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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 14–26
DOI: https://doi.org/10.4213/tm4145 (Mi tm4145) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Filtration under a Stepped Dam and Riemann Theta Functions

A. B. Bogatyrev, O. A. Grigor'ev

Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333 Russia
Full-text PDF (536 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4145
Abstract: A novel semi-analytical method for calculating the characteristics of the flow in a porous medium bounded by a rectangular polygonal barrier is proposed. The method is based on the usage of Riemann theta functions. It allows one to effectively solve certain filtration problems with machine accuracy and obtain some characteristics of the solutions without solving the problem as a whole.
Keywords: porous media, Schwarz–Christoffel integral, theta functions, real meromorphic differentials, moduli spaces, hydraulic structures.
Funding agency Grant number
Russian Science Foundation 16-11-10349
Moscow Center of Fundamental and Applied Mathematics 075-15-2019-1624/2
The work presented in Sections 1–5 is supported by the Russian Science Foundation under grant 16-11-10349. The numerical computations (Sections 6 and 7) were performed in the INM RAS Department of the Moscow Center for Fundamental and Applied Mathematics and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1624/2).
Received: February 25, 2020
Revised: June 19, 2020
Accepted: July 21, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 10–21
DOI: https://doi.org/10.1134/S0081543820060024
Bibliographic databases:
Document Type: Article
UDC: 517.542+517.545
MSC: 30C20, 14H42, 30C30
Language: Russian
Citation: A. B. Bogatyrev, O. A. Grigor'ev, “Filtration under a Stepped Dam and Riemann Theta Functions”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 14–26; Proc. Steklov Inst. Math., 311 (2020), 10–21
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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