Simplified P${}_N$ Equations for Nonclassical Transport with Isotropic Scattering

Abstract

An asymptotic analysis is used to derive a set of diffusion approximations to the nonclassical transport equation with isotropic scattering. These approximations are shown to reduce to the simplified P${}_N$ equations under the assumption of classical transport, and therefore are labeled nonclassical SP${}_N$ equations. In addition, the nonclassical SP${}_N$ equations can be manipulated into a classical form with modified parameters, which can be implemented in existing SP${}_N$ codes. Numerical results are presented for an one-dimensional random periodic system, validating the theoretical predictions.

Comments: 24 pages, 1 figure, to appear in Proceedings of M&C2017: Int. Conf. on Mathematics & Computational Methods Applied to Nuclear Science & Engineering