Date of Award

2025

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Area of Concentration

Applied Mathematics

Abstract

This thesis presents a deterministic numerical solver for the Generalized Linear Boltzmann Equation (GLBE), a model that describes nonclassical neutral particle transport in heterogeneous media with spatially correlated structures [6, 10]. In such media, the classical assumption of exponentially distributed free paths fails, necessitating a formulation that explicitly accounts for the distance s traveled since the last collision. The proposed method approximates the angular flux using a spectral expansion in generalized Laguerre polynomials over the free-path variable s, discretizes the angular domain using the discrete ordinates (SN) method [8], and applies a diamonddifference scheme for spatial discretization. The resulting system of coupled spectral moment equations is lower-triangular and is efficiently solved via Gauss–Seidel iteration, which preserves angular causality. Benchmark comparisons with reference solutions from Moraes et al. [9] demonstrate accurate scalar flux predictions with spectral convergence. The method exhibits numerical stability and is extensible to multidimensional domains, anisotropic scattering, and energy-dependent transport models.

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