Correlation diagnosis method for heterogeneous Monte Carlo eigenvalue simulations based on a diffusion approximation. (August 2019) - Miao, Jilang; Forget, Benoit; Smith, Kord
Highlights: Quick correlation estimation was developed for Monte Carlo eigenvalue simulations. Exact solution of correlation coefficients was derived for homogeneous 1D transport problems. Solution on homogeneous 3D problems was derived by diffusion approximation. Solution on heterogeneous problems was approximated by homogenization preserving migration area. Predictive accuracy was verified on the 2D BEAVRS benchmark. Abstract: This paper presents a predictive model of the correlation level present in tally regions of any mesh size without requiring extensive high accuracy discrete tallies. This model provides a quick indication of the accuracy of the variance estimated from uncorrelated statistics. The prediction is developed from the generalization of the Multitype Branching Processes (MBP) model to a continuous space and solving correlation coefficients (and thus variance correction factors) exactly in an equivalent homogeneous problem. The real heterogeneous problem is homogenized in a way that preserves neutron migration area. Correlation coefficients and the asymptotic variance underestimation ratio of the homogenized problem provide a rough estimate of the correlations observed in the real heterogeneous problem for a given tally region size.