[J14] Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering

Journal article

Robert K. Palmer, Richard Vasques
Journal of Computational and Theoretical Transport, vol. 49(7), 2020 Sep, pp. 331-348

DOI: 10.1080/23324309.2020.1816552

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APA Click to copy
Palmer, R. K., & Vasques, R. (2020). [J14] Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering. Journal of Computational and Theoretical Transport, 49(7), 331–348. https://doi.org/10.1080/23324309.2020.1816552

Chicago/Turabian Click to copy
Palmer, Robert K., and Richard Vasques. “[J14] Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering.” Journal of Computational and Theoretical Transport 49, no. 7 (September 2020): 331–348.

MLA Click to copy
Palmer, Robert K., and Richard Vasques. “[J14] Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering.” Journal of Computational and Theoretical Transport, vol. 49, no. 7, Sept. 2020, pp. 331–48, doi:10.1080/23324309.2020.1816552.

BibTeX Click to copy

@article{robert2020a,
  title = {[J14] Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering},
  year = {2020},
  month = sep,
  issue = {7},
  journal = {Journal of Computational and Theoretical Transport},
  pages = {331-348},
  volume = {49},
  doi = {10.1080/23324309.2020.1816552},
  author = {Palmer, Robert K. and Vasques, Richard},
  month_numeric = {9}
}

ABSTRACT: In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.