Zero-variance schemes for kinetic Monte Carlo simulations
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Zero-variance schemes for kinetic Monte Carlo simulations Davide Mancusia , Andrea Zoiab DEN-Service d’études des réacteurs et de mathématiques appliquées (SERMA), CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France Received: 5 February 2020 / Accepted: 6 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Solving time-dependent transport problems for neutrons and precursors in a nuclear reactor is a daunting task in a naive Monte Carlo framework, mainly because of the enormous difference between the time scale associated with the prompt fission chains and that associated with the decay of delayed neutron precursors. Recently, the development of variance reduction techniques specific for reactor kinetics and the rapidly increasing computer power have paved the way towards the possibility of obtaining reference solutions to the time-dependent transport problem. However, the application of time-dependent Monte Carlo to large systems (i.e. at the scale of a full reactor core) is still considerably hindered by the huge computational requirements. In this paper, we construct an ideal Monte Carlo game that results in a zero-variance estimator for specific observables in time-dependent transport. Our derivation follows the pattern of the existing schemes for stationary problems. To the best of our knowledge, zero-variance Monte Carlo schemes for time-dependent transport including delayed neutrons precursors have never been considered before. As a proof of principle, we verify our construction for a simplified benchmark configuration where analytical reference solutions for the transport problem can be explicitly obtained.
1 Introduction The system of equations describing the time evolution of neutrons coupled to that of delayed neutron precursors is stiff: the time scale of the prompt fission chains is much smaller than the time scale of precursor decay, by a factor of about 10−4 in a typical pressurized water reactor in stationary conditions. As a consequence, solving reactor kinetics problems including neutrons and precursors by a naive Monte Carlo simulation represents a formidable task, which has been out of reach for many years. It is only very recently that these problems have become tractable, by virtue of the groundbreaking work of Sjenitzer and Hoogenboom [1,2] and the subsequent emergence of a new class of variance reduction techniques for the time variable, which go under the name of kinetic Monte Carlo methods. However, despite these prominent advances, the computation cost of kinetic Monte Carlo simulations is still prohibitively high: the size of the systems that can be treated in a reasonable time is currently limited to a cluster
a e-mail: [email protected] (corresponding author) b e-mail: [email protected]
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of fuel assemblies at most [3]. Extending kinetic Monte Carlo methods to the simulation of larger systems is mandatory for the validation of kin
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