Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering
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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. |
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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 |
work_keys_str_mv |
AT palmerrobertk asymptoticderivationofthesimplifiedpnequationsfornonclassicaltransportwithanisotropicscattering |
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1719457575768948736 |