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.

An improved spectral approach for solving the nonclassical neutron particle transport equation

“…In this work we described a simple and useful modification of the spectral approach [4] used for solving nonclassical transport problems in a deterministic fashion. This modification, in some cases, allows the decrease of the truncation order M of the Laguerre series used to represent the nonclassical angular flux, as we presented in the previous section.…”

“…The nonclassical transport theory has received increasing attention in the last few years, being applied in a number of different areas, including nuclear engineering [2] and computer graphics [3]. Recently, in the work [4], a mathematical approach that allows one to solve Eq. (1.1a) in a deterministic fashion was first described.…”

“…where M is the truncation order for the Laguerre series and L m (s) is the Laguerre polynomial of degree m. The function ψ m (x, Ω) is the solution of the equation [4]…”

“…Bearing this in mind, we describe in Section 2 a simple and useful modification of the Spectral Approach [4]. In the present modified SA we slightly change the representation of Ψ (Eq.…”

On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

“…Recently, a spectral method has been developed [11] to represent the nonclassical angular flux as a series of Laguerre polynomials in s. This method produces a system of equations that have the form of classical transport equations and can therefore be solved by current deterministic algorithms. In short, we define ψ such that Ψ(x, Ω, s) ≡ ψ(x, Ω, s)e − s 0 Σt(Ω,s )ds ,…”