[J24] On the application of the Nystrom method to two-dimensional neutral particle transport problems in heterogeneous media


Journal article


Gustavo A. Lorensi, Leonardo R.C. Moraes, Richard Vasques, Esequia Sauter, Fabio S. Azevedo
Nuclear Science and Engineering, 2024


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Cite

APA   Click to copy
Lorensi, G. A., Moraes, L. R. C., Vasques, R., Sauter, E., & Azevedo, F. S. (2024). [J24] On the application of the Nystrom method to two-dimensional neutral particle transport problems in heterogeneous media. Nuclear Science and Engineering. https://doi.org/10.1080/00295639.2024.2342498


Chicago/Turabian   Click to copy
Lorensi, Gustavo A., Leonardo R.C. Moraes, Richard Vasques, Esequia Sauter, and Fabio S. Azevedo. “[J24] On the Application of the NystrOm Method to Two-Dimensional Neutral Particle Transport Problems in Heterogeneous Media.” Nuclear Science and Engineering (2024).


MLA   Click to copy
Lorensi, Gustavo A., et al. “[J24] On the Application of the NystrOm Method to Two-Dimensional Neutral Particle Transport Problems in Heterogeneous Media.” Nuclear Science and Engineering, 2024, doi:10.1080/00295639.2024.2342498.


BibTeX   Click to copy

@article{gustavo2024a,
  title = {[J24] On the application of the Nystrom method to two-dimensional neutral particle transport problems in heterogeneous media},
  year = {2024},
  journal = {Nuclear Science and Engineering},
  doi = {10.1080/00295639.2024.2342498},
  author = {Lorensi, Gustavo A. and Moraes, Leonardo R.C. and Vasques, Richard and Sauter, Esequia and Azevedo, Fabio S.}
}

ABSTRACT:  Over time, several methods were developed to deal with neutral particle transport problems. The interest in these problems is related to their wide range of applications, from neutron transport and heat transfer in nuclear reactors to radiative transfer in atmospheric clouds. Unlike the discrete ordinates or discrete ordinates–like methods, integral methods do not require discretization of angular variables. Instead, angular variables are completely eliminated by an integration procedure over the solid angle, which allows elimination of the ray effect. That said, this paper presents a new approach to estimate the scalar flux in two dimensional fixed-source neutron transport problems in a heterogeneous medium, considering isotropic scattering and vacuum and reflective boundary conditions. Here, the Nyström method is combined with the singularity-subtraction technique to present an integral formulation for the scalar flux in a mesh grid over all regions of the domain. The iterative method of the Neumann series is used as an alternative to direct methods to solve the resulting system of equations generated from the domain discretization. Numerical results are given to verify the offered method.

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