A Time-Dependent Method of Characteristics Formulation with Time Derivative Propagation.

We developed a new time-dependent neutron transport method for nuclear reactor kinetics using method of characteristics (MOC) with angular flux time derivative propagation. In contrast to conventional time integration methods which use local finite difference approximations to treat the time derivative, the new method solves for the spatially-dependent angular flux time derivative by propagation along characteristics in space. This results in the angular flux time derivative being recast in terms of the neutron source time derivatives, and thus the new method is called Source Derivative Propagation (SDP). We developed three SDP methods using different approximations, and they require much less memory than the conventional methods. For SDP, we approximate the source derivatives using backward differences. This is analogous to the backward differentiation formula (BDF), and our results confirmed that the high-order SDP approximations reproduced the high-order angular flux derivative approximation of equivalent order BDF. We assessed SDP by comparison to conventional time-dependent MOC methods. This included both a reference method (RBDC) which stored the angular flux and a popular approximate method (IBDC). We performed error analysis for SDP, RBDC, and IBDC. This informed the refinement of the SDP methods, and clarified when SDP will be accurate. We tested SDP using the computer code DeCART, which was used to model three transients based on the TWIGL and C5G7 benchmarks. A fine time step reference solution was generated using RBDC. The SDP methods converged to the reference when the time step was refined and the BDF order increased. In addition, we observed that SDP accurately replicated the RBDC solution when the same time step and BDF order was used. This indicates that the propagated angular flux time derivative of SDP reproduced the RBDC angular flux derivative. SDP was much more accurate than the IBDC. We assessed the efficiency of SDP by comparing the run-time and memory requirements to RBDC and IBDC. SDP required slightly more memory and run-time than IBDC, but much less memory than RBDC. Our results demonstrate that, for the problems tested, SDP can efficiently and accurately solve the time-dependent transport equation for reactor kinetics without excessive memory.PhDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102321/1/adamhoff_1.pd