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.

arXiv comment24 pages, 1 figure, to appear in Proceedings of M&C2017: Int. Conf. on Mathematics & Computational Methods Applied to Nuclear Science & Engineering

References in corpus (1)

• Non-classical transport with angular-dependent path-length distributions. 2: Application to pebble bed reactor cores

Cited by in corpus (2)

• A Spectral Approach for Solving the Nonclassical Transport Equation
• Asymptotic Derivation of the Simplified $P_N$ Equations for Nonclassical Transport with Anisotropic Scattering