Comparing the 1st and 2nd moment approaches to variance reduction in Monte Carlo: Two examples

• Published in: Annals of nuclear energy Vol. 186; p. 109745
• Main Author: Burn, K.W.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15-06-2023
• Subjects: Direct Statistical Approach; Eigenvalue calculation; First moment; Importance; Monte Carlo; Second moment; Variance reduction; Importance; First moment; Second moment; Eigenvalue calculation; Monte Carlo; Direct Statistical Approach; Variance reduction
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2023.109745

•The employment of the adjoint flux to execute variance reduction in Monte Carlo is evaluated.•Variance reduction with the adjoint flux is benchmarked against a method based on the 2nd moment.•The variance reduction is made within a reactor core eigenvalue calculation.•Two test problems, both containing an activation cross-section with high, nattow resonances, based on the VERA computation benchmark are used.•Differences in the figure-of-merit of factors of 50 and 7 respectively are observed.
Variance reduction in Monte Carlo particle transport calculations nearly always relies on the generation of information based on the first moment (viz. the adjoint flux or importance). In this paper we revisit the question of the non-optimal nature of this approach. Whilst it has already been shown to be deficient in duct streaming problems, we look at another kind of problem, namely the activation of nuclides whose cross-sections contain resonances. As a benchmark a second moment-based approach that gives near-optimum results is employed. We find important differences in efficiency between the first and second-moment-based approaches. Some discussion is made on the reasons for these differences.