A Steady-State Nonlinear Analytic Nodal Method for Two-Group Multi-Dimensional Neutron Diffusion Calculations

A Cartesian geometry steady-state nonlinear analytic nodal method for solving two-group multi-dimensional neutron diffusion equation is described. The method incorporated into a code NODAN is developed based on the nonlinear iteration technique and the analytic nodal method (ANM). The method uses low-order coarse-mesh finite difference method (CMFD) as global solution method, and uses coupling correction factors to modify the coupling relationships in the low-order approximation. The coupling correction factors are determined by the analytic solution of the two-node problems, and are updated periodically as the calculation proceeds so as to cause the CMFD surface-averaged current values to match those of the high-order solution. A stabilization technique is developed to resolve the numerical instability problem that might be encountered in the two-node ANM calculations for near-critical nodes. This nonlinear method, combined with effective numerical method and the stabilization technique, provides an efficient algorithm for solving the nodal equations. The NODAN method is applied to several two- and three-dimensional light water reactor (LWR) benchmark problems. The numerical results demonstrate that this method can yield accurate results with considerably smaller computational expense than that required by a conventional transverse-integration nodal method NEMC.