A CMFD formulation of the HEXNEM3 method for solving the neutron diffusion equation through modal decomposition

Abstract

A CMFD (Coarse-Mesh-Finite-Difference) formulation of the HEXNEM3 nodal flux expansion method for solving the neutron transport equation in two-group diffusion approximation is developed. One- and two-dimensional versions are created which are then used to solve three-dimensional problems through transverse integration. The CMFD formulation is constructed directly for the node-averaged scalar fluxes. The resulting balance equations are cast in the standard form of a nonhomogeneous system of linear algebraic equations, with a full freedom of choosing an appropriate solution method. The modal decomposition, i.e. matrix diagonalization in the energy domain, is applied mainly to avoid source iteration when solving time-dependent problems through an implicit scheme, i.e. backward differencing in time.