Geodesic
Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2014), pp. 114-122 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the derivation of the fundamental velocity and traction tensor components is presented for Stokes equations in the cylindrical coordinate system for axisymmetric viscous flows. The derivation is based on a three-dimensional singular solution in Cartesian coordinates. Using the presented formulas, the boundary integral equations are constructed in accordance with the potential theory conception. A simple numerical solution algorithm that is an implementation of principles of the indirect boundary element method is proposed. Reliability of the results is verified by solving a test problem the role of which is played by the problem about a flow in a cylindrical tube (the Poiseuille flow) with mixed boundary conditions. The developed method of solving boundary problems for Stokes equations can be used for modeling creeping flows of a viscous fluid with a free surface.
Mots-clés : viscous fluid
Keywords: boundary element method, fundamental solutions, axisymmetric flow. 
@article{VTGU_2014_5_a11,
     author = {V. A. Yakutenok and M. A. Ponomareva and A. E. Kuznetsova},
     title = {Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {114--122},
     year = {2014},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2014_5_a11/}
}
TY  - JOUR
AU  - V. A. Yakutenok
AU  - M. A. Ponomareva
AU  - A. E. Kuznetsova
TI  - Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2014
SP  - 114
EP  - 122
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VTGU_2014_5_a11/
LA  - ru
ID  - VTGU_2014_5_a11
ER  - 
%0 Journal Article
%A V. A. Yakutenok
%A M. A. Ponomareva
%A A. E. Kuznetsova
%T Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2014
%P 114-122
%N 5
%U http://geodesic.mathdoc.fr/item/VTGU_2014_5_a11/
%G ru
%F VTGU_2014_5_a11
V. A. Yakutenok; M. A. Ponomareva; A. E. Kuznetsova. Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2014), pp. 114-122. http://geodesic.mathdoc.fr/item/VTGU_2014_5_a11/

[1] Banerjee P. K., Butterfield R., Boundary Element Methods in Engineering Science, McGraf-Hill book company, UK, 1981 | MR | MR | Zbl

[2] Brebbia C. A., Telles J. C. F., Wrobel L. C., Boundary Element Techniques. Theory and applications in engineering, Sprinqer-Verlag, Berlin, 1984 | MR

[3] Yakutenok V. A., “Chislennoe modelirovanie medlennykh techeniy vyazkoy zhidkosti so svobodnoy poverkhnost'yu metodom granichnykh elementov”, Matematicheskoe modelirovanie, 4:10 (1992), 62–70 (in Russian)

[4] Yakutenok V. A., “Chislennoe reshenie trekhmernykh zadach o polzushchem techenii vyazkoy zhidkosti so svobodnoy poverkhnost'yu metodom granichnykh elementov”, Matematicheskoe modelirovanie, 11:10 (1999), 92–99 (in Russian)

[5] Shrager G. R., Shtokolova M. N., Yakutenok V. A., “Formation of the free surface of a viscous fluid volume inside a rotating horizontal cylinder”, Fluid Dynamics, 44:2 (2009), 322–327 | DOI | Zbl

[6] Ponomareva M. A., Shrager G. R., Yakutenok V. A., “Stability of a Plane Jet of a Highly Viscous Fluid Impinging on a Horizontal Solid Wall”, Fluid Dynamics, 46:1 (2011), 44–50 | DOI | Zbl

[7] Novoshintsev A. V., Shrager G. R., Yakutenok V. A. et al., “Numerical modeling of the outflow of a viscous liquid from a bulk mixer”, Theoretical Foundations of Chemical Engineering, 40:6 (2006), 626–632 | DOI

[8] Ponomareva M. A., Shrager G. R., Yakutenok V. A., “Ispol'zovanie uravneniya Dyupre–Yunga dlya resheniya zadachi o rastekanii zhidkosti pri ogranichennom smachivanii”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2008, no. 1, 90–96 (in Russian)

[9] Yakutenok V. A., Shtokolova M. N., “Chislennoe modelirovanie ploskikh techeniy nen'yutonovskoy zhidkosti so svobodnoy poverkhnost'yu nepryamym metodom granichnykh elementov”, Vychislitel'nye tekhnologii, 11:5 (2006), 106–118 (in Russian) | Zbl

[10] Yun B. I., Ang W. T., “A dual-reciprocity boundary element method for axisymmetric thermoelastostatic analysis of nonhomogeneous materials”, Engineering Analysis with Boundary Elements, 36 (2012), 1776–1786 | DOI | MR

[11] Karageorghis A., Fairweather G., “The method of fundamental solutions for axisymmetric elastisity problems”, Computational Mechanics, 25 (2000), 524–532 | DOI | Zbl

[12] Pozrikidis C., Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, 1992 | MR | Zbl

[13] Park K. H., Benerjee P. K., “A new BEM formulation for transient axisymmetric poroelasticity via particular integrals”, International Journal of Solids and Structures, 44 (2007), 7276–7290 | DOI | Zbl

[14] Ladyzhenskaya O. A., The Mathematical Theory of Viscous Incompressible Flow, 2nd ed., Gordon Breach, New York, 1969 | MR | MR | Zbl

[15] Ponomareva M. A., “Analiz effektivnosti ispol'zovaniya sredstv raspredelennykh vychisleniy dlya sistem s obshchey pamyat'yu pri modelirovanii techeniy vyazkoy zhidkosti metodom granichnykh elementov”, Sed'maya Sibirskaya konferentsiya po parallel'nym i vysokoproizvoditel'nym vychisleniyam, Izd-vo Tom. un-ta, Tomsk, 2014, 137–144 (in Russian)