A modal ACMFD formulation of the HEXNEM3 method for solving the time-dependent neutron diffusion equation

Abstract

An analytical coarse-mesh finite-difference (ACMFD) formulation of the HEXNEM3 nodal flux expansion method for solving the two-group neutron diffusion equation in hexagonal-z geometry is developed. In the time-dependent case, where an implicit differencing scheme in time is required for stability, nodal flux expansion necessitates iterating on the group sources. In order to avoid convergence issues, modal decomposition through matrix diagonalisation in the energy domain is first performed, and then the HEXNEM3 nodal expansion model is applied to the modes instead of fluxes, with boundary and continuity conditions on the scalar flux and the net current. The ACMFD formulation of HEXNEM3 has the advantage to produce an explicit non-homogeneous linear algebraic system for either the node-averaged fluxes or modes in all groups and nodes of a three-dimensional problem, with a free choice of any appropriate solution method.