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Numerical simulation of multiply connected axisymmetric discontinuous incompressible potential flows

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Abstract

The ascend and evolution of an axisymmetric gas bubble are studied numerically using an inviscid incompressible potential flow model. The volume of the gas bubble varies adiabatically. The transition from a simply connected bubble to a doubly connected toroidal one and its interaction with the free surface are simulated. The change in connectedness is accompanied by a nonzero velocity circulation and a discontinuous velocity potential occurring over an arbitrary toroidal liquid surface enclosing the bubble.

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References

  1. L. V. Ovsyannikov, “Bubble rise,” in Certain Problems in Mathematics and Mechanics (Nauka, Leningrad, 1970) [in Russian].

    Google Scholar 

  2. M. A. Lavrent’ev and B. V. Shabat, Fluid Dynamics Problems and Their Mathematical Models (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  3. O. V. Voinov and V. V. Voinov, “Numerical method for calculating inviscid incompressible unsteady flows with free surfaces,” Dokl. Akad. Nauk SSSR 221, 559–562 (1975).

    Google Scholar 

  4. A. Prosperetti, L. A. Crum, and K. W. Commander, “Nonlinear bubble dynamics,” J. Acoust. Soc. Am. 83, 502–514 (1998).

    Article  Google Scholar 

  5. A. A. Aganin, L. A. Kosolapova, and V. G. Malakhov, “Nonlinear radial vibrations and displacements of a nonspherical gas bubble in liquid,” Mat. Model. 23(5), 56–70 (2011).

    MATH  Google Scholar 

  6. A. M. Gudov, “Numerical study of water surface phenomena in gas cavity collapse,” Vychisl. Tekhnol. 2(4), 49–59 (1997).

    Google Scholar 

  7. V. K. Kedrinskii, “Underwater explosion near free surface,” Dokl. Akad. Nauk SSSR 212, 324–326 (1973).

    Google Scholar 

  8. V. A. Korobitsyn, “Numerical modeling of axisymmetric potential flows of an incompressible fluid,” Mat. Model. 3(10), 42–49 (1991).

    MATH  MathSciNet  Google Scholar 

  9. V. A. Korobitsyn and V. I. Pegov, “Numerical study of liquid-liquid interface evolution,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 128–133 (1993).

    Google Scholar 

  10. V. A. Korobitsyn, “Basis difference method for orthogonal systems on a surface,” Comput. Math. Math. Phys. 51, 1222–1230 (2011).

    Article  MathSciNet  Google Scholar 

  11. V. A. Korobitsyn, “Numerical modeling of multiply connected incompressible flows,” International Conference on Mathematical and Information Technologies for Science, Engineering, and Education, MIT2011, Vrnjacka Banja and Budva, August 27–September 5, 2011, pp. 94–95.

  12. V. A. Korobitsyn, “Covariant transformations of basis differential-difference schemes in a plane,” Comput. Math. Math. Phys. 51, 1915–1922 (2011).

    Article  MathSciNet  Google Scholar 

  13. S. A. Beizel, L. B. Chubarov, D. Dutykh, et al., “Simulation of surface waves generated by an underwater landslide in a bounded reservoir,” Russ. J. Numer. Anal. Math. Model. 27, 539–558 (2013).

    MathSciNet  Google Scholar 

  14. K. Lipnikov, G. Manzini, and M. Shashkov, “Mimetic finite difference method,” J. Comput. Phys. B, No. 257, 1163–1227 (2014).

    Google Scholar 

  15. V. A. Gasilov, V. M. Goloviznin, M. D. Taran, et al., Preprint No. 70, IPM AN SSSR (Keldysh Inst. of Applied Mathematics, USSR Academy of Sciences, Moscow, 1979).

    Google Scholar 

  16. R. T. Knapp, J. W. Daily, and F. G. Hammitt, Cavitation (McGraw-Hill, New York, 1970; Mir, Moscow, 1974).

    Google Scholar 

  17. A. Prosperetti and J. W. Jacobs, “A numerical method for potential flows with a free surface,” J. Comput. Phys. 51, 365–386 (1983).

    Article  MATH  Google Scholar 

  18. V. V. Pukhnachev and V. A. Solonnikov, “On the dynamic contact angle,” Prikl. Mat. Mekh. 46(6) (1982).

    Google Scholar 

  19. C. W. Hirt, J. L. Cook, and T. D. Butler, “A Lagrangian method for calculating the dynamics of an incompressible fluid with free surface,” J. Comput. Phys. 5(2), 103–124 (1970).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia

    A. M. Bubenchikov, V. A. Korobitsyn & P. P. Kotov

  2. Tomsk State University of Control Systems and Radio Electronics, pr. Lenina 40, Tomsk, 634050, Russia

    D. V. Korobitsyn

  3. Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, pr. Akademika Lavrent’eva 6, 630090, Russia

    Yu. I. Shokin

Authors
  1. A. M. Bubenchikov
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  2. V. A. Korobitsyn
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  3. D. V. Korobitsyn
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  4. P. P. Kotov
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  5. Yu. I. Shokin
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Corresponding author

Correspondence to V. A. Korobitsyn.

Additional information

Original Russian Text © A.M. Bubenchikov, V.A. Korobitsyn, D.V. Korobitsyn, P.P. Kotov, Yu.I. Shokin, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 7, pp. 1194–1202.

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Bubenchikov, A.M., Korobitsyn, V.A., Korobitsyn, D.V. et al. Numerical simulation of multiply connected axisymmetric discontinuous incompressible potential flows. Comput. Math. and Math. Phys. 54, 1167–1175 (2014). https://doi.org/10.1134/S0965542514070057

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  • DOI: https://doi.org/10.1134/S0965542514070057

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