Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering

Bibliographic Details
Main Author: Palmer, Robert K.
Language:English
Published: The Ohio State University / OhioLINK 2020
Subjects:
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1594397838852992
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu15943978388529922021-08-03T07:15:41Z Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering Palmer, Robert K. Nuclear Engineering nonclassical transport diffusion anisotropic scattering Levy motion SPN equations Many systems in which nonclassical particle transport occurs are best modeled as stochastic systems in which the physical nature of the medium at any specific location is not known precisely, but is predicted by a probability. Many stochastic transport media can be modeled as diffusive systems, which are optically thick and in which particle scattering is the dominant particle interaction. In such diffusive systems, a diffusion equation can accurately model particle transport. The simplified spherical harmonic equations, or SPN equations, are diffusion equations which were created as multi-dimensional analogues to the slab geometry spherical harmonic equations, or PN equations, and the SPN equations are easier to solve in higher dimensions than the PN equations. SPN equations which can model classical transport with anisotropic scattering have been derived, and SPN equations which can model nonclassical transport with isotropic scattering have also been determined. Therefore, SPN equations which can model nonclassical transport with anisotropic scattering are needed. This work describes the development of a method which can explicitly derive the nonclassical SPN equations with anisotropic scattering. The first three of these equations are explicitly derived, and then they are shown to reduce to their nonclassical isotropic and classical anisotropic counterparts. The nonclassical SPN equations with anisotropic scattering are then expressed in modified forms so that vacuum boundary conditions can be applied. Finally, these equations are validated numerically in slab geometry, showing that they become more accurate as the system becomes more diffusive. 2020-11-13 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1594397838852992 http://rave.ohiolink.edu/etdc/view?acc_num=osu1594397838852992 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Nuclear Engineering
nonclassical transport
diffusion
anisotropic scattering
Levy motion
SPN equations
spellingShingle Nuclear Engineering
nonclassical transport
diffusion
anisotropic scattering
Levy motion
SPN equations
Palmer, Robert K.
Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
author Palmer, Robert K.
author_facet Palmer, Robert K.
author_sort Palmer, Robert K.
title Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
title_short Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
title_full Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
title_fullStr Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
title_full_unstemmed Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
title_sort asymptotic derivation of the simplified pn equations for nonclassical transport with anisotropic scattering
publisher The Ohio State University / OhioLINK
publishDate 2020
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1594397838852992
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