Systematic derivation of GSP3(0) equations, its discretization using GTIN method and development of a switchable SP3 to GSP3(0) neutron transport solver

Abstract

The Generalized Simplified Spherical Harmonics (GSP_N) method has drawn recent interest owing to the fact that theoretically, it is equivalent to the P_N and does not rely on any assumption other than piecewise homogeneity. Its level wise approach to P_N offers an agreeable balance between the accuracy and computational efficiency making it a valuable mathematical tool for analyzing neutron transport problems pertaining to nuclear engineering and reactor physics. The lowest level approximation for N = 3, expressed as ${\text{GSP}}_3^{\left(0\right)}$, offers reducing the complexity while still capturing the essential physics. In the current work, ${\text{GSP}}_3^{\left(0\right)}$ equations are derived along with the interface and boundary conditions for linear anisotropic scattering. These equations are then discretized using the generalized transverse integration nodal method for a two-dimensional system of piecewise homogeneous rectangular regions. The discretization is done with an option kept for reducing the ${\text{GSP}}_3^{\left(0\right)}$ formalism to the conventional SP₃. Subsequently, a computer code has been developed to solve these discretized equations in the multigroup structure for vacuum, reflective or albedo boundaries. At present, this switchable SP₃/${\text{GSP}}_3^{\left(0\right)}$ code has the capability of estimating k-eigenvalue and position dependent scalar neutron flux within a given two-dimensional rectangular geometry. The code has been verified by solving SP₃, ${\text{GSP}}_3^{\left(0\right)}$ and other benchmark problems from available literature. The results obtained from our code demonstrate that ${\text{GSP}}_3^{\left(0\right)}$ is superior to the conventional SP₃ and comparable to the recently proposed SDP_N (N = 1,2,3) [M. Nazari, A. Zolfaghari, M. Abbasi, Prog. Nucl. Energy, 2023; 166, 104,933] in terms of accuracy as well as computation time.