Skip to main content
Log in

Numerical simulation of underwater explosion bubble with a refined interface treatment

  • Article
  • Condensed Matter Physics
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

With the intermediate flow states predicted by local two phase Riemann problem, the modified ghost fluid method (MGFM) and its variant (rGFM) have been widely employed to resolve the interface condition in the simulation of compressible multi-medium flows. In this work, the drawback of the construction procedure of local two phase Riemann problem in rGFM was investigated in detail, and a refined version of the construction procedure was specially developed to make the simulation of underwater explosion bubbles more accurate and robust. Beside the refined rGFM, the fast and accurate particle level set method was also adopted to achieve a more effective and computationally efficient capture of the evolving multi-medium interfaces during the simulation. To demonstrate the improvement brought by current refinement, several typical numerical examples of underwater explosion bubbles were performed with original rGFM and refined rGFM, respectively. The results indicate that, when compared with original rGFM, numerical oscillations were effectively removed with the proposed refinement. Accordingly, with present refined treatment of interface condition, a more accurate and robust simulation of underwater explosion bubbles was accomplished in this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Liu T G, Khoo B C, Xie W F. Isentropic one-fluid modelling of unsteady cavitating flow. J Comput Phys, 2004, 201: 80–108

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Liu T G, Khoo B C, Xie W F. The modified ghost fluid method as applied to extreme fluid-structure interaction in the presence of cavitation. Commun Comput Phys, 2006, 1: 898–919

    MATH  Google Scholar 

  3. Xie W F, Young Y L, Liu T G. Multiphase modeling of dynamic fluid-structure interaction during close-in explosion. Int J Numer Meth Eng, 2008, 74: 1019–1043

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen W, Liu Y N, Huang W, et al. Dynamics and measurement of cavitation bubble. Sci China Ser G-Phys Mech Astron, 2006, 49: 385–395

    Article  ADS  Google Scholar 

  5. Saito T, Marumoto M, Yamashita H, et al. Experimental and numerical studies of underwater shock wave attenuation. Shock Waves, 2003, 13: 139–148

    Article  ADS  Google Scholar 

  6. Klaseboer E, Hung K C, Wang C, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J Fluid Mech, 2005, 537: 387–413

    Article  ADS  MATH  Google Scholar 

  7. Liang C, Tai Y. Shock responses of a surface ship subjected to noncontact underwater explosions. Ocean Eng, 2006, 33: 748–772

    Article  Google Scholar 

  8. Zhang A M, Yao X. Interaction of underwater explosion bubble with complex elastic-plastic structure. Appl Math Mech, 2008, 29: 89–100

    Article  MATH  MathSciNet  Google Scholar 

  9. Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys, 1981, 39: 201–225

    Article  ADS  MATH  Google Scholar 

  10. Unverdi S O, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys, 1992, 100: 25–37

    Article  ADS  MATH  Google Scholar 

  11. Blake J R, Gibson D C. Growth and collapse of a vapour cavity near a free surface. J Fluid Mech, 1981, 111: 123–140

    Article  ADS  Google Scholar 

  12. Shu C, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys, 1988, 77: 439–471

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Enright D, Fedkiw R, Ferziger J, et al. A hybrid particle level set method for improved interface capturing. J Comput Phys, 2002, 183: 83–116

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer, 2003

    Book  MATH  Google Scholar 

  15. Sethian J A, Smereka P. Level set methods for fluid interfaces. Annu Rev Fluid Mech, 2003, 35: 341–372

    Article  ADS  MathSciNet  Google Scholar 

  16. Losasso F, Gibou F, Fedkiw R. Simulating water and smoke with an octree data structure. ACM Transactions on Graphics (TOG), 2004

    Google Scholar 

  17. Enright D, Nguyen D, Gibou F, et al. Using the particle level set method and a second order accurate pressure boundary condition for free surface flows. In: 4th ASME JSME Joint Fluids Engineering Conference, Honolulu, Hawaii USA, 2003

    Google Scholar 

  18. Johnsen E, Colonius T. Implementation of WENO schemes in compressible multicomponent flow problems. J Comput Phys, 2006, 219: 715–732

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. Fedkiw R P, Aslam T, Merriman B, et al. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J Comput Phys, 1999, 152: 457–492

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. Fedkiw R P, Marquina A, Merriman B. An isobaric fix for the overheating problem in multimaterial compressible flows. J Comput Phys, 1999, 148: 545–578

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. Takahira H, Matsuno T, Shuto K. Numerical investigations of shock-bubble interactions in mercury. Fluid Dyn Res, 2008, 40: 510–520

    Article  ADS  MATH  Google Scholar 

  22. Takahira H, Kobayashi K, Matsuno T. Direct numerical simulations of interaction of strong shock waves with nonspherical gas bubbles near glass boundaries in mercury. Int J Emerging Multidisc Fluid Sci, 2009, 1: 85–99

    Article  Google Scholar 

  23. Fedkiw R P, Aslam T, Xu S. The ghost fluid method for deflagration and detonation discontinuities. J Comput Phys, 1999, 154: 393–427

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Fedkiw R P. Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method. J Comput Phys, 2002, 175: 200–224

    Article  ADS  MATH  Google Scholar 

  25. Caiden R, Fedkiw R P, Anderson C. A numerical method for two-phase flow consisting of separate compressible and incompressible regions. J Comput Phys, 2001, 166: 1–27

    Article  ADS  MATH  Google Scholar 

  26. Liu T G, Khoo B C, Yeo K S. Ghost fluid method for strong shock impacting on material interface. J Comput Phys, 2003, 190: 651–681

    Article  ADS  MATH  Google Scholar 

  27. Liu T G, Khoo B C, Wang C W. The ghost fluid method for compressible gas-water simulation. J Comput Phys, 2005, 204: 193–221

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. Liu T G, Khoo B C, Yeo K S. The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases. Comput Fluids, 2001, 30: 291–314

    Article  MATH  Google Scholar 

  29. Liu T G, Khoo B C, Yeo K S. The simulation of compressible multi-medium flow: II. Applications to 2D underwater shock refraction. Comput Fluids, 2001, 30: 315–337

    Article  Google Scholar 

  30. Wang C W, Liu T G, Khoo B C. A real ghost fluid method for the simulation of multimedium compressible flow. Siam J Sci Comput, 2006, 28: 278–302

    Article  MATH  MathSciNet  Google Scholar 

  31. Hu X Y, Khoo B C, Adams N A, et al. A conservative interface method for compressible flows. J Comput Phys, 2006, 219: 553–578

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. Xie W F, Liu T G, Khoo B C. The simulation of cavitating flows induced by underwater shock and free surface interaction. Appl Numer Math, 2007, 57: 734–745

    Article  MATH  MathSciNet  Google Scholar 

  33. Sambasivan S K, Udaykumar H S. Ghost fluid method for strong shock interactions Part 1: Fluid-fluid interfaces. AIAA J, 2009, 47: 2907–2922

    Article  ADS  Google Scholar 

  34. Sambasivan S K, Udaykumar H S. A sharp interface method for high-speed multi-material flows: Strong shocks and arbitrary materialpairs. Int J Comput Fluid D, 2011, 25: 139–162

    Article  MATH  Google Scholar 

  35. Jiang G, Peng D. Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J Sci Comput, 2000, 21: 2126–2143

    Article  MATH  MathSciNet  Google Scholar 

  36. Sethian J A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge: Cambridge University Press, 1999

    MATH  Google Scholar 

  37. Enright D, Losasso F, Fedkiw R. A fast and accurate semi-Lagrangian particle level set method. Comput Struct, 2005, 83: 479–490

    Article  MathSciNet  Google Scholar 

  38. Losasso F, Fedkiw R, Osher S. Spatially adaptive techniques for level set methods and incompressible flow. Comput Fluids, 2006, 35: 995–1010

    Article  MATH  MathSciNet  Google Scholar 

  39. Sethian J A. Fast marching methods. Siam Rev, 1999, 41: 199–235

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. Sethian J A. Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J Comput Phys, 2001, 169: 503–555

    Article  ADS  MATH  MathSciNet  Google Scholar 

  41. Müller S, Bachmann M, Kröninger D, et al. Comparison and validation of compressible flow simulations of laser-induced cavitation bubbles. Comput Fluids, 2009, 38: 1850–1862

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Liang Jiang or DaRong Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, L., Ge, H., Feng, C. et al. Numerical simulation of underwater explosion bubble with a refined interface treatment. Sci. China Phys. Mech. Astron. 58, 1–10 (2015). https://doi.org/10.1007/s11433-014-5616-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-014-5616-9

Keywords

Navigation