Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations. (June 2016)

• Record Type: Journal Article
• Authors: Miao, J.; Forget, B.; Smith, K.
• Is Part Of: Annals of nuclear energy. Volume 92(2016:Jun.)
• Page Start: 81
• Page End: 95
• Publication Date: 2016-06
• Subjects: Monte Carlo -- Tally convergence -- Autocorrelation -- Confidence intervals; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2016.01.037
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: Convergence behavior of Monte Carlo eigenvalue simulation was analyzed. Exponential behavior of correlation coefficients was used to predict convergence. Convergence rate asymptotically approaches 1/ N and is independent of generation size. Optimal efficiency and error prefers fewer generations for fixed computational cost. Three statistical methods were compared in determining confidence intervals. Abstract: This paper provides an analysis of the generation-to-generation correlations as observed when solving full core eigenvalue problems on PWR systems. Many studies have in the past looked at the impact of these correlations on reported variance and this paper extends the analysis to the observed convergence rate on the tallies, the effect of tally size and the effect of generation size. Since performing meaningful analysis on such a large problem is inherently difficult, a simple homogeneous reflective cube problem with analytical solution was developed that exhibits similar behavior to the full core PWR benchmark. The data in this problem was selected to match the dimensionality of the reactor problem and preserve the migration length travelled by neutrons. Results demonstrate that the variance will deviate significantly from the 1/ N ( N being the number of simulated particles) convergence rate associated with truly independent generations, but will eventually asymptote to 1/ N after 1000's of generations regardless of the numbers of neutrons per generation. This indicates that optimal run strategies should emphasize lower number of active generations with greater number of neutrons per generation to produce the most accurate tally results. This paper also describes and compares three techniques to evaluate suitable confidence intervals in the presence of correlations, one based on using history statistics, one using generation statistics and one batching generations to reduce batch-to-batch correlation.