On October 25, 2021, Jiahao Chen successfully defended his PhD dissertation, A Novel Fission Diffusion Synthetic Acceleration Method for Criticality Calculations. Jiahao’s committee consisted of his advisor, Jason Hou, and members, Kostadin Ivanov, Dmitriy Anistratov, Zhilin Li.

Abstract

CHEN, JIAHAO. A Novel Fission Diffusion Synthetic Acceleration Method for Criticality Calculations. (Under the advisement of Dr. Jason Hou.)A wide selection of deterministic and stochastic methods have been developed to conduct criticality calculations and to improve the efficiency of these methods, a branch of neutronics method research focuses on the acceleration of source convergence process which is solved with power iteration method. These acceleration schemes have a history almost as long as the deterministic methods themselves with different levels of versatility. With the increasing popularity of Monte Carlo methods, the so-called hybrid neutronics methods have been introduced for the same purpose, though these hybrid neutronics methods, because of the characteristics of Monte Carlo methods on both theory and algorithmic levels, demonstrate unique performance and behaviors.

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is proposed in this work for the acceleration of source convergence process in both deterministic and stochastic methods which utilize the power iteration method. This method is based on the previous work on a similar topic with several modifications to improve the convergence stability and application range. A multigroup one-dimensional derivation of the novel FDSA method is developed and numerically tested with both one-group and multigroup cases to prove its feasibility. Further, comparisons against contemporary acceleration methods, both theoretically and numerically, are made in order to better evaluate the performance of the novel FDSA method in the same cases.

The FDSA method is then implemented in a hybrid neutronics solver with the intention to achieve source convergence acceleration and variance reduction in Monte Carlo simulations. As an extension to the numerical tests, a series of Monte Carlo simulations with continuous energy cross section are conducted with the hybrid solvers, the results of which demonstrate that the source convergence could be immediately attained with the FDSA feedback to the high order transport calculations. The speedup in source convergence ranges from 10 to 20 times faster than the original Monte Carlo simulations for both simple homogeneous slab and complex C5G7 full core geometry, while the acceleration in power iterations for deterministic methods is about 60% to 10 times faster. As for variance reduction, MC-FDSA is also competitive to MC-CMFD and is shown to reduce the real variance in fission source by up to 20%. Overall the proposed MC-FDSA method is proved to be successful in accelerating power iteration and source convergence acceleration, and reducing variance in Monte Carlo methods.