High-Order Finite Difference Nodal Method for Neutron Diffusion Equation

Abstract

A nodal method has been developed which accurately and rapidly solves the three-dimensional neutron diffusion equation in both Cartesian and hexagonal geometries. To reduce the number of unknowns in comparison with the interface current method in favor of short computation time and a small computer memory requirement, this method employs the finite difference method (FDM) as its global neutron balance solution method. In the global neutron balance solution, the coupling coefficients are modified in such a way as to conserve the nodal interface neutron currents which are obtained by a local neutron balance solution method fit to each geometry. To validate the method developed here, it has been applied to neutron diffusion calculations for reactor cores, typical of Cartesian and hexagonal geometries, with different core sizes, assembly pitches, core configurations, control rod patterns, etc. For a large FBR (hexagonal geometry), for example, errors in power distribution and control rod worth by the method are less than 1/2 and 1/10, respectively, compared to an ordinary FBR core design method, while the computation time is 1/8 that of the latter method.