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Article information
2017 , Volume 22, ¹ 3, p.3-15
Shurina E.P., Epov M.I., Kutishcheva A.Y.
Numerical simulation of the percolation threshold of the electric resistivity
Theoretical estimation, laboratory experiments and numerical simulations are the typical approaches to homogenization. In this paper, we propose a numerical method for obtaining effective resistivity. This approach is based on the simulation of the electrostatic field in heterogeneous media. We employ heterogeneous multi-scale finite element method (FE-HMM) to solve this problem in complex media (i. e. we consider materials with high contrast micro inclusions). FE-HMM is a two stage method. On the first stage a macro-scale solver is selected and missing macroscopic data are estimated. This makes it possible to study percolation (the flow of the electric current through the complex media) without any simplifications of the model. In this paper we consider a 3D problem that requires to determine effective resistivity of an object with cuprum plate inclusions necessary for the study of the percolation processes. Developed FE-HMM algorithm allows us to obtain effective scalar characteristics (e. g., thermal conductivity, electrical resistivity etc.) of the materials containing high-contrast inclusions. Developed algorithms are implemented in C++ for parallel architectures and are adaptable for the use on modern supercomputers. In order to obtain effective resistivity of the samples with inclusions with different shape and physical characteristics, we carried out a number of computational experiments. Our study indicates that the surface square of each inclusion is inversely related to the percolation threshold of the material with the inclusions. Our studies also indicate that if inclusions are localized in the subdomain of the media, a simplification of the model to the uniform distribution will be unacceptable.
[full text]
Keywords: effective resistivity, heterogeneous multiscale finite element method (FE-HMM), heterogeneous media, percolation threshold
Author(s):
Shurina Ella Petrovna
Dr. , Professor
Position: General Scientist
Office: Novosibirsk State Technical University, Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Address: 630073, Russia, Novosibirsk, Karl Marx Ave. 20
Phone Office: (343) 223-72-95
E-mail: shurina@online.sinor.ru
Epov Mihail Ivanovich
Dr. , Academician RAS, Professor
Position: Director
Office: A.A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Address: 630090, Russia, Novosibirsk, Akademika Koptyuga Prosp. 3
Phone Office: (383)330-13-81
E-mail: EpovMI@ipgg.sbras.ru
SPIN-code: 5421-0812Kutishcheva Anastasiya Yuryevna
Position: Student
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, Marx ave. 20
E-mail: Kutischeva.Anastasia@yandex.ru
SPIN-code: 3506-7327 References:
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Bibliography link:
Shurina E.P., Epov M.I., Kutishcheva A.Y. Numerical simulation of the percolation threshold of the electric resistivity // Computational technologies. 2017. V. 22. ¹ 3. P. 3-15
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