American Nuclear Society

Home / Store / Journals / Electronic Articles / Nuclear Science and Engineering / Volume 141 / Number 3 / Pages 218-235

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

Makoto Tsuiki, Sverre Hval

Nuclear Science and Engineering / Volume 141 / Number 3 / Pages 218-235

July 2002


Member Price:$27.00
Member Savings:$3.00

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.

Questions or comments about the site? Contact the ANS Webmaster.