SUBJECT: Ph.D. Dissertation Defense
BY: Steven Douglass
TIME: Wednesday, March 28, 2012, 12:00 p.m.
PLACE: Boggs, 3-47
TITLE: Consistent Energy Treatment for Radiation Transport Methods
COMMITTEE: Dr. Farzad Rahnema, Chair (NRE)
Dr. Dingkang Zhang (NRE)
Dr. Bojan Petrovic (NRE)
Dr. Tom Morley (MATH)
Dr. Doron Lubinsky (MATH)


The approximations used in the standard multigroup method and cross section condensation procedure introduce several known errors, such those caused by spectral core environment effects and the neglect of the energy and angular coupling of the flux when condensing the total cross section. In this dissertation, a multigroup formulation is developed which maintains direct consistency with the continuous energy or fine-group structure, exhibiting the accuracy of the detailed energy spectrum within the coarse-group calculation. Two methods are then developed which seek to invert the condensation process – turning the standard one-way condensation (from fine-group to coarse-group) into the first step of a two-way iterative process. The first method is based on the previously published Generalized Energy Condensation, which established a framework for obtaining the finegroup flux by preserving the flux energy spectrum in orthogonal energy expansion functions, but did not maintain a consistent coarse-group formulation. It is demonstrated that with a consistent extension of the GEC, a cross section recondensation scheme can be used to correct for the spectral core environment error. This is then verified numerically in a 1D VHTR core. In addition, a more practical and efficient new method, termed the “Subgroup Decomposition Method,” is developed which eliminates the need for expansion functions altogether, and allows the fine-group flux to be decomposed from a consistent coarse-group flux with minimal additional computation or memory requirements. This method, as a special case of a more general spline-approximation for radiation transport, is shown to be highly effective in a cross section recondensation scheme, providing fine-group results in a fraction of the time generally necessary to obtain a fine-group solution. In addition, a whole-core BWR benchmark problem is generated based on operating reactor parameters, in 2D and 3D. This contributes to the furthering of new methods development from the proof-of-concept level to the whole-core direct 3D transport level. A set of 1D benchmarks is also developed for a BWR, PWR, and VHTR core. These provide significant value both in preliminary testing of the new methods presented in this dissertation and in the future testing of new transport methods.