Science China Technological Sciences

, Volume 60, Issue 3, pp 479–490 | Cite as

Two-phase smooth particle hydrodynamics modeling of air-water interface in aerated flows

  • HuiXia Yang
  • Ran Li
  • PengZhi Lin
  • Hang Wan
  • JingJie Feng


The large deformations associated with air and water interactions are critical factors that affect the hydrodynamic characteristics of hydraulic structures. As a type of Lagrange meshless particle method, smoothed particle hydrodynamics (SPH) has been shown to have many advantages when modeling the interface flow and tracing the free surface because the particles inherit the velocity, mass, and density properties. Significant theoretical and numerical studies have been performed recently in this area. In the present study, a two-phase SPH framework was developed based on these previous studies and we explored its capacity to capture the main features of large density ratio aerated flows. The cohesive pressure was included only in the momentum equation of the air phase for additional amendments to ensure the stability and accuracy of the two-phase SPH model. Three case studies were performed to test the performance of the two-phase SPH model. A convergence study demonstrated the need to balance the CPU time consumption and the real-time requirements. A dam-break simulation based on pressure variation in the air pocket showed the superior analytical performance of the two-phase model compared with the single-phase model. The results of a hydraulic jump simulation were compared with the theoretical results in order to understand the collision between the solid and liquid using the SPH method more clearly. Thus, the consistency between the simulation and the theoretical and experimental results demonstrated the feasibility and stability of the two-phase SPH framework.


aerated flow dam break density difference hydraulic jump interface smoothed particle hydrodynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys, 1981, 39: 201–225CrossRefMATHGoogle Scholar
  2. 2.
    Monaghan J J. Simulating free surface flows with SPH. J Comput Phys, 1994, 110: 339–406CrossRefMATHGoogle Scholar
  3. 3.
    Liu G R, Liu M B. Smoothed particle hydrodynamics: A meshfree particle method. World Scientific, London, 2003Google Scholar
  4. 4.
    Lucy L B. A numerical approach to the testing of the fission hypothesis. Astron J, 1977, 82: 1013–1024CrossRefGoogle Scholar
  5. 5.
    Gingold R A, Monaghan J J. Smoothed particle hydrodynamics -theory and application to non-spherical stars. Mon Not R Astron Soc, 1977, 181: 375–389CrossRefMATHGoogle Scholar
  6. 6.
    Monaghan J J. Gravity currents and solitary waves. Physica D, 1996, 98: 523–533CrossRefMATHGoogle Scholar
  7. 7.
    Monaghan J J. SPH compressible turbulence. Mon Not R Astron Soc, 2002, 335: 843–852CrossRefGoogle Scholar
  8. 8.
    Monaghan J J. Smoothed particle hydrodynamics. Annu Rev Astron Astr, 1992, 30: 543–574CrossRefGoogle Scholar
  9. 9.
    López D, Marivela R, Garrote L. Smoothed particle hydrodynamics model applied to hydraulic structure: a hydraulic jump test case. J Hydraul Res, 2010, 48: 142–158CrossRefGoogle Scholar
  10. 10.
    Faltinsen O M, Landrini M, Greco M. Slamming in marine applications. J Eng Math, 2004, 48: 187–217CrossRefMATHGoogle Scholar
  11. 11.
    Sun J W, Liang S X, Sun Z C, et al. A Two-phase simulation of wave impact on a horizontal deck based on SPH method. J Mar Sci Appl, 2010, 9, 372–378CrossRefGoogle Scholar
  12. 12.
    Colagrossi A, Landrini M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys, 2003, 191: 448–475CrossRefMATHGoogle Scholar
  13. 13.
    Chen Z, Zong Z, Liu M B, et al. An SPH model for multiphase flows with complex interfaces and large density differences. J Comput Phys, 2015, 283: 169–188MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Zhang M, Deng X L. A sharp interface method for SPH. J Comput Phys, 2015, 302: 469–484MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Wang Z B, Chen R, Wang H, et al. An overview of smoothed particle hydrodynamics for simulating multiphase flow. Appl Math Model, 2016, 40: 9625–9655MathSciNetCrossRefGoogle Scholar
  16. 16.
    Monaghan J J, Kos A M. Solitary waves on a cretan beach. J Waterw Port C-ASCE, 1999, 125: 145–154CrossRefGoogle Scholar
  17. 17.
    Crespo A J C, Dominguez J M, Rogers B D,et al. DualSPHysics: open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH). Comput Phys Commun, 2015, 187: 204–216CrossRefMATHGoogle Scholar
  18. 18.
    Molteni, D., Colagrossi, A. A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput Phys Commun, 2009, 180: 861–872MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Nugent S, Posch H A. Liquid drops and surface tension with smoothed particle applied mechanics. Phys Rev E, 2000, 64: 4968–4975CrossRefGoogle Scholar
  20. 20.
    Mokos A, Rogers B D, Stansby P K, et al. Multiphase SPH modelling of violent Hydrodynamics on GPUs. Comput Phys Commun, 2015, 196: 304–316CrossRefGoogle Scholar
  21. 21.
    Shao S. Incompressible smoothed particle hydrodynamics simulation of multifluid flows. Int J Numer Meth Fl, 2012, 69: 1715–1735MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Issa R, Lee E S, Violeau D, et al. Incompressible separated flows simulations with the smoothed particle hydrodynamics gridless method. Int J Numer Meth Fl, 2004, 47: 1101–1106CrossRefMATHGoogle Scholar
  23. 23.
    Monaghan J J. On the problem of penetration in particle methods. J Comput Phys, 1989, 82: 1–15CrossRefMATHGoogle Scholar
  24. 24.
    Jiao P G, Zhou Y Q, Li Z R, et al. Simulation of two phase flow using smooth particle hydrodynamics. IEEE KAM 2008 Workshop. Wuhan: IEEE, 2009. 296–300Google Scholar
  25. 25.
    Verlet L. Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Health Phys, 1967, 159: 98–103Google Scholar
  26. 26.
    Zhang A M, Sun P N, Ming F R. An SPH modeling of bubble rising and coalescing in three dimensions. Comput Method Appl M, 2015, 294: 189–209MathSciNetCrossRefGoogle Scholar
  27. 27.
    Gomez-Gesteira M, Rogers B D, Crespo A J C, et al. SPHysics–development of a free-surface fluid solver–Part 1: Theory and formulations. Comput Geosci-UK, 2012, 48: 289–299CrossRefGoogle Scholar
  28. 28.
    Gomez-Gesteira M, Rogers B D, Dalrymple R A, et al. State-of-theart classical SPH for free-surface flows. J Hydraul Res, 2009, 48: 6–27CrossRefGoogle Scholar
  29. 29.
    Zhou Z Q, Kat J O D, Buchner B. A nonlinear 3-D approach to simulate GREEN WATER dynamics on deck. In: Proceeding of the 7th International Conference on Numerical Ship Hydrodynamics, Nantes: 1999Google Scholar
  30. 30.
    Jonsson P, PÄR Jonsén P, Andreasson P, et al. Smoothed particle hydrodynamics modeling of hydraulic jumps. International Conference on Particle-based Methods–Fundamentals and Applications, 2011, 97: 373–379Google Scholar
  31. 31.
    Chanson H. Hydraulics of open channel flow, 2nd ed. Oxford, London, 2004Google Scholar
  32. 32.
    Liu Z W, Chen Y C, Zhu D J. Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge. Environ Fluid Mech, 2007, 7: 509–517CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Civil EngineeringGuizhou UniversityGuiyangChina
  2. 2.State Key Laboratory of Hydraulics and Mountain River EngineeringSichuan UniversityChengduChina

Personalised recommendations