Parallel, hierarchical solution algorithms for diffusion synthetic Acceleration of the neutron transport equation

Abstract

The ability to obtain fast and accurate solutions of the neutron transport equation is of great importance for various reactor physics and radiation shielding applications. This thesis first presents an overview of the techniques used to solve the neutron transport equation using discontinuous Galerkin finite element methods. It then presents two sets of techniques which aim to improve the effectiveness of a neutron transport code and provides various computational results to support their effectiveness.

The first methods studied are two preconditioners designed to accelerate the solution of the neutron diffusion equation which in turn is used to accelerate the neutron transport equation using diffusion synthetic acceleration. They are first presented in a form appropriate for solving finite element problems using first-order basis functions, and then expanded so that they may be used on problems containing second and higher-order basis functions. The second study is for sets of basis functions for pyramid finite elements used in the solution of neutron transport and neutron diffusion problems, demonstrating the effectiveness of these elements in comparison to other element types.

This thesis provides substantial evidence for the effectiveness of the methods described alongside an analysis of where their use is appropriate. Numerous computational examples are used, including several reactor physics and radiation shielding benchmark problems obtained from benchmark specifications. These serve to demonstrate the strengths and in some cases the weaknesses of the techniques presented. The methods presented have significant practical applications in the fields of reactor physics and radiation shielding.