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Numerical Simulation of Unsteady Capillary-Gravity Waves

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Abstract

In this work, plane problems of numerical simulation of wave motion are studied. Potential flows of a perfect incompressible fluid are considered. A numerical algorithm for calculating the shape of a free boundary is proposed. The algorithm is based on the boundary element method with the use of quadrature formulas with no saturation. The algorithm is used for studying the breaking of capillary gravity waves and calculating thin cumulative jets. The stability of the scheme and high accuracy in calculations of sharp cumulative jets are achieved due to special control for the distribution of grid points and a decrease in the grid step in the neighborhood of the forward end of the cumulative jet with an ultimately rapid growth of the curvature.

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REFERENCES

  1. A. G. Petrov, Analytical Hydrodynamics (Fizmatlit, Moscow, 2010) [in Russian].

    Google Scholar 

  2. N. D. Baikov and A. G. Petrov, Moscow Univ. Mech. Bull. 72, 119 (2017).

    Article  Google Scholar 

  3. K. I. Babenko, Foundations of Numerical Analysis (RKhD, Izhevsk, 2002).

  4. A. G. Petrov, Comput. Math. Math. Phys. 48, 1266 (2008).

    Article  MathSciNet  Google Scholar 

  5. A. G. Petrov, Dokl. Phys. (in press).

  6. D. H. Peregrine, Annu. Rev. Fluid Mech. 15, 149 (1983).

    Article  ADS  Google Scholar 

  7. M. S. Longuet-Higgins and E. D. Cokelet, Proc. R. Soc. London, Ser. A 350, 1 (1976).

    Article  ADS  Google Scholar 

  8. A. G. Petrov and V. G. Smolyanin, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 3, 92 (1991).

  9. G. D. Crapper, J. Fluid Mech. 2, 532 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. G. Petrov, J. Appl. Math. Mech. 81, 317 (2017).

    Article  MathSciNet  Google Scholar 

  11. M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  12. E. A. Karabut, A. G. Petrov, and E. N. Zhuravleva, Eur. J. Appl. Math. (2018). doi 10.1017/S0956792518000098

  13. E. A. Karabut and E. N. Zhuravleva, J. Fluid Mech. 754, 308 (2014).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, 119899, Moscow, Russia

    N. D. Baikov

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    A. G. Petrov

Authors
  1. N. D. Baikov
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  2. A. G. Petrov
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Correspondence to N. D. Baikov.

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Translated by A. Nikol’skii

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Baikov, N.D., Petrov, A.G. Numerical Simulation of Unsteady Capillary-Gravity Waves. Dokl. Phys. 63, 430–434 (2018). https://doi.org/10.1134/S1028335818100087

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  • DOI: https://doi.org/10.1134/S1028335818100087

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