[J14] A spectral approach for solving the nonclassical transport equation

Journal article

Richard Vasques, Leonardo R. C. Moraes, Ricardo Carvalho de Barros, Rachel N. Slaybaugh
Journal of Computational Physics, vol. 402(-), 2020, p. 109078

DOI: 10.1016/j.jcp.2019.109078

View PDF

Cite

APA Click to copy
Vasques, R., Moraes, L. R. C., de Barros, R. C., & Slaybaugh, R. N. (2020). [J14] A spectral approach for solving the nonclassical transport equation. Journal of Computational Physics, 402(-), 109078. https://doi.org/10.1016/j.jcp.2019.109078

Chicago/Turabian Click to copy
Vasques, Richard, Leonardo R. C. Moraes, Ricardo Carvalho de Barros, and Rachel N. Slaybaugh. “[J14] A Spectral Approach for Solving the Nonclassical Transport Equation.” Journal of Computational Physics 402, no. - (2020): 109078.

MLA Click to copy
Vasques, Richard, et al. “[J14] A Spectral Approach for Solving the Nonclassical Transport Equation.” Journal of Computational Physics, vol. 402, no. -, 2020, p. 109078, doi:10.1016/j.jcp.2019.109078.

BibTeX Click to copy

@article{richard2020a,
  title = {[J14] A spectral approach for solving the nonclassical transport equation},
  year = {2020},
  issue = {-},
  journal = {Journal of Computational Physics},
  pages = {109078},
  volume = {402},
  doi = {10.1016/j.jcp.2019.109078},
  author = {Vasques, Richard and Moraes, Leonardo R. C. and de Barros, Ricardo Carvalho and Slaybaugh, Rachel N.}
}

ABSTRACT: This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths between scattering centers is nonexponential. We use a spectral method to represent the nonclassical flux as a series of Laguerre polynomials in the free-path variable s, resulting in a nonclassical equation that has the form of a classical transport equation. We present numerical results that validate the spectral approach, considering transport in slab geometry for both classical and nonclassical problems in the discrete ordinates formulation.