SUBJECT: Ph.D. Dissertation Defense
BY: Gabriel Kooreman
TIME: Monday, October 17, 2016, 11:00 a.m.
PLACE: Boggs, 3-47
TITLE: Iterative Homogenization Method for Improving Computational Efficiency in Solving Eigenvalue Problems in Neutron Transport
COMMITTEE: Dr. Farzad Rahnema, Chair (NRE)
Dr. Bojan Petrovic (NRE)
Dr. Dingkang Zhang (NRE)
Dr. Tom Morley (Math)
Jeffery Densmore (Bettis)


Multiple homogenization techniques for reactor eigenvalue problems in neutron transport have been developed in CRMP lab in recent years. These include several promising methods based on the Consistent Spatial Homogenization (CSH) method which have been developed and implemented in 1-D. More recently, the Diffusion-Transport hybrid Homogenization (DTH) method and its enhanced version have been developed. Neither method nor any of their extensions have as of yet been implemented in two or three dimensions. This work will continue to improve the CSH and DTH methods, and will implement the methods to solve 2-D transport eigenvalue equation for large-scale reactor benchmark problems. Both the CSH and DTH methods involve iterative homogenization of the neutron transport equation with an auxiliary source term used to correct for the heterogeneity of the problem. The homogenization process allows simple implementation of low-order acceleration, and the iterative re-homogenization allows for the full heterogeneous solutions to be computed with very little loss of accuracy compared to purely high-order transport methods. The novelty of this work will come from its implementation in higher dimensionality as well as significant improvements to the spatial and angular variable approximations used in the method. These changes should result in significant and continued improvements to both the accuracy and the computational efficiency of the method.