[P40] P1 synthetic acceleration and convergence analysis for the solution of one-speed nonclassical spectral SN equations in slab geometry

Conference paper

Alan S. Silva, Leonardo R.C. Moraes, Ricardo C. Barros, Richard Vasques
Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada, 2023 Aug

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APA Click to copy
Silva, A. S., Moraes, L. R. C., Barros, R. C., & Vasques, R. (2023). [P40] P1 synthetic acceleration and convergence analysis for the solution of one-speed nonclassical spectral SN equations in slab geometry. In Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada.

Chicago/Turabian Click to copy
Silva, Alan S., Leonardo R.C. Moraes, Ricardo C. Barros, and Richard Vasques. “[P40] P1 Synthetic Acceleration and Convergence Analysis for the Solution of One-Speed Nonclassical Spectral SN Equations in Slab Geometry.” In Proceedings of International Conference on Mathematics &Amp; Computational Methods Applied to Nuclear Science &Amp; Engineering, Niagara Falls, Canada, 2023.

MLA Click to copy
Silva, Alan S., et al. “[P40] P1 Synthetic Acceleration and Convergence Analysis for the Solution of One-Speed Nonclassical Spectral SN Equations in Slab Geometry.” Proceedings of International Conference on Mathematics &Amp; Computational Methods Applied to Nuclear Science &Amp; Engineering, Niagara Falls, Canada, 2023.

BibTeX Click to copy

@inproceedings{alan2023a,
  title = {[P40] P1 synthetic acceleration and convergence analysis for the solution of one-speed nonclassical spectral SN equations in slab geometry},
  year = {2023},
  month = aug,
  journal = {Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada},
  author = {Silva, Alan S. and Moraes, Leonardo R.C. and Barros, Ricardo C. and Vasques, Richard},
  month_numeric = {8}
}

ABSTRACT: In classical transport theory, the distribution of free-path lengths of particles traveling through the 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. This has motivated the derivation of a generalized transport theory, also referred to as nonclassical transport, in which no assumption is made about the shape of the particle’s free-path length distribution. In nonclassical transport, the free-path length of the particle is an independent variable in the (generalized) nonclassical transport equation. Recently, a Spectral Approach (SA) was introduced to deal with the free-path dependency on the nonclassical transport equation. In the SA, the nonclassical angular flux is represented as a truncated Laguerre series in the free-path variable. As an outcome, this representation generates a system of equations that have the form of classical transport equations. In this work, we use a synthetic acceleration scheme to speed up the iteration algorithm for the solution of the one-speed nonclassical spectral equations in the discrete ordinates formulation. The results of our numerical experiments indicate that the synthetic acceleration scheme is effective in reducing the number of iterations needed to obtain an accurate solution.