A spectral approach for solving the nonclassical transport equation

•We derive a mathematical approach to solve the nonclassical transport equation.•We use spectral methods to represent the nonclassical flux as Laguerre polynomials.•We show that the nonclassical equations can be solved using traditional methods.•We present numerical results in slab geometry for homo...

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Bibliographic Details
Published in:Journal of computational physics 2020-02, Vol.402, p.109078, Article 109078
Main Authors: Vasques, R., Moraes, L.R.C., Barros, R.C., Slaybaugh, R.N.
Format: Article
Language:English
Subjects:
Computational physics
Discrete ordinates
Distribution functions
Mathematical analysis
Nonclassical transport
Polynomials
Random media
Slab geometry
Spectra
Spectral method
Spectral methods
Transport equations
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Summary:•We derive a mathematical approach to solve the nonclassical transport equation.•We use spectral methods to represent the nonclassical flux as Laguerre polynomials.•We show that the nonclassical equations can be solved using traditional methods.•We present numerical results in slab geometry for homogeneous and random systems. 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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.109078