Nodal synthetic kernel (N-SKN) method for solving neutron transport equation in one- and two-dimensional X–Y geometries

Abstract

In this study, a nodal method based on the synthetic kernel (SKN) approximation is presented for solving the neutron transport equation in one- and two-dimensional cartesian geometries. The two-dimensional neutron transport equation for a node is transformed to one-dimensional transport equation based on the face-averaged scalar flux and the current. At the node interfaces, DP1 expansion is employed to the surface angular fluxes in conjunction with isotropic angular dependence of the transverse leakage term. The one-dimensional integral transport equation is obtained in terms of the node-face-averaged incoming/outgoing neutron flux and the currents. The synthetic kernel approximation is employed to the transport kernels and nodal-face contributions. The resulting SKN equations are solved analytically. One-dimensional interface-coupling nodal SK1 and SK2 equations (incoming/outgoing flux and current) are derived for the small nodal-mesh limit. These equations have simple recursive forms which do not pose burden on either the memory or the computational time. The method was applied to one- and two-dimensional benchmark problems and compared with the solutions obtained with nodal integral method.