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

TL;DR

This paper derives simplified P$_N$ equations for nonclassical transport with isotropic scattering, enabling easier implementation and validation through numerical results in a one-dimensional system.

Contribution

It introduces nonclassical SP$_N$ equations derived via asymptotic analysis, bridging nonclassical and classical transport models with practical implementation benefits.

Findings

The nonclassical SP$_N$ equations reduce to classical P$_N$ equations under classical assumptions.

Numerical results validate the theoretical predictions in a 1D random periodic system.

The equations can be reformulated into a classical form with modified parameters.

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.