[J13] A spectral approach for solving the nonclassical transport equation
Richard Vasques, Leonardo R. C. Moraes, Ricardo Carvalho de Barros, Rachel N. Slaybaugh
Journal of Computational Physics, vol. 402(109078), 2020 Feb
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.
Vasques, R., Moraes, L. R. C., de Barros, R. C., & Slaybaugh, R. N. (2020). [J13] A spectral approach for solving the nonclassical transport equation. Journal of Computational Physics, 402(109078).
Vasques, Richard, Leonardo R. C. Moraes, Ricardo Carvalho de Barros, and Rachel N. Slaybaugh. “[J13] A Spectral Approach for Solving the Nonclassical Transport Equation.” Journal of Computational Physics 402, no. 109078 (February 2020).
Vasques, Richard, et al. “[J13] A Spectral Approach for Solving the Nonclassical Transport Equation.” Journal of Computational Physics, vol. 402, no. 109078, Feb. 2020.