Computation of Viscous Flow between Two Arbitrarily Moving Cylinders of Arbitrary Cross Section

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 r...

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Bibliographic Details
Published inComputational mathematics and mathematical physics Vol. 59; no. 6; pp. 1030 - 1048
Main Authors Kazakova, A. O., Petrov, A. G.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.06.2019
Springer Nature B.V
Subjects
Algorithms
Biharmonic equations
Boundary element method
Circular cylinders
Computational fluid dynamics
Computational Mathematics and Numerical Analysis
Cross-sections
Harmonic functions
Mathematics
Mathematics and Statistics
Velocity distribution
Viscous flow
stream function
boundary element method
Stokes approximation
viscous flow
biharmonic equation
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519060095