Multigroup form of simplified spherical harmonics (SPN) equations for neutron transport

Abstract

SPN equations offer an attractive and superior alternative to standard diffusion approximation of neutron transport equation. From the standpoint of numerical solvers, SPN equations significantly reduce the computational cost as compared to solving full PN equations. This makes it more appealing for analysis of advanced reactor designs. Recently, we have reported the mathematically consistent derivation of second order differential form of SPN equations utilizing the trial function proposed by Pomraning. We also improved the conventional SPN model by deriving appropriate interface and boundary conditions. Further, we formally demonstrated that the new SPN model is identical to the zeroth layer of newly proposed GSPN model. However, the mathematical framework established so far was restricted to one speed neutrons. In the current work, we extend our SPN model to multigroup transport formalism. We also derive the relevant interface and boundary conditions.