An integral formulation for some slow viscous flows with free surfaces

Abstract

For some viscous incompressible flows at low Reynolds numbers we deduce a system of nonlinear integral equations for stream function and vorticity. A coating flow problem and a capillary free boundary problem are considered in details.

Authors

Mirela Kohr Ile
Babes-Bolyai University, Faculty of Mathematics

Calin-Ioan Gheorghiu
Institute of Mathematics

Keywords

slow viscous flow; free surface; stream function; vorticity; integral equation; nonlinear; coating flow; capillary flow;

References

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Paper coordinates

C.I. Gheorghiu, M. Kohr-Ile, An integral formulation for some slow viscous flows with free surfaces, Mathematica, 36 (59) (1994), pp. 43-54.

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Mathematica

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Romanian Academy, Publishing House of the Romanian Academy 

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References

References

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[2] C. Cuvelier, On e Computation of Free Boundaries, Research in Numerical Gluid Mechanics, (Delft 1986), 18-29, Notes Numer. Fluid Mech., 17, Vieweg, Braunschweig, 1987.

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[5] M.A. Kelmanson, A Direct Boundary Integral Formulation for the Oseen Flow Past a Two-Dimensional Cylinder for Arbitrary Cross-Section, Acta-Mechanica, 68 (1987), 99-119.

[6] M.A. Kelmanson, An Integral  Equation Method for the Solution of Singular Stow Flows Problems, Journal Comp. Physics, 51 (1983), 139-158.

[7] M.E. O’Neil, F. Chorlton, Ideal and incompressibile fluid dynamics, Ellis Horwood, Chichester, West Sussox, 1986.

[8] T. Petrila, C.I. Gheorghiu, Finite Element Methods and Applications, Ed. Academiei București, 1987, (in Romanian)

[9] T. Petrila, M. Kohr,  Some boundary techniques for viscous flows,  Rev. D’Analyse Numerique et de Theorie de l’Approx., 21, 2 (1992) 167-182.

[10] H. Saito, I. E. Scriven,  Study of Coating Flow by the finite Element Method, Journal of  Comp. Physics, 42 (1981), 53-76.

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