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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2022, Volume 15, Issue 4, Pages 90–98
DOI: https://doi.org/10.14529/mmp220408
(Mi vyuru664)
 

Short Notes

Numerical method for solving the inverse problem of non-stationary flow of viscoelastic fluid in the pipe

A. R. Alievab, Kh. M. Gamzaevb, A. A. Darwishc, T. A. Nofalde

a Azerbaijan State Oil and Industry University, Baku, Azerbaijan
b Institute of Mathematics and Mechanics of ANAS, Baku, Azerbaijan
c Helwan University, Cairo, Egypt
d Taif University, Taif, Saudi Arabia
e El-Minia University, Minia, Egypt
References:
Abstract: The process of unsteady flow of incompressible viscoelastic fluid in a cylindrical tube of constant cross-section is considered. To describe the rheological properties of a viscoelastic fluid, the Kelvin–Voigt model is used and the mathematical model of this process is presented as an integro-differential partial differential equation. Within the framework of this model, the problem is to determine the pressure drop along the length of the pipe, which ensures the passage of a given flow rate of viscoelastic fluid through the pipe. This problem belongs to the class of inverse problems related to the recovery of the right parts of integro-differential equations. By replacing variables, the integro-differential equation is transformed into a third-order partial differential equation. First, a discrete analog of the problem is constructed using finite-difference approximations. To solve the resulting difference problem, we propose a special representation that allows splitting the problems into two mutually independent second-order difference problems. As a result, an explicit formula is obtained for determining the approximate value of the pressure drop along the length of the pipeline for each discrete value of the time variable. Based on the proposed computational algorithm, numerical experiments were performed for model problems.
Keywords: viscoelastic fluid, Kelvin–Voigt model, integro-differential equation, pressure drop along the length of the pipe, inverse problem.
Funding agency Grant number
Taif University TURSP-2020/031
The authors received financial support from Taif University Researches Supporting Project number TURSP-2020/031, Taif University, Taif, Saudi Arabia.
Received: 23.10.2021
Document Type: Article
UDC: 532.546+519.6
MSC: 65M32, 76A10
Language: English
Citation: A. R. Aliev, Kh. M. Gamzaev, A. A. Darwish, T. A. Nofal, “Numerical method for solving the inverse problem of non-stationary flow of viscoelastic fluid in the pipe”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 15:4 (2022), 90–98
Citation in format AMSBIB
\Bibitem{AliGamDar22}
\by A.~R.~Aliev, Kh.~M.~Gamzaev, A.~A.~Darwish, T.~A.~Nofal
\paper Numerical method for solving the inverse problem of non-stationary flow of viscoelastic fluid in the pipe
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2022
\vol 15
\issue 4
\pages 90--98
\mathnet{http://mi.mathnet.ru/vyuru664}
\crossref{https://doi.org/10.14529/mmp220408}
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