LAUSR

Abstract Although diffusion theory is still the most widely applied deterministic method in reactor physics calculations, due to the increasing complexity of material composition and geometric structures in today's reactor design, and as a result of rapid development of computational technologies, neutronics codes based on higher-order transport approximations and advanced numerical approaches are becoming widespread. One promising alternative of diffusion theory is the simplified spherical harmonics (SPN) method. Since Gelbard heuristically proposed an approximate form of the multidimensional spherical harmonics equations, firm theoretical substantiation and – quite recently – generalization of the theory have been elaborated, thus several neutron physics code are being developed based on its application. In this paper, semi-analytical solutions of the steady-state, one-group SP3 equations are presented for homogeneous slab, cylindrical and spherical geometries assuming up to third-order scattering anisotropy. The developed methods are applied for preliminary verification of a finite-element-based SP3 solver developed by the authors.