Abstract
Abstract A 2-D multi-group nodal diffusion code is developed. The code is formulated based on Nodal Green’s Function Method together with coarse mesh finite difference method (CMFD), which is coupling with nodal averaged fluxes as unknowns. The code is applicable in either rectangle geometry or hexagonal geometry with arbitrary prompt neutron groups. For hexagonal geometry, singular terms arise from the transverse integration procedure. Wagner’s approximation is applied, which omits these terms and then, following Fitzpatrick and Ougouag, we compensate for the omitted terms through rigorous nodal balance equations. There are two different coupling methods used in this code development. One is traditionally 1-D coupling, which is achieved by spatial sweeping through a set of 1-D equation systems. Another is full-scale coupling, which is achieved by using multi-dimensional nodal balance equation to couple all the spatial nodes. Therefore, a “sweep-free” algorithm is formed. Transient calculations routine is further developed for rectangle geometry and slab geometry. Backward difference method was used to approximate the time derivative terms in space-time kinetic equations. Several benchmark problems have been performed. All the results agree well with results of other codes in the literatures.