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Unified Formulation of Nodal Expansion Method and Analytic Nodal Method Solutions to Two-Group Diffusion Equations

Hyun Chul Lee, Chang Hyo Kim

Nuclear Science and Engineering

Volume 138 / Number 2 / June 2001 / Pages 192-204


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This paper demonstrates that the analytic nodal method (ANM) solution to two-group (2-G) diffusion equations can be formulated in the same way as the nodal expansion method (NEM) solution, and thereby, the two most popular transverse integrated nodal method formulations can be integrated into a unified nodal method (UNM) formulation. For this purpose, the analytic solution, i.e., the combined homogeneous and particular solution, of transverse-integrated one-dimensional, 2-G diffusion equations is represented by an expansion of analytic basis functions while the expansion coefficients are obtained in the same way as the NEM. The advantages of the UNM formulation are then discussed. It is a stable method in itself so that it does not require approximate schemes to avoid the instability at the near-critical nodes. Because it does not introduce any approximate scheme in conjunction with the stability questions at the near-critical nodes, it is more accurate than the conventional ANM formulation in the case where the latter needs to introduce approximations. It is readily incorporated into a number of existing NEM production codes. These advantages are demonstrated in terms of numerical solutions of Nuclear Energy Agency Committee on Reactor Physics pressurized water reactor benchmark problems.

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