New Finite Element Solution Technique for Neutron Diffusion Equations

Abstract

A new, finite element solution technique for neutron diffusion equations has been developed. In this method, calculational accuracy is improved by adding imaginary nodal points, subdividing each triangular element into three quadrilateral subelements, and approximating the spatial variation of neutron flux within each element by three linear planes. In the process of solving the algebraic equations, the additional unknown variables are eliminated so that the number of unknowns remains the same as that in the usual finite element method. This technique has been applied to two types of one-group neutron diffusion equations to test its accuracy. It has been shown that the method yields the same degree of accuracy, in eigenvalues and neutron flux distributions, as the usual finite element method when four times as many elements are used. Under the same degree of accuracy, the computing time of the new method is about 1/4 that of the usual method.