A Spectral Approach for Solving the Nonclassical Transport Equation

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.

arXiv comment25 pages, 6 figures, 4 tables

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Cited by in corpus (2)

• On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry
• An improved spectral approach for solving the nonclassical neutron particle transport equation