Transient method of characteristics via the Adiabatic, Theta, and Multigrid Amplitude Function methods

Abstract

In this thesis, we investigated the Adiabatic, Theta, and Multigrid Amplitude Function (MAF) methods for solving the Method of Characteristics (MOC) formulation of the time-dependent neutron transport equation. The transient transport versions of the 2D LRA and C5G7 benchmarks were used to assess the performance and accuracy of these methods. We began by deriving the CMFD-accelerated MOC algorithm in 2D steady state form and examining the effects of various MOC and CMFD parameters on eigenvalue convergence. The C5G7 problem showed similar acceleration performance for 2, 4, and 7 CMFD energy group structures. CMFD meshes at or near the pin-cell level resulted in the greatest speedups of 15-45x in run time and 30-240 x in number of MOC iterations for both problems. A relaxation factor on the nonlinear diffusion coefficient was required to maintain stability for both problems with optimum values between 0.4-0.7. A sensitivity study was conducted on the C5G7 and LRA transient problems to understand the effects of time step and spatial mesh sizes on the solution accuracy and run time performance. The shape function time step size had a large effect on the solution accuracy for the MAF and Theta methods in solving the LRA problem. All methods showed moderate sensitivity to the amplitude function step size, where increasing step size shifted the peak power to earlier times. The coarse mesh size did not have a significant effect on solution accuracy, but meshes on the pin-cell level were clearly preferred to reduce run time. The overall run time performance between the three methods was mixed. The MAF and Theta methods displayed ~84% speedup over the Adiabatic method for the LRA problem, but all methods had similar run times for the C5G7 problem. This inconsistency is likely due to the more drastic flux shape change during the LRA transient and the ability of the MAF and Theta methods to more accurately treat the flux shape temporal derivative. These results demonstrate that the Adiabatic, Theta, and MAF methods are computationally efficient methods for solving the time-dependent neutron transport equation and warrant further investigation. There are clear advantages to each method and the optimal method will likely depend on the transient characteristics of the problem being studied.