Advertisement

Journal of Engineering Mathematics

, Volume 58, Issue 1–4, pp 19–30 | Cite as

A 3D numerical model for computing non-breaking wave forces on slender piles

  • Weihua Mo
  • Kai Irschik
  • Hocine Oumeraci
  • Philip L. -F. Liu
Original Paper

Abstract

In this paper a numerical model for water-wave-body interaction is validated by comparing the numerical results with laboratory data. The numerical model is based on Euler’s equation without considering the effects of energy dissipation. The Euler equations are solved by a two-step projection finite-volume scheme and the free-surface displacements are tracked by the volume-of-fluid method. The numerical model is used to simulate solitary waves as well as periodic waves and their interaction with a vertical slender pile. A very good agreement between the experimental data and numerical results is observed for the time history of free-surface displacement, fluid-particle velocity, and dynamic pressure on the pile.

Keywords

Circular cylinder Experimental data Numerical modeling Wave forces 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Morison JR, O’Brien MP, Johson JW, Schaaf SA (1950) The forces exerted by surface waves on piles. J Petroleum Technol, Petroleum Trans AIME 189:149–154Google Scholar
  2. 2.
    Sapkaya T, Issacson St MQ (1981) Mechanics of wave forces on offshore structures. Van Nostrand Reinold, New YorkGoogle Scholar
  3. 3.
    Xue M, Xu H, Liu, Y, Yue DKP (2001) Computations of fully nonlinear three dimensional wave–wave and wave–body interaction. Part 1. Dynamics of steep three-dimensional waves. J Fluid Mech 438:11–39zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Liu Y, Xue M, Yue DKP (2001) Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body. J Fluid Mech 438:41–65zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Guyenne P, Grilli ST (2006) Numerical study of three-dimensional overturning waves in shallow water. J Fluid Mech (to appear)Google Scholar
  6. 6.
    Kim J, Moin P, Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133–166zbMATHCrossRefADSGoogle Scholar
  7. 7.
    Pope SB (2001) Turbulent flows. Cambridge University PressGoogle Scholar
  8. 8.
    Lin P, Liu PL-F (1998a) A numerical study of breaking waves in the surf zone. J Fluid Mech 359:239–264zbMATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Liu PL-F, Lin P, Chang KA (1999) Numerical modeling of wave interaction with porous structures. J Wtrwy Port, Coast Ocean Engng ASCE 125(6):322–330CrossRefGoogle Scholar
  10. 10.
    Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic equations. Mon. Weather Rev 91:99–164CrossRefGoogle Scholar
  11. 11.
    Watanabe Y, Saeki H (1999) Three-dimensional large eddy simulation of breaking waves. Coastal Engng 41(3/4):281–301Google Scholar
  12. 12.
    Lin P, Li CW (2002) A σ-coordinate three-dimensional numerical model for surface wave propagation. Int J Numer Meth Fluids 38:1048–1068CrossRefMathSciNetGoogle Scholar
  13. 13.
    Christensen ED, Deigaard R (2001) Large eddy simulation of breaking waves. Coastal Engng 42:53–86CrossRefGoogle Scholar
  14. 14.
    Liu PL-F, Wu T-R, Raichlen F, Synolakis CE, Borrero JC (2005) Runup and rundown generated by three-dimensional sliding masses. J Fluid Mech 536:107–144zbMATHCrossRefADSGoogle Scholar
  15. 15.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comp Phys 39:201–225zbMATHCrossRefADSGoogle Scholar
  16. 16.
    Wu T-R (2004) A numerical study of three-dimensional breaking waves and turbulence effects. PhD dissertation, Cornell UniversityGoogle Scholar
  17. 17.
    Rider WJ, Kothe DB (1998) Reconstructing volume tracking. J Comp Phys 141:112–152zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Wienke J, Oumeraci H (2005) Breaking wave impact force on a vertical and inclined slender pile. Coastal Eng 52:435–462CrossRefGoogle Scholar
  19. 19.
    Irschik K, Sparboom U, Oumeraci H (2003) Breaking wave characteristics for the loading of a slender pile. Proc. 28th Int. Conf. Coastal Eng., ICCE 2002, pp 1341–1352Google Scholar
  20. 20.
    Goring DJ, Raichlen F (1980) The generation of long waves in the laboratory. Proc. 17th Int. Conf. Coastal Eng ASCE, New York, pp 763–783Google Scholar
  21. 21.
    Fenton JD (1988) The numerical solution of steady water wave problems. Comput Geosci 14(3):357–368CrossRefGoogle Scholar
  22. 22.
    Sobey RJ (1989) Variations on Fourier wave theory. Int J Nume Meth in Fluids 9:1453–1467zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Weihua Mo
    • 1
  • Kai Irschik
    • 2
  • Hocine Oumeraci
    • 2
  • Philip L. -F. Liu
    • 1
  1. 1.School of Civil and Environmental EngineeringCornell UniversityIthacaUSA
  2. 2.Leichtweiß-InstituteBraunschweigGermany

Personalised recommendations