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 , 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.
Cite
@article{arxiv.1812.04811,
title = {A Spectral Approach for Solving the Nonclassical Transport Equation},
author = {R. Vasques and L. R. C. Moraes and R. C. Barros and R. N. Slaybaugh},
journal= {arXiv preprint arXiv:1812.04811},
year = {2020}
}
Comments
25 pages, 6 figures, 4 tables