[P32] The nonclassical simplified P2 and P3 equations with anisotropic scattering

Conference paper

Robert K. Palmer, Richard Vasques
Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC), 2021 Oct, pp. 368-378

DOI: 10.13182/M&C21-33637

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APA Click to copy
Palmer, R. K., & Vasques, R. (2021). [P32] The nonclassical simplified P2 and P3 equations with anisotropic scattering. In Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC) (pp. 368–378). https://doi.org/10.13182/M&C21-33637

Chicago/Turabian Click to copy
Palmer, Robert K., and Richard Vasques. “[P32] The Nonclassical Simplified P2 and P3 Equations with Anisotropic Scattering.” In Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC), 368–378, 2021.

MLA Click to copy
Palmer, Robert K., and Richard Vasques. “[P32] The Nonclassical Simplified P2 and P3 Equations with Anisotropic Scattering.” Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC), 2021, pp. 368–78, doi:10.13182/M&C21-33637.

BibTeX Click to copy

@inproceedings{robert2021a,
  title = {[P32] The nonclassical simplified P2 and P3 equations with anisotropic scattering},
  year = {2021},
  month = oct,
  pages = {368-378},
  doi = {10.13182/M&C21-33637},
  author = {Palmer, Robert K. and Vasques, Richard},
  booktitle = {Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC)},
  month_numeric = {10}
}

ABSTRACT: In classical transport, the locations of scattering centers (atoms, molecules, etc.) are not spatially correlated, and as a result, the distribution of free path lengths of particles which travel through such media is exponential. However, in certain inhomogeneous media, the locations of scattering centers are spatially correlated, leading to a free path length distribution that is not exponential. The theory of nonclassical transport seeks to accurately model particle transport in such nonclassical media. In this nonclassical transport theory, no assumption is made about the shape of the particle’s free path length distribution, and the free path length of the particle is allowed to be an independent variable in the nonclassical transport equation. For diffusive regimes, one can approximate this equation using nonclassical versions of the simplified spherical harmonic equations (SPN). Recently, a novel mathematical method to explicitly derive the nonclassical SPN equations with anisotropic scattering was proposed. In this work, we use this method to explicitly derive the first three of these equations, this being the first time in which nonclassical SP2 and SP3 equations with anisotropic scattering are given. These equations are generalizations of previous results, and can be shown to reduce to their nonclassical counterparts with isotropic scattering and to their classical counterparts with anisotropic scattering. The nonclassical SPN equations with anisotropic scattering are then expressed in modified forms so that vacuum boundary conditions can be applied. Finally, these modified equations are validated numerically in slab geometry, showing that they become more accurate as the system becomes more diffusive.