SUBJECT: Ph.D. Dissertation Defense
BY: Christopher Edgar
TIME: Thursday, July 9, 2015, 10:00 a.m.
PLACE: Boggs, 3-39
TITLE: An Adaptive Runge-Kutta-Fehlberg Method for Time-Dependent Discrete Ordinate Transport
COMMITTEE: Dr. Farzad Rahnema, Chair (NRE)
Dr. Glenn Sjoden (AFTAC)
Dr. Alireza Haghighat (Vigringia Tech, NRE)
Dr. Bojan Petrovic (NRE)
Dr. Ce Yi (NRE)
Dr. Mark Costello (AE)


The major emphasis of this research focuses on the development and implementation of time-dependent transport solution optimization methods for discrete ordinates (Sn) form of the transport equation. A 1-D Discrete Ordinates transport solver was be produced, which functions in both steady-state and time-dependent modes, including the effects of delayed neutron. The time-dependent transport equation is be solved by coupling the standard source iteration used in steady state transport codes for the spatial domain, with an adaptive Runge–Kutta–Fehlberg (RKF) method for the time domain in an iterative sequence. This allows the code to automatically select the minimum time step required for a convergent solution on each time step, before the time step is actually performed on the global solution space. Furthermore it allows one to solve the explicit form of the time-dependent transport equation, which is generally avoided due to the possibility of non-convergent solutions with fixed time steps. Lastly, the expansion of the RKF solver is also automatically optimized, allowing for a lower order time domain expansion in areas where the solution is well behaved in the time domain.