Mathematical modeling

Multiscale model reduction for neutron diffusion equation

A. O. Vasilev^a, D. A. Spiridonov^a, A. V. Avvakumov<sup>b

a</sup> International Research Laboratory "Multisclae Model Reduction" Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk, 677980, Russia
^b National Research Centre "Kurchatov Institute", 1, Akademika Kurchatova pl., Moscow, 123182, Russia

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.

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

UDC: 519.63

Received: 18.01.2021
Revised: 22.04.2021
Accepted: 26.05.2021

Language: English

DOI: 10.25587/SVFU.2021.27.52.008

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