Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Ma, Q.; Zheng, X.; Duan, W.Y. (2014)
Publisher: ELSEVIER
Languages: English
Types: Article
Subjects: TA
With wide applications, the smoothed particle hydrodynamics method (abbreviated as SPH) has become an important numerical tool for solving complex flows, in particular those with a rapidly moving free surface. For such problems, the incompressible Smoothed Particle Hydrodynamics (ISPH) has been shown to yield better and more stable pressure time histories than the traditional SPH by many papers in literature. However, the existing ISPH method directly approximates the second order derivatives of the functions to be solved by using the Poisson equation. The order of accuracy of the method becomes low, especially when particles are distributed in a disorderly manner, which generally happens for modelling violent water waves. This paper introduces a new formulation using the Rankine source solution. In the new approach to the ISPH, the Poisson equation is first transformed into another form that does not include any derivative of the functions to be solved, and as a result, does not need to numerically approximate derivatives. The advantage of the new approach without need of numerical approximation of derivatives is obvious, potentially leading to a more robust numerical method. The newly formulated method is tested by simulating various water waves, and its convergent behaviours are numerically studied in this paper. Its results are compared with experimental data in some cases and reasonably good agreement is achieved. More importantly, numerical results clearly show that the newly developed method does need less number of particles and so less computational costs to achieve the similar level of accuracy, or to produce more accurate results with the same number of particles compared with the traditional SPH and existing ISPH when it is applied to modelling water waves.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] L.B. Lucy, A numerical approach to the testing of the fusion process, Astron J. 88 (1977) 1013-1024.
    • [2] R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astron. Soc. 181 (1977) 375-389.
    • [3] M.B. Liu, G.R. Liu, K.Y. Lam, Z. Zong, Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Comput. Mech. 30(2) (2003) 106-118.
    • [4] J.P. Morris, P.J. Fox, Y. Zhu, Modeling low Reynolds number incompressible flows using SPH, J. Comput. Phys. 136 (1997) 214-226.
    • [5] P.W. Cleary, J.J. Monaghan, Conduction modeling using smoothed particle hydrodynamics, J. Comput. Phys. 148 (1999) 227-264.
    • [6] J.J. Monaghan, Simulation Free Surface Flows with SPH, J. Compu. Phys. 110 (4) (1994) 399-406.
    • [7] J.N. Fang, R.G. Owens, L. Tacher, A. Parriaux, A numerical study of the SPH method for simulating transient viscoelastic free surface flows, J. Non-Newtonian Fluid Mech. 139(1-2) (2006) 68-84.
    • [8] X. Zheng, Q.W. Ma, W.Y. Duan, Simulation of breaking waves by using an improved SPH method, in: Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, June 17-22, 2012, pp.1051-1056.
    • [9] J.J. Monaghan, SPH and Riemann Solvers, J. Comput. Phys. 136 (1997) 298-307.
    • [10] M. Antuono, A. Colagrossi, S. Marrone, D. Molteni, Free-surface flows solved by means of SPH schemes with numerical diffusive terms, Computer Physics Communications 181 (2010) 532-549.
    • [11] S.I. Inutsuka, Reformulation of Smoothed Particle Hydrodynamics with Riemann solver, J. Comput. Phys. 179 (2012) 238-267.
    • [12] R.Gao B.Ren, G.Y. Wang, Y.X. Wang, Numerical modeling of regular wave slamming on subface of open-piled structures with the corrected SPH method, Applied Ocean Research 34 (2012) 172-186.
    • [13] A.R. Rafiee, S. Cummins, M. Rudman, K. Thiagarajan, Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows, Europen Journal of Mechanics B/Fluids 36 (2012) 1-16.
    • [14] S.J. Cummins, Rudman M, An SPH projection method, J. Comput. Phys. 152 (1999) 584-607.
    • [15] Y.M. Lo Edmond, S.D. Shao, Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Applied Ocean research 24 (2002) 275-286.
    • [16] S.D. Shao, Y.M. Lo Edmond, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Adv. Water Resour. 26(7) (2003) 787-800.
    • [17] S D Shao, C.M. Ji, D.I. Graham, D.I. Graham, D.E. Reeve, P.W. James, A.J. Chadwick, Simulation of wave overtopping by an incompressible SPH model, Coast Eng. 53(9) (2006) 723-735.
    • [18] S.D. Shao, Incompressible SPH simulation of water entry of a free-falling object, Int. J. Numer. Meth. Fluids 59(1) (2009) 91-115.
    • [19] X.Y. Hu, N.A. Adams, An incompressible multi-phase SPH method, J. Comput. Phys. 227 (2007) 264-278.
    • [20] X. Liu , H. Xu , S.D. Shao, P. Lin, An improved incompressible SPH model for simulation of wave-structure interaction, Computers&Fluids, 71 (2013) 113-123.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article