Deterministic Truncation of the Monte Carlo Transport Solution for Reactor Eigenvalue and Pinwise Power Distribution

Abstract

This paper presents a systematic way to truncate the high-fidelity Monte Carlo (MC) solution to reduce the computational cost without compromising the essential reliability of the solution. Based on the fine-mesh finite difference (FMFD) acceleration for the MC analysis, the deterministic truncation of the Monte Carlo (DTMC) solution method is developed and investigated for a systematic approximation to the MC solution of the reactor eigenvalue problem. This deterministic solution is used for the acceleration of the MC simulation as well as the solution prediction itself. The concept, motivations, and challenges of the DTMC method are described in detail, and theoretical backgrounds of the FMFD method are discussed. In addition, an unbiased ratio estimator for more accurate FMFD parameter generation and a modified particle ramp-up method for the determination of optimal generation size in the MC simulation are also introduced and explained. Both the C5G7 benchmark and a small modular reactor (SMR) core are analyzed to characterize the numerical performance of the DTMC method in this work. Convergence behavior of the fission source distribution is examined, and reactor parameters such as the multiplication factor and three-dimensional pin power distribution are estimated and compared to the reference solution. The stochastic features of the DTMC solutions are also discussed in terms of the apparent and real standard deviations. For the pin power distribution, the root-mean-square error and relative error for the reactor core are also evaluated and compared. The computing time and figure of merit are compared for each method.