On the use of spherical harmonic approximations in nonclassical particle transport problems

Abstract

Presented here is the application of the spherical harmonic expansion to the nonclassical transport equation to derive a system of equations for the nonclassical flux moments, namely nonclassical spherical harmonic approximations (NSHA). The nonclassical transport equation is a recently developed mathematical model that allows the modeling of transport problems wherein the particle flux does not undergo exponential attenuation. We employ a Spectral Approach technique to depict the nonclassical flux by expressing it as a truncated series of Laguerre polynomials with respect to the free-path variable s. This yields a system of equations for the nonclassical flux moments structured similarly to the classical PN equations. We show that the NSHA is reduced to the classical PN equation in a special case. Numerical results for slab-geometry test problems are given to verify the derivation.