Application of ‘natural coordinate system’ in the finite element solution of multigroup neutron diffusion equation

Abstract

A simple method of generating stiffness matrices for the solution of multigroup diffusion equation by ‘natural coordinate system’ has been presented. A comparative study has been made using triangular elements with linear model, triangular elements with quadratic model and rectangular elements with bilinear model to demonstrate their relative efficiencies. The quadratic interpolation model has been shown to be superior to linear and bilinear models with respect to computing time, computer storage and relative error in K eff for a two group diffusion example. The flexibility of the finite element treatment has been demonstrated by the calculation of the reactivity of a partially inserted control rod. Good agreement has been obtained with a perturbation calculation.