Banner image placeholder
Banner image

Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering


Ph.D. thesis


Robert K. Palmer
Richard Vasques (Advisor), Ph.D. in Nuclear Engineering, The Ohio State University, Columbus, OH, 2020 Aug

Dissertation Robert K. Palmer
Cite

Cite

APA   Click to copy
Palmer, R. K. (2020, August). Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering (PhD thesis). (R. V. (Advisor), Ed.), Ph.D. in Nuclear Engineering. The Ohio State University, Columbus, OH.


Chicago/Turabian   Click to copy
Palmer, Robert K. “Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering.” Edited by Richard Vasques (Advisor). Ph.D. in Nuclear Engineering. PhD thesis, The Ohio State University, 2020.


MLA   Click to copy
Palmer, Robert K. “Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering.” Ph.D. in Nuclear Engineering, edited by Richard Vasques (Advisor), The Ohio State University, Aug. 2020.


BibTeX   Click to copy

@phdthesis{robert2020a,
  title = {Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering},
  year = {2020},
  month = aug,
  address = {Columbus, OH},
  journal = {Ph.D. in Nuclear Engineering},
  school = {The Ohio State University},
  author = {Palmer, Robert K.},
  editor = {(Advisor), Richard Vasques},
  month_numeric = {8}
}

Dr. Robert Palmer
ABSTRACT: 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.


Translate to