A nodal method for the solution of the static, few-group diffusion equations in hexagonal geometry

Many of the nodal methods that have been devised have been formulated only for reactor cores that have Cartesian geometry. Several reactors, such as LMFBR's, HTGR's and HWR's, however, have cores with hexagonal geometry. The objective of this research is to develop a nodal method which can be applied to these hexagonal cores. Beginning with the steady-state Boltzmann transport equation, formally exact few-group nodal equations are derived by the introduction of correction factors (called ''discontinuity factor''). These equations have the same mathematical form as mesh-centered finite-difference equations and are shown to converge to the exact solution of the diffusion equation in the limit of very fine mesh spacing. The accuracy of the nodal method is determined for cell-sized and seven-hex, patch-sized nodes by the analysis of a benchmark problem. For the cell-sized nodes the method is shown to calculate the eigenvalue within 0.14% and the node-average power within 1.4%. The use of patch-sized nodes, however, results in limited accuracy in the analysis of the benchmark problem. This is attributed to the small size of the benchmark core. The results indicate that the hexagonal nodal method does have potential for accurate and efficient analysis of reactor cores