[J21] On the use of spherical harmonic approximations in nonclassical particle transport problems

Journal article

Sunday A. Agbo, Leonardo R.C. Moraes, Richard Vasques
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 324, 2024, p. 109048

DOI: 10.1016/j.jqsrt.2024.109048

Cite

APA Click to copy
Agbo, S. A., Moraes, L. R. C., & Vasques, R. (2024). [J21] On the use of spherical harmonic approximations in nonclassical particle transport problems. Journal of Quantitative Spectroscopy and Radiative Transfer, 324, 109048. https://doi.org/10.1016/j.jqsrt.2024.109048

Chicago/Turabian Click to copy
Agbo, Sunday A., Leonardo R.C. Moraes, and Richard Vasques. “[J21] On the Use of Spherical Harmonic Approximations in Nonclassical Particle Transport Problems.” Journal of Quantitative Spectroscopy and Radiative Transfer 324 (2024): 109048.

MLA Click to copy
Agbo, Sunday A., et al. “[J21] On the Use of Spherical Harmonic Approximations in Nonclassical Particle Transport Problems.” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 324, 2024, p. 109048, doi:10.1016/j.jqsrt.2024.109048.

BibTeX Click to copy

@article{sunday2024a,
  title = {[J21] On the use of spherical harmonic approximations in nonclassical particle transport problems},
  year = {2024},
  journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
  pages = {109048},
  volume = {324},
  doi = {10.1016/j.jqsrt.2024.109048},
  author = {Agbo, Sunday A. and Moraes, Leonardo R.C. and Vasques, Richard}
}

ABSTRACT: Presented here is the application of the spherical harmonic expansion to the nonclassical transport equation to derive a system of equations for the nonclassical flux moments, namely nonclassical spherical harmonic approximations (NSHA). The nonclassical transport equation is a recently developed mathematical model that allows the modeling of transport problems wherein the particle flux does not undergo exponential attenuation. We employ a Spectral Approach technique to depict the nonclassical flux by expressing it as a truncated series of Laguerre polynomials with respect to the free-path variable s. This yields a system of equations for the nonclassical flux moments structured similarly to the classical PN equations. We show that the NSHA is reduced to the classical PN equation in a special case. Numerical results for slab-geometry test problems are given to verify the derivation.