Three dimensional heterogeneous finite element method for static multi-group neutron diffusion

Abstract

Because current full-core neutronic-calculations use two-group neutron diffusion and rely on homogenizing fuel assemblies, reconstructing pin powers from such a calculation is an elaborate and not very accurate process; one which becomes more difficult with increased core heterogeneity. A three-dimensional Heterogeneous Finite Element Method (HFEM) is developed to address the limitations of current methods by offering fine-group energy representation and fuel-pin-level spatial detail at modest computational cost. The calculational cost of the method is roughly equal to the calculational cost of the Finite Differences Method (FDM) using one mesh box per fuel assembly and a comparable number of energy groups. Pin-level fluxes are directly obtained from the method’s results without the need for reconstruction schemes.