Development of the 3D SP$_{N}$ transport solver KANECS for nuclear reactor analysis

For practical reactor analysis, a low-order transport approximation such as simplified spherical harmonics (SPN) has become widely used due to its improved accuracy over diffusion and lower computational cost compared to spherical harmonics (PN) and discrete-ordinate (SN) methods. This paper introduces and verifies KANECS, a new neutronic solver that employs the SPN approximation and continuous Galerkin finite-element method (CGFEM) for angular and spatial discretization respectively, to solve the 3D steady-state multigroup neutron transport equation in Cartesian geometry. For the numerical verification, the KAIST and C5G7 benchmarks were selected. The results show that KANECS predicts with promising accuracy the keff and power distribution, fairly close to the ones of transport approach. Consequently, KANECS demonstrates that it can effectively perform a pin-by-pin core analysis.