A Variational Nodal Expansion Method for the Solution of Multigroup Neutron Diffusion Equations with Heterogeneous Nodes

A new nodal diffusion method for the neutronics analysis of light water reactor cores has been developed. The method is based on an expansion of neutron fluxes within a node into a series of functions that are numerically obtained from single-assembly calculations without the process of assembly homogenization. The assembly heterogeneity effect can be taken into account in whole-core calculations in a consistent way with the heterogeneous single-assembly calculations, providing highly accurate results including intranodal pin-power distributions. The expansion coefficients are determined by a classical Ritz procedure in such a way that the solution becomes the most accurate - in the least squares sense - approximation to the exact solution. The present method was implemented in a two-dimensional nodal diffusion code and tested for benchmark cases both for boiling water reactors and pressurized water reactors. The root-mean-square errors of both node average powers and nodal maximum pin powers were observed to be <1%, with computing time of less than a few percent of the reference, fine-mesh calculation. It was also observed that the accuracy of the present method could be improved to almost any desired degree only by increasing the order of expansion polynomials.