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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 6, Pages 1063–1082 (Mi zvmmf10915)  

Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section

A. O. Kazakovaa, A. G. Petrovb

a Chuvash State University, Cheboksary, 428015 Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 117526 Russia

Abstract: An algorithm is constructed for numerical study of the plane viscous flow (in the Stokes approximation) between two arbitrarily moving cylinders of arbitrary cross section. The mathematical model of the problem is described by the biharmonic equation, which is reduced, with the help of the Goursat representation, to a system of equations for two harmonic functions. The system is solved numerically by applying the boundary element method without saturation. As a result, the desired biharmonic stream function and the velocity field are determined. Test examples are used to compare the results with well-known exact solutions for circular cylinders.

Key words: viscous flow, Stokes approximation, stream function, biharmonic equation, boundary element method.

Funding Agency Grant Number
Russian Science Foundation 19-19-00373
This work was supported by the Russian Science Foundation, project no. 19-19-00373.


DOI: https://doi.org/10.1134/S0044466919060097


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:6, 1030–1048

Bibliographic databases:

UDC: 519.635
Received: 11.04.2017
Revised: 30.01.2019
Accepted:08.02.2019

Citation: A. O. Kazakova, A. G. Petrov, “Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 1063–1082; Comput. Math. Math. Phys., 59:6 (2019), 1030–1048

Citation in format AMSBIB
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\paper Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 59
\issue 6
\pages 1063--1082
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\crossref{https://doi.org/10.1134/S0044466919060097}
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\transl
\jour Comput. Math. Math. Phys.
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\pages 1030--1048
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