FINITE ELEMENT LINEAR DISCONTINUOUS METHOD WITH SPECTRAL-NODAL APPROXIMATION FOR ONE-SPEED DIFFUSION EIGENVALUE PROBLEMS

摘要

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. One of the mathematical models that allow us to describe this physical phenomenon is the neutron diffusion equation, a simple model that provides accurate results for the distribution of neutron flux and the effective coefficient of multiplication. This paper presents a new hybrid formulation to solve eigenvalue problems of neutron diffusion in one-dimensional domains and one-speed approximation. This formulation combines the Finite Element Linear Discontinuous Method, considered an intermediate mesh method, with the Spectral-Nodal 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 hybrid 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.