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Nonlinear Analytic and Semi-Analytic Nodal Methods for Multigroup Neutron Diffusion Calculations

Two advanced nodal methods for the solution of the multigroup neutron diffusion equations are developed, using the nonlinear coarse-mesh finite difference (CMFD) scheme. Based on the analytic and semi-analytic methods, the relationships between the flux and current on the nodal surface are derived, by which the two-node problem is formulated in an efficient way. The issue of the complex eigenmodes and the instability problem inherent in the analytic solution are considered in order to have an efficient and stable algorithm. The numerical results demonstrate the effectiveness of the two methods.