Numerical Study of Shock Propagation in Liquid/Gas Media

  • N. ApazidisEmail author
Conference paper


A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between the constituents. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles and a bubble array is investigated. Several features of the interaction process are studied, including propagation and focusing of the transmitted (refracted) shock within the deformed bubble, creation of a water hammer by a diffracted shock in water, and generation of high-speed liquid jet due to induced flow vorticity in the later stages of the process.



The financial support of Vetenskapsrådet (VR) (the Swedish Research Council) is gratefully acknowledged.


  1. 1.
    R. Abgrall, S. Karni, J. Comput. Phys. 169 (2001)Google Scholar
  2. 2.
    G. Allaire, S. Clerc, S. Kokh, J. Comput. Phys. 181 (2002)Google Scholar
  3. 3.
    D. Igra, K. Takayama, Int. J. Numer. Methods Fluids 38 (2002)Google Scholar
  4. 4.
    E. Johnsen, T. Colonius, J. Fluid Mech. 629 (2009)Google Scholar
  5. 5.
    M. Ozlem, D.W. Schwendeman, A.K. Kapilla, W.D. Henshaw, Shock Waves 22 (2012)Google Scholar
  6. 6.
    K.M. Shyue, J. Comput. Phys. 142 (1998)Google Scholar
  7. 7.
    K.M. Shyue, J. Comput. Phys. 200 (2004)Google Scholar
  8. 8.
    K.M. Shyue, Shock Waves 15 (2006)Google Scholar
  9. 9.
    K.M. Shyue, J. Comput. Phys. 229 (2010)Google Scholar
  10. 10.
    J. Quirk, S. Karni, J. Fluid Mech. 318 (1996)Google Scholar
  11. 11.
    J.H.J. Niederhaus, J.A. Greenough, J.G. Oakley, D. Ranjan, M.H. Anderson, R. Bonazza J. Fluid Mech. 594 (2008)Google Scholar
  12. 12.
    M. Sun, K. Takayama, J. Comput. Phys. 189 (2003)Google Scholar
  13. 13.
    H.A. Luther, Math. Comput. 22 (1968)Google Scholar
  14. 14.
    J.F. Haas, B. Sturtevant, J. Fluid Mech. 18 (1987)Google Scholar
  15. 15.
    J.W. Jacobs, Phys. Fluids A 5 (1993)Google Scholar
  16. 16.
    G. Layes, G. Jourdan, L. Houas, Phys. Fluids 21 (2009)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanics, KTH Royal Institute of TechnologyStockholmSweden

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