The HEXNEM3 nodal flux expansion method for the hexagonal geometry in the code DYN3D

Abstract

This paper describes the derivation of the nodal flux expansion method HEXNEM3, its implementation into the nodal diffusion code DYN3D and the corresponding testing versus benchmarks. As in the earlier versions of expansion method HEXNEM1 and HEXNEM2, the neutron flux in a hexagonal node is expanded into superposition of orthogonal polynomials and exponential functions. The main difference of the HEXNEM3 method is the additional use of tangentially weighted exponential functions and the coupling of neighboring nodes by tangentially weighted fluxes and currents on node surfaces.The HEXNEM3 method was tested in several benchmark problems, including numerical benchmarks with given cross sections set and reference solutions by fine-mesh finite difference diffusion and a real plant benchmark with Monte Carlo reference solution. The test results demonstrate good agreement with reference solutions and improvement of method accuracy in comparison with HEXNEM1 and HEXNEM2.