Numerical qualification of the GSP₃⁽⁰⁾ theory using the analytic function expansion nodal method

Shanghai Nuclear Engineering Research & Design Institute Co., Ltd., Shanghai 200233, China

^* Corresponding author: shijun2@snerdi.com.cn

Published online: 15 October 2024

Abstract

The simplified P₃ (SP₃) method is an important way to implement the pin-by-pin neutron transport calculation of the core. This method has the high accuracy but costs twice the computing time of the diffusion method. Recently, the Generalized SP_N (GSP_N) theory has been developed, and the ad hoc SP_N theory is resolved through rigorous theoretical derivation. GSP₃⁽⁰⁾ theory is the 3^rd order and the 0^th layer of GSPN theory. Compared with GSP₃⁽⁰⁾ theory, the SP₃ theory with Marshak boundary condition is regarded as the traditional SP₃ theory. The equations of the two theories are the same while the interface and the boundary conditions are different. Based on the GSP₃⁽⁰⁾ theory and the traditional SP₃ theory, transport calculation codes have been developed using the analytical function expansion nodal (AFEN) method. The numerical results show that both of the two SP₃ theories are more accurate than the diffusion theory, and the GSP₃⁽⁰⁾ theory can further improve the accuracy of the pin power calculation compared to the traditional SP₃ theory.