The stochastic implicit Euler method – A stable coupling scheme for Monte Carlo burnup calculations

Dufek, Jan; Kotlyar, Dan; Shwageraus, Eugene

doi:10.1016/j.anucene.2013.05.015

Cited by 47 publications

(26 citation statements)

References 9 publications

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“…core of LWR or HTR reactor) show instabilities for burnup simulations when the staircase step model is used. This problem has been presented and explained theoretically in the article of (Dufek et al, 2013a). We confirmed the presence of this phenomenon in our HTR full-core burnup simulation.…”

Section: Step Modelsupporting

confidence: 88%

“…This methodology has significant drawback of multiple Monte Carlo iterations at each time step, which increases overall computational cost. An effectiveness of SIE model has been confirmed on the simplified PWR model reported in the articles by (Dufek et al, 2013a) and additionally by self calculations using MCB5 code (Kepisty and Cetnar, 2015).…”

Section: Stochastic Implicit Euler Methodsmentioning

confidence: 62%

“…The problem related to the oscillations caused by strong coupling between neutron flux and nuclide field can be overcome by iterative averaging of EOS neutron flux and repetitive applying it for depletion. So called Stochastic Implicit Euler method (SIE) has been proposed by (Dufek et al, 2013a). The model provides unconditional spatial stability of simulation, when other approaches failed.…”

Section: Stochastic Implicit Euler Methodsmentioning

confidence: 99%

“…The theoretical consideration by (Dufek et al, 2013a) concerning the limited Monte Carlo statistics indicates that instabilities of burnup simulation is not related to the precision of Monte Carlo run and statistical fluctuations. The computational results in our work based on HTR system show that applied statistical precision is at least in some range responsible for the moment when the oscillation emerges.…”

Section: Monte Carlo Precisionmentioning

confidence: 98%

See 3 more Smart Citations

Burnup instabilities in the full-core HTR model simulation

Kępisty

Cetnar

2015

Annals of Nuclear Energy

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Section: Step Modelsupporting

confidence: 88%

Section: Stochastic Implicit Euler Methodsmentioning

confidence: 62%

Section: Stochastic Implicit Euler Methodsmentioning

confidence: 99%

Section: Monte Carlo Precisionmentioning

confidence: 98%

See 2 more Smart Citations

Burnup instabilities in the full-core HTR model simulation

Kępisty

Cetnar

2015

Annals of Nuclear Energy

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“…The main feature of acceptable approach is unconditional spatial stability. We have chosen, so-called, stochastic implicit Euler method (SIEM, [3]) and adjusted it to our continuous energy version of Monte Carlo. The scheme can be found in Table 4.…”

Section: Methodology Of Time-stepmentioning

confidence: 99%

Assesment of advanced step models for steady state Monte Carlo burnup calculations in application to prismatic HTGR

Kępisty

Cetnar

2015

Nukleonika

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IntroductionThe concept of using continuous energy Monte Carlo simulations for critical systems as a precise tool for burnup calculations is well known in the fi eld of research and development of fuel cycle. The beginning-of-step approximation of neutron fl ux over the time-step is often applied by many burnup codes for its simplicity. This approach assumes constant fl ux/power profi le during entire step, which can cause problems such as spatial instability of reaction rates in the simulated system [1]. Spatial oscillations of fl ux and xenon concentration appear for relatively short steps, thus affecting the core's equilibrium. Regarding fuel cycle analysis of prismatic HTGR, the spatial fl ux distribution of the core varies strongly in the vicinity of compensation rods, which are being slowly withdrawn in order to compensate the reactivity loss. In order to handle this problem properly, a better fl ux normalization procedure -so-called bridge scheme -was developed and applied in the study of PuMA project [2]. An optimal model of time-step is necessary to account for the non-constant system's behavior as well as to provide stability of burnup. Abstract. In this paper, we compare the methodology of different time-step models in the context of Monte Carlo burnup calculations for nuclear reactors. We discuss the differences between staircase step model, slope model, bridge scheme and stochastic implicit Euler method proposed in literature. We focus on the spatial stability of depletion procedure and put additional emphasis on the problem of normalization of neutron source strength. Considered methodology has been implemented in our continuous energy Monte Carlo burnup code (MCB5). The burnup simulations have been performed using the simplifi ed high temperature gas-cooled reactor (HTGR) system with and without modeling of control rod withdrawal. Useful conclusions have been formulated on the basis of results.

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Study of radionuclide inventory in nuclear fuel under uncertainties in boron concentration using high‐fidelity models

Castagna

Gilad

2022

Intl J of Energy Research

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Summary Uncertainties in the critical boron concentration during reactor burnup calculations strongly affect the spectrum, thus propagating to the 1‐group cross sections and reaction rates used in the Bateman equations and eventually affecting the resulting nuclide densities. These, in turn, alter the calculated critical boron concentration and so on. Usually, the uncertainty due to this nonlinear feedback is overlooked since only final (ie, at the end of the cycle) radionuclide densities are considered for fuel and waste management. However, for source term analysis, an accurate estimation of the core's radionuclide inventory is required at any time during the irradiation cycle. This paper presents an in‐depth uncertainty analysis on the nuclide inventory calculations by considering the nonlinear feedback due to deviation from the critical boron concentration during calculation. In particular, the physical characterization of the interrelated effects among spectrum, cross‐sections, reaction rates, and boron concentration are highlighted. The results indicate that deviation from the critical boron concentration during calculation may lead to significant discrepancies in nuclide densities during the irradiation cycle, which tends to decrease towards the end of the cycle. The physical processes underlying this behaviour are studied in depth using a high‐fidelity model and the Monte Carlo transport calculations. The methodology presented in this study may be used for systematic uncertainty and sensitivity analysis.

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The stochastic implicit Euler method – A stable coupling scheme for Monte Carlo burnup calculations

Cited by 47 publications

References 9 publications

Burnup instabilities in the full-core HTR model simulation

Burnup instabilities in the full-core HTR model simulation

Assesment of advanced step models for steady state Monte Carlo burnup calculations in application to prismatic HTGR

Study of radionuclide inventory in nuclear fuel under uncertainties in boron concentration using high‐fidelity models

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