULTIPLYING MEDIA control of the neutron population in the reactor For this reason, during the design and operation of nuclear plants, we need accurate and efficient numerical methods to assess the neutron flux distribution and the effective multiplication factor. The formulation proposed in this work combines the linear approximation of FEM method with a quasi-analytic approach of SGF to solve neutron diffusion eigenvalue problems in slab geometry and one energy group. The combination of these methods aims to generate accurate results with high computational performance, preserving the analytical spectral solutions inside the elements.
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