Skip to main content
SpringerLink
Log in

Numerical simulation of solitary wave breaking and impact on seawall using a modified turbulence SPH method with Riemann solvers

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

In this paper, the Weakly Compressible Smoothed Particle Hydrodynamic method was modified to simulate two-dimensional plunging solitary wave breaking process. This model solves the Navier–Stokes equations to obtain both velocity field and density and also solves the equation of state to obtain the pressure field. To simulate the turbulent behavior of fluid flow in a wave breaking procedure, Sub Particle Scale model was used. To correct the Pressure and velocity field in SPH, Riemann Solver was also implemented. This method was modified with a kernel and gradient of kernel correction to overcome the problems associated with the usage of viscous terms in Navier–Stokes equations. The modified kernel gradient was implemented to the model based on modified kernel in Element Free Galerkin Method. To consider the accuracy of the modified model, a dam break test was performed and model results were compared with available experimental data and unmodified models. These comparisons showed good agreement between modified results and the experimental data. Finally, the transform of plunging solitary wave breaking on a slope was simulated using the modified model. The results showed that this model better agrees with the experiments in the plunging jet impact and splash-up processes. Finally, solitary wave impact on a seawall was simulated by the modified model. The results showed that the modified model has good agreement with experimental data.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Ketabdari MJ, Nobari MRH, Larmaei MM (2008) Simulation of waves group propagation and breaking in coastal zone using a Navier-Stokes solver with an improved VOF free surface treatment. Appl Ocean Res 30(2):130–143

    Article  Google Scholar 

  2. Rezaei H, Ketabdari MJ (2013) Numerical simulation of solitary wave-catamaran breakwater interaction using MFCT model. J Braz Soc Mech Sci Eng 35(4):441–456

    Article  Google Scholar 

  3. Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68:1703–1759

    Article  MathSciNet  Google Scholar 

  4. Lo EYM, Shao S (2002) Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Appl Ocean Res 24(5):275–286

    Article  Google Scholar 

  5. Mirmohammadi A, Ketabdari MJ (2011) Numerical simulation of wave scouring beneath marine pipeline using Smoothed Particle Hydrodynamics Int. J Sediment Transp 26(2011):331–342

    Google Scholar 

  6. Crespo AJC, Gomez-Gesteira M, Dalrymple RA (2008) Modeling dam break behavior over a wet bed by a SPH technique. J Waterw Port Coast Ocean Eng 134(6):313–320

    Article  Google Scholar 

  7. Monaghan JJ, Kos A (1999) Solitary waves on a Cretan beach. J Waterw Port Coast Ocean Eng 125(3)

  8. Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191(2):448–475

    Article  MATH  Google Scholar 

  9. Ketabdari MJ, Nemati A (2011) Numerical Simulation of Breaking Solitary Wave on the Sloping Beach Using WCSPH Method. Iranian J Marine Tech (in Persian)

  10. Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110:399–406

    Article  MATH  Google Scholar 

  11. Dalrymple RA, Rogers BD (2006) Numerical Modeling of Water Waves with the SPH Method. Coast Eng 53(2–3):141–147

    Article  Google Scholar 

  12. Monaghan JJ (1997) SPH and Riemann solvers. J Comput Phys 136(2):298–307

    Article  MATH  MathSciNet  Google Scholar 

  13. Parshikov AN, Medin SA (2002) Smoothed particle hydrodynamics using interparticle contact algorithm. J Comput Phys 180:358–382

    Article  MATH  Google Scholar 

  14. Rogers BD, Dalrymple RA, Stansby PK (2010) Simulation of caisson breakwater movement using SPH. J Hydraul Res 48:135–141

    Article  Google Scholar 

  15. Monaghan JJ (1992) Smoothed particle hydrodynamics. Annual Rev Astron Appl 30

  16. Gotoh H, Shibihara T, Hayashi M (2001) Sub-particle-scale model for the MPS method-Lagrangian flow model for hydraulic engineering. Comput Fluid Dyn J 9(4):247–339

    Google Scholar 

  17. Khayyer A, Gotoh H, Shao SD (2008) Corrected incompressible SPH method for accurate water surface tracking in breaking waves. Coast Eng 55(3):236–250

    Article  Google Scholar 

  18. Monaghan JJ, Lattanzio JC (1985) A refined method for astrophysical problems. Astron Astrophys 149

  19. Batchelor GK (1967) Introduction to fluid dynamics. Cambridge Univ. Press, Cambridge

    MATH  Google Scholar 

  20. Blin L, Hadjadj A, Vervisch L (2003) Large eddy simulation of turbulent flows in reversing systems. J Turbul 4

  21. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164

    Article  Google Scholar 

  22. Bonet J, Lok T-SL (1999) Variational and momentum preservation aspects of smoothed particle hydrodynamic formulations. Comput Methods Appl Mech 180:97–115

    Article  MATH  MathSciNet  Google Scholar 

  23. Dilts GA (1999) Moving-Least–Squares-Particle Hydrodynamics––I. Consistency and stability. Int J Numer Meth Eng. 44

  24. Bonet J, Kulasegaram S (2000) Correction and stabilization of smoothed particle hydrodynamics methods with applications in metal forming simulations. Int J Numer Meth Eng 47(6):1189–1214

    Article  MATH  Google Scholar 

  25. Belytschko T, Krongauz Y, Dolbow J, Gerlach C (1998) On the completness of meshfree particle methods. Int J Numer Meth Eng 43(5):785–819

    Article  MATH  MathSciNet  Google Scholar 

  26. Monaghan JJ (1989) On the problem of penetration in particle methods. J Compu Phys 82(1)

  27. Dalrymple RA, Knio O (2001) SPH modeling of water waves. ASCE, San francisco

    Google Scholar 

  28. Crespo AJC, Gómez-Gesteira M, Dalrymple RA (2007) Boundary conditions generated by dynamic particles in SPH methods. CMC-Tech Sci Press 5(3)

  29. Hu CH, Kashiwagi M (2004) A cip method for numerical simulations of violent free surface flows. J Mar Sci Tech 9(4):143–157

    Article  Google Scholar 

  30. Martin JC, Moyce WJ (1952) Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans Royal Soc London Series A, Math Phys Sci 244(882): p 312

  31. Grilli ST, Svendsen IA, Subramanya R (1997) Breaking criterion and characteristics for solitary waves on slopes. J Waterw Port Coast Ocean Eng 123(3):102–112

    Article  Google Scholar 

  32. Li Y Tsunamis: Non-breaking and breaking solitary wave run-up, in Rep. KH-R-60. 2000, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology: Pasadena, CA

  33. Li Y, Raichlen F (1998) Breaking criterion and characteristics for solitary waves on slopes-discussion. J Waterw Port Coast Ocean Eng 124(6):329–333

    Article  Google Scholar 

  34. Guizien K, Barthe’lemy E (2002) Accuracy of solitary wave generation by a piston wave maker. J Hydraul Res 40(3):321–331

    Article  Google Scholar 

  35. Li Y, Raichlen F (2003) Energy balance model for breaking solitary wave runup. J Waterw Port Coast Ocean Eng 129(2):47–59

    Article  Google Scholar 

  36. Lachaume C, Biausser B, Grilli ST, Fraunie P, Guignard S (2003) Modeling of breaking and post-breaking waves on slopes by coupling of BEM and VOF methods, in Proc. 13th Offshore and Polar Engineering Conf., ISOPE03. Honolulu, USA, pp 353–359

    Google Scholar 

  37. Hsiao S-C, Lin T-C (2010) Tsunami-like solitary waves impinging and overtopping an impermeable seawall: experiment and RANS modeling. Coast Eng 57:1–18

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Marine Technology, Amirkabir University of Technology, Tehran, Iran

    M. Rostami Varnousfaaderani & M. J. Ketabdari

Authors
  1. M. Rostami Varnousfaaderani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. J. Ketabdari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. Ketabdari.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rostami Varnousfaaderani, M., Ketabdari, M.J. Numerical simulation of solitary wave breaking and impact on seawall using a modified turbulence SPH method with Riemann solvers. J Mar Sci Technol 20, 344–356 (2015). https://doi.org/10.1007/s00773-014-0287-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-014-0287-9

Keywords

Search

Navigation