Ph.D. Thesis Defense by Michael Scott McKinley
Wednesday, December 13, 2000

(Dr. Farzad Rahnema, advisor)

"Higher-Order Boundary Condition Perturbation Methods in Transport and Diffusion Theory"

Abstract

Perturbation techniques are frequently used in reactor physics to derive a formalism for a slightly changed problem that is easier and faster to compute than resolving the original problem with just a slight change. The perturbations can be a small change in the operators, boundary or the boundary condition. Most work in boundary condition perturbation has focused on first-order perturbation theory for reactor physics applications.

Higher-order theory can greatly improve the accuracy of computed eigenvalues, functionals, and the solution to the system. Predicting the state of the system better, a higher-order theory can more accurately estimate homogenization parameters based on the flux shape. In addition, it allows for a more accurate discontinuity factor for use in equivalence theory.

The goal of this research has been to develop a higher-order perturbation technique in diffusion and transport theory. In diffusion theory, analytical and numerical examples will be provided to validate the theory. However, in transport theory, several numerical examples will demonstrate the validity of the higher-order theory. Numerical methods specific to the applications of this theory will be discussed in detail. Also, a nodal code that uses homogenization parameters and discontinuity factors that are corrected by this theory has been developed in monoenergetic, one-dimensional diffusion theory.