A Time-dependent Slice Balance Method for High-fidelity Radiation Transport Computations

ACKNOWLEDGEMENTS I would like to truly thank all of my committee members for their encouragement and guidance in the preparation of this thesis. I especially want to express my gratitude to Dr. Kevin Clarno for his insight and assistance. My advisor, Dr. Cassiano de Oliveira, has been immensely helpful with his continuous encouragement and unique perspectives. Perhaps most of all, I want to thank Beth for her neverending love and support. A general finite difference discretization of the time-dependent radiation transport equation is developed around the framework of an existing steady-state three dimensional radiation transport solver based on the slice-balance approach. Three related algorithms are outlined within the general finite difference scheme: an explicit, an implicit, and a semi-implicit approach. The three algorithms are analyzed with respect to the discretizations of each element of the phase space in the transport solver. The explicit method, despite its small computational cost per time step, is found to be unsuitable for many purposes due to its inability to accurately handle rapidly varying solutions. The semi-implicit method is shown to produce results nearly as reliable as the fully implicit solver, while requiring significantly less computational effort.