Convergence characteristics and acceleration of the transient fixed source equation solved by Monte Carlo method

Abstract

The safety analysis of nuclear systems such as nuclear reactors requires transient calculation. The Monte Carlo (MC) method has grown rapidly in recent years because of its high-fidelity modelling and simulation capability. The predictor-corrector quasi-static (PCQS) MC method has been investigated for kinetic calculation. However, the approach to shorten the computational time required to solve the transient fixed source equation (TFSE) is still under development. The convergence characteristic of the neutron source iteration algorithm of the PCQS MC method is analyzed in this study with a simplified model. It is found that the convergence rate of the iteration algorithm is governed by the effective spectral radius (ESR). The lower the ESR is, the faster the convergence is. In order to reduce the ESR, the asymptotic superhistory method (ASM) is developed for the PCQS MC method in the RMC code. The performance of ASM is evaluated by the C5G7-TD benchmark. Results show that the reduction in the number of inactive cycles is more than 85%, and over 15% of computational time including active cycles is saved. It is demonstrated how ASM speeds up the iterations using the Wasserstein distance measure.