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7Multiscale and high.performance computing for multiphysical problems
fractured porous media. We investigate relative errors between reference fine grid solution and presented
coarse grid approximation using GMsFEM with different numbers of multiscale basis functions. Our results indicate
that the proposed method is able to give accurate solutions with few degrees of freedoms.
Ageneralized multiscale finite element method for neutron transport problems in SP3 approximation
A. O. Vasilev1, D. A. Spiridonov1, A. V. Avvakumov2
1M. K. Ammosov North.Eastern FederalUniversity, Yakutsk
2National Research Center �Kurchatov Institute�, Moscow
Email: haska87@gmail.com
DOI 10.24412/cl.35065.2021.1.02.86
The SP3 approximation of the neutron transport equation allows improving the accuracy for both static
and transient simulations for reactor core analysis compared with the neutron diffusion theory. Besides, the
SP3 calculation costs are much less than higher order transport methods (SN or PN).Another advantage of the
SP3 approximation is a similar structure of equations that is used in the diffusion method. Therefore, there is
no difficulty to implement the SP3 solution option to the multi.group neutron diffusion codes.
In this paper, we attempt to employ a model reduction technique based on the multiscale method for
neutron transport equation in SP3 approximation. The proposed method is based on the use of a generalized
multiscale finite element method (GmsFEM).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 application of the SP3 methodology based on solution of the lambda.spectral problems has been tested
for the some reactor benchmarks. The results calculated with the GMsFEM are compared with the reference
transport calculation results.
