GAMBET, M. Matthis (2021) *Utilisation du flux adjoint dans les méthodes de réduction de variance pour les simulations Monte Carlo cinétiques* PFE - Project Graduation, ENSTA.

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## Abstract

Monte Carlo simulations are high fidelity methods to solve the neutrons transport problem. Neutrons are modelized particles by particles through random sampling. Kinetic Monte Carlo simulations are Monte Carlo methods taking into account reactivity changes through time. It implies simulating particle by particle, not only neutrons but also precursors (with their decay time scale and particles number different from prompt neutron characteristic values). Those simulations aim at forecasting power level in nuclear reactors and in particular for the cases of accidental transients which are currently treated with deterministic methods. In kinetic Monte Carlo, the main issue is to fasten the convergence of simulations. In one hand it is necessary to lower the estimator’s variance around the estimated mean value in order to improve precision and to reduce the number of simulated particles. In the other hand the neutrons and precursors populations need to be controlled in order to avoid populations death or explosion (in case of subcritical or supercritical systems). These tasks are partially achieved by biasing method which consists in modifying the rules of the Monte Carlo game with respect to the physical laws while maintaining the score unbiased. For example branchless collisions, precursors forced decay and a population control method called combing were used in this study. This study goal was to improve this last method using an importance function (method called Importance Combing or IC) given by adjoint quantities (adjoint flux for prompt neutrons and adjoint concentrations for precursors). The hypothesis of point reactor allows to separate the problem of getting spatio-temporal adjoint flux into two separate resolutions : a static deterministic calculation gave this study’s spatial adjoint flux, and a resolution of adjoint point kinetic equations via time discretization gave this study’s temporal profile. The Adjoint quantities obtained by the multiplication of those two components is used in a monoenergetic Monte Carlo toy model code developped in IRSN for proof of concept in kinetic Monte Carlo variance reduction. The current implementation of IC in this code is time consuming and restricts the calculation to simple cases like 1D homogenous case with leakage. The results obtained on this geometry do not show significant variance reduction along the transient. This behavior is not explained yet and could be due to a lack of particles discrimination (the adjoint quantities are cosine shaped). However, the method is not biased and gives consistent results (compared to simulation using basic combing). Besides, the internship as raised questions about uncertainty bars in kinetic Monte Carlo simulations. Those error bars are made under the hypothesis of Central Limit theorem applicability. This theorem allows to quantify the risk taken in locating the target value in the confidence interval represented by the error bars. The study has nonetheless shown simulations concerning the same physical transient leading to different values with uncertainty interval not overlapping. This might indicate that central limit theorem is not applicable in the case of kinetic Monte Carlo simulations and require changing the way the uncertainty is defined.

Item Type: | Thesis (PFE - Project Graduation) |
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Subjects: | Mathematics and Applications Physics, Optics |

ID Code: | 9008 |

Deposited By: | Matthis GAMBET |

Deposited On: | 23 nov. 2021 10:06 |

Dernière modification: | 23 nov. 2021 10:06 |

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