Sub-plane scheme for a radial transport and axial diffusion code

The SANM solution, a new transverse leakage approximation and a sub-plane scheme are introduced to the axial solver of the DeCART code to improve the solution accuracy and to obtain the nodal solutions efficiently, and their solutions are examined for a demonstrative problem of Ref. 2 and the C5G7MOX 3-D extension benchmark problems. The proposed transverse leakage scheme determines the three expansion coefficients of the second-order approximation by using the three intra-nodal sub-node fluxes, and it shows a good performance for improving the accuracy of the nodal solution when compared with the conventional scheme. The SANM solutions using the proposed transverse leakage approximation are shown to be much more accurate than the NEM solutions. The sub-plane scheme in which multiple sub-planes are introduced within a thick MOC plane and share the equivalence parameters determined for a thick MOC plane shows a very good efficiency in that it produces as accurate solutions as the conventional multi MOC planes scheme but it requires a slightly more computational burden than the one sub-plane per MOC plane case. In the demonstrative problem, the SANM calculation with the proposed transverse leakage approximation and using three sub-planes per MOC plane shows less than 6 pcm eigenvalue and 0.7 % power errors. In the C5G7MOX benchmark problem, the SANM calculation with the proposed transverse leakage approximation and using three sub-planes per MOC plane also shows a good performance by reducing a large eigenvalue and the pin power errors to a trivial error level of less than 5 pcm eigenvalue and 0.1 % power errors. Therefore, it is concluded that the SANM calculation with the proposed transverse leakage approximation and introducing a few sub-planes is very effective in obtaining a very accurate solution efficiently.