Acceleration methods for Monte Carlo particle transport simulations

Abstract

Performing nuclear reactor core physics analysis is a crucial step in the process of both designing and understanding nuclear power reactors. Advancements in the nuclear industry demand more accurate and detailed results from reactor analysis. Monte Carlo (MC) eigenvalue neutron transport methods are uniquely qualified to provide these results, due to their accurate treatment of space, angle, and energy dependencies of neutron distributions. Monte Carlo eigenvalue simulations are, however, challenging, because they must resolve the fission source distribution and accumulate sufficient tally statistics, resulting in prohibitive run times. This thesis proposes the Low Order Operator (LOO) acceleration method to reduce the run time challenge, and provides analyses to support its use for full-scale reactor simulations. LOO is implemented in the continuous energy Monte Carlo code, OpenMC, and tested in 2D PWR benchmarks. The Low Order Operator (LOO) acceleration method is a deterministic transport method based on the Method of Characteristics. Similar to Coarse Mesh Finite Difference (CMFD), the other acceleration method evaluated in this thesis, LOO parameters are constructed from Monte Carlo tallies. The solutions to the LOO equations are then used to update Monte Carlo fission sources. This thesis deploys independent simulations to rigorously assess LOO, CMFD, and unaccelerated Monte Carlo, simulating up to a quarter of a trillion neutron histories for each simulation. Analysis and performance models are developed to address two aspects of the Monte Carlo run time challenge. First, this thesis demonstrates that acceleration methods can reduce the vast number of neutron histories required to converge the fission source distribution before tallies can be accumulated. Second, the slow convergence of tally statistics is improved with the acceleration methods for the earlier active cycles. A theoretical model is developed to explain the observed behaviors and predict convergence rates. Finally, numerical results and theoretical models shed light on the selection of optimal simulation parameters such that a desired statistical uncertainty can be achieved with minimum neutron histories. This thesis demonstrates that the conventional wisdom (e.g., maximizing the number of cycles rather than the number of neutrons per cycle) in performing unaccelerated MC simulations can be improved simply by using more optimal parameters. LOO acceleration provides reduction of a factor of at least 2.2 in neutron histories, compared to the unaccelerated Monte Carlo scheme, and the CPU time and memory overhead associated with LOO are small.