Hybrid Monte Carlo-CMFD Methods for Accelerating Fission Source Convergence

Abstract

In this paper, two modifications to improve the efficiency of Lee et al.’s recently proposed “CMFD [coarse-mesh finite difference]-accelerated Monte Carlo” method for neutron criticality problems are presented and tested. This CMFD method employs standard Monte Carlo techniques to estimate nonlinear functionals (ratios of integrals), which are used in low-order CMFD equations to obtain the eigenvalue and discrete representations of the eigenfunction. In a “feedback” procedure, the Monte Carlo fission source is then modified to match the resulting CMFD fission source. The proposed new methods differ from the CMFD-accelerated Monte Carlo method only in the definition of the nonlinear functionals. The new methods are compared with the CMFD-accelerated Monte Carlo method for two high-dominance-ratio test problems. All of the hybrid methods rapidly converge the Monte Carlo fission source, enabling a large reduction in the number of inactive cycles. However, the new methods stabilize the fission source more efficiently than the CMFD-accelerated Monte Carlo method, enabling a reduction in the number of active cycles as well. Also, in all the hybrid methods, the apparent variance of the eigenfunction is nearly equal to the real variance, so the real statistical error is well estimated from a single calculation. This is a major advantage over the standard Monte Carlo method, in which the real variance is typically underestimated due to intercycle correlations.