Solving the static-neutron diffusion equation in 2D-Cartesian geometry with Lagrange interpolation

• The 2D-static neutron diffusion equation was solved with Lagrange polynomial (LAP).
• No variational principle was used in the development of the LAP algorithms.
• The progressive polynomial approximation was used in the LAP algorithms.
• The LAP algorithms showed better accuracy than a finite difference method.

Cell centered (LAPc) and cell edge (LAPe) algorithms were developed to solve the static neutron diffusion equation in 2D Cartesian geometry using Lagrange interpolation with the progressive polynomial approximation. Two benchmark problems were used to test the algorithms: the two-group TWIGL problem and a one-group IAEA benchmark problem. The LAP algorithms showed to be more accurate than a finite difference method (FDM) and for about the same level of accuracy, the LAP numerical methods have an efficiency advantage because they have to solve for less number of unknowns. The LAP algorithms showed more sensitivity to the mesh size than what QUANDRY results showed. Even though the FDMs algorithm, for the calculation of keff, showed systematically to be less accurate than QUANDRY, LAPc, and that LAPe, it was the only one that did not produce negative flux in any location for all the mesh structures analyzed in the IAEA problem. Other variants of the Lagrange interpolation polynomial did not show systematically good reliability and/or accuracy.