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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 12, Pages 2143–2161
DOI: https://doi.org/10.31857/S0044466920120133 (Mi zvmmf11177) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Mathematical physics

Numerical solution of a stationary filtration problem of viscous fluid in a piecewise homogeneous porous medium by applying the boundary integral equation method

A. V. Setukhaab, R. M. Tretiakovaab

a Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, 119992 Russia
b Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 117333 Russia
Citations (4)
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DOI: https://doi.org/10.31857/S0044466920120133
Abstract: A numerical method based on boundary integral equations is constructed for simulating three-dimensional stationary filtration flow through a homogeneous porous medium with homogeneous inclusions. The flow is simulated taking into account the viscosity of the fluid. Boundary integral equations are written on the outer boundary of the flow region and on the boundary surfaces of the inclusions. The integral equations are solved numerically using the methods of piecewise constant approximation and collocations. The numerical method is tested on model problems.
Key words: boundary element method, filtration flow, integral equations, potential theory.
Funding agency Grant number
Russian Science Foundation 18-11-00171
Ministry of Education and Science of the Russian Federation 075-15-2019-1624
This work was supported by the Russian Science Foundation, project no. 18-11-00171. Tretyakova acknowledges the partial support of the Moscow Center for Fundamental and Applied Mathematics, project no. 075-15-2019-1624.
Received: 28.02.2020
Revised: 28.02.2020
Accepted: 04.08.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 12, Pages 2076–2093
DOI: https://doi.org/10.1134/S0965542520120131
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: A. V. Setukha, R. M. Tretiakova, “Numerical solution of a stationary filtration problem of viscous fluid in a piecewise homogeneous porous medium by applying the boundary integral equation method”, Zh. Vychisl. Mat. Mat. Fiz., 60:12 (2020), 2143–2161; Comput. Math. Math. Phys., 60:12 (2020), 2076–2093
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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