Three-Dimensional Discrete Heterogeneous Finite Element Method and Code for Static Multi‐Group Neutron Diffusion

Abstract

Accurate prediction of the neutron flux and power at the fuel pin level rather than at the fuel- assembly level requires, in principle, lengthy many-group transport-theory calculations using a detailed (fuel-pin level) geometrical representation of the core. Many-group fine-mesh diffusion theory, in conjunction with advanced fuel-pin-cell homogenization techniques, can also be used successfully to predict individual fuel pin powers but the computational effort is still sizeable because of the many regions and groups involved. A three dimensional diffusion code was developed which reduces the time taken by such full-core fine-mesh fine-group diffusion calculations by applying the finite-element method to the discrete form of the many-group fine- mesh diffusion equation and thus reducing the number of unknowns. Preliminary tests performed on a highly-heterogeneous three dimensional three-group model found the code to produce pin power results with a maximum error of 3.5% of the maximum pin power value, with an eight-fold reduction in computational time compared to a regular full-core fine-mesh calculation.