2016/10/14 by Richard Vasques, R. Vasques, Vasques, R. +3 · 5 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Asymptotic analysis #Computer science #Convection–diffusion equation #Differential equation #Diffusion #FOS: Physical sciences #Isotropy #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Nuclear Theory (nucl-th) #Nuclear reactor physics and engineering #Numerical methods in inverse problems #Physics #Quantum mechanics #Scattering #Set (abstract data type) #Simultaneous equations #math-ph #math.MP #nucl-th
paper · pdf · doi:10.48550/arxiv.1610.04314
published in arXiv (Cornell University) (Cornell University) · 24 pages, 1 figure, to appear in Proceedings of M&C2017: Int. Conf. on Mathematics & Computational Methods Applied to Nuclear Science & Engineering
openalex publication_date 2016/10/14 · openalex created_date 2016/10/28 · arxiv created 2017/02/09 · arxiv updated 2017/02/10 · openalex updated_date 2026/08/05
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 PN equations under the assumption of classical transport, and therefore are labeled nonclassical SPN equations. In addition, the nonclassical SPN equations can be manipulated into a classical form with modified parameters, which can be implemented in existing SPN codes. Numerical results are presented for an one-dimensional random periodic system, validating the theoretical predictions.