A heterogeneous finite element method in diffusion theory

Abstract

A new Heterogeneous Finite Element Method (HFEM) is presented, which does not require prior assembly-level homogenization and which accounts for the leakage effect. The HFEM is developed in diffusion theory. The method is a Lagrange Finite Element Method, that uses basis functions that include fine mesh detail. The elementary basis functions are generated from fixed-boundary-flux fine mesh heterogeneous assembly calculations. The FEM equations are generated using a Galerkin scheme derived from a variational principle. The method is tested on three two-dimensional configurations typical of Boiling Water Reactors, and is shown to be as accurate as the combination Assembly Homogenization—Nodal Method for low-leakage cores and significantly more accurate than the mentioned combination for high-leakage cores