Computation of standard deviations in Eigenvalue calculations

Gelbard, E.M.; Prael, R.E.

doi:10.1016/0149-1970(90)90041-3

Cited by 45 publications

(28 citation statements)

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“…Recent results with MC21 [11] indicate that the batching method of Prael and Gelbard [22] may remedy this problem.…”

Section: Discussionmentioning

confidence: 99%

“…Ueki [21] introduced the term apparent variance, which is the expected value of the sample variance of the mean, and derived an expression for the bias in the apparent variance, which is simply the difference between the true variance and the apparent variance. This has been a longstanding problem [21][22][23][24][25][26] for two decades but more attention has been placed on this issue in recent years as numerous groups continue to develop and enhance their Monte Carlo codes for full core analysis. Brown [25,26] reported ratios of real to apparent standard deviations in assembly powers (2D full core PWR) that approached a factor of 5.…”

Section: Apparent Versus True Variancementioning

confidence: 99%

“…To address this issue, the "batching" method has been examined with MC21 [11]. This method, suggested two decades ago by Gelbard and Prael [22], combines successive generations into batches and tallies are accumulated for these batches rather than for generations. The idea is that batches of generations will not be as correlated as generations.…”

Section: Apparent Versus True Variancementioning

confidence: 99%

See 2 more Smart Citations

Challenges and Prospects for Whole-Core Monte Carlo Analysis

Martin¹

2012

Nuclear Engineering and Technology

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“…Recent results with MC21 [11] indicate that the batching method of Prael and Gelbard [22] may remedy this problem.…”

Section: Discussionmentioning

confidence: 99%

Section: Apparent Versus True Variancementioning

confidence: 99%

Section: Apparent Versus True Variancementioning

confidence: 99%

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Challenges and Prospects for Whole-Core Monte Carlo Analysis

Martin¹

2012

Nuclear Engineering and Technology

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“…These algorithms can apply in continuous-energy Monte Carlo simulations as well as multigroup Monte Carlo simulations. Additionally, as several studies have found that the correlation of fission source between cycles may cause underestimation of variance of k eff and fluxes (Gelbard and Prael, 1990), the differences in estimation of variance of k eff and kinetic parameters among different algorithms were compared.…”

Section: Introductionmentioning

confidence: 99%

Calculation of adjoint-weighted kinetic parameters with the reactor Monte Carlo code RMC

Qiu

Wang

et al. 2017

Progress in Nuclear Energy

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a b s t r a c tIn this work, the capability of computing adjoint-weighted kinetic parameters, including effective delayed neutron fraction and neutron generation time, was implemented in the Reactor Monte Carlo (RMC) code based on the iterated fission probability (IFP) method. Three algorithms, namely, the NonOverlapping Blocks (NOB) algorithm, the Multiple Overlapping Blocks (MOB) algorithm and the superhistory algorithm, were implemented in RMC to investigate their accuracy, computational efficiency and estimation of variance. The algorithms and capability of computing kinetic parameters in RMC were verified and validated by comparison with MCNP6 as well as experimental results through a set of multigroup problems and continuous-energy problems.

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“…One method of minimizing the correlation between successive tallies is by combining multiple successive fission cycles into batches, and defining the tally variables over the batches rather than over the cycles. 7) Here, an estimate of the dominance ratio obtained during the inactive cycle phase of the calculation is helpful in automatically determining the number of cycles per batch to use during the active cycle phase.…”

mentioning

confidence: 99%

On-the-Fly Monte Carlo Dominance Ratio Calculation Using the Noise Propagation Matrix

Sutton

Romano

Nease

2011

Progress in Nuclear Science and Technology

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Two Monte-Carlo-based methods for computing the dominance ratio in reactor calculations are the Fission Matrix Method (FMM) and the Coarse Mesh Projection Method (CMPM). The FMM allows an estimate of the dominance ratio to be computed before the fission source has converged, but requires a fine mesh-and hence considerable computational resources-for sufficient accuracy. Conversely, the CMPM gives very accurate results on a coarse mesh with very little computational effort, but can be used only after the fission source has converged. In this paper we describe a new method called the Noise Propagation Matrix Method (NPMM) that has the same coarse-mesh accuracy properties as the CMPM while also permitting an 'on-the-fly' estimation of the dominance ratio during fission source convergence. Like the CMPM, the NPMM uses the noise propagation matrix (NPM) in determining the dominance ratio. The two methods differ, however, in how the matrix is used to obtain the dominance ratio. A new derivation of the equations used to compute the NPM in a Monte Carlo calculation is presented that eliminates an approximation made in an earlier work on the CMPM. It is shown that by using the improved expression for the NPM, the dominance ratio can be found directly and simply as the largest-modulus eigenvalue of the matrix-thereby eliminating the more complicated time-series-analysis method used by the CMPM. Results for several problems are presented that demonstrate the validity of the method.

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Computation of standard deviations in Eigenvalue calculations

Cited by 45 publications

References 1 publication

Challenges and Prospects for Whole-Core Monte Carlo Analysis

Challenges and Prospects for Whole-Core Monte Carlo Analysis

Calculation of adjoint-weighted kinetic parameters with the reactor Monte Carlo code RMC

On-the-Fly Monte Carlo Dominance Ratio Calculation Using the Noise Propagation Matrix

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