Multiscale model reduction for neutron diffusion equation

Aleksandr O. Vasilev; Denis A. Spiridonov; Alexander V. Avvakumov

doi:10.25587/SVFU.2021.27.52.008

Vasilev Aleksandr O., haska87@gmail.com International Research Laboratory "Multisclae Model Reduction" Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk, 677980, Russia
Spiridonov Denis A., d.stalnov@mail.ru International Research Laboratory "Multisclae Model Reduction" Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk, 677980, Russia
Avvakumov Alexander V., avvakumov2009@rambler.ru National Research Center "Kurchatov Institute" Moscow, Russia 1, Akademika Kurchatova pl., Moscow, 123182, Russia

DOI: https://doi.org/10.25587/SVFU.2021.27.52.008

Keywords: parabolic equation, neutron diffusion, multiscale simulation, generalized multiscale finite element method (GMsFEM)

Abstract

Modelling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The neutron diffusion approximation is widely used for reactor analysis and applied in most engineering calculation codes. In this paper, we attempt to employ a model reduction technique based on the multiscale method for neutron diffusion equation. The proposed method is based on the use of a generalized multiscale finite element method. The main idea is to create multiscale basis functions that can be used to effectively solve on a coarse grid. From calculation results, we obtain that multiscale basis functions can properly take into account the small-scale characteristics of the medium and provide accurate solutions. The results calculated with the GMsFEM are compared with the reference fine-grid calculation results.

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