Skip to main content
Log in

A three-dimensional coupled numerical model of nonlinear waves in a harbor

  • Published:
Science in China Series E: Technological Sciences Aims and scope Submit manuscript

Abstract

A 3-D time-domain numerical coupled model for nonlinear waves acting on a ship in a harbor has been developed in the present study. The whole domain is divided into the inner domain and the outer domain. The inner domain is the area around the ship, where the flow is expressed by the Laplace equation and numerically solved by the finite element method. The other area is the outer domain, where the flow is described by the higher-order Boussinesq equations and numerically solved by the finite difference method. The matching conditions on the interfaces between the inner domain and the outer domain, the procedure of coupled solution, the length of common domain and the mesh generation in the inner domain are discussed in detail. The other coupled model with the flow in the inner domain governed by the simplified linear Euler equations and relevant physical experiment are adopted to validate the present coupled model, and it is shown that the numerical results of the present model agree with the experimental data, so the present model can be used for the study on the effect of nonlinear waves acting on a fixed ship in a large area and provide a reference for the time-domain simulation of nonlinear wave forces on an arbitrary object in a large harbor and the 3-D district computation in the future.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Wang D G, Xing W, Hong L. Time stepping solutions of nonlinear wave forces on ship section in harbor (in Chinese). J Liaoning Tech U, 2006, 25(5): 692–695

    Google Scholar 

  2. Zhang X T, Teng B, Ning D Z. Simulation of fully nonlinear 3-D numerical wave tank. China Ocean Eng, 2004, 18: 59–68

    Google Scholar 

  3. Liu H, Lin Y R, Zhang Z, et al. A 3-D numerical wave tank based on higher-order BEM (in Chinese). Ocean Eng, 2004, 22(2): 1–6

    Google Scholar 

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

    Article  MATH  Google Scholar 

  5. Wang Y X, Sy T C. Numerical simulation of breaking waves against vertical wall. Proc 2nd Int Offshore Polar Eng Conf, San Francisco, 1992. 139–145

  6. Madsen P A, Schaffer H A. Higher-order Boussinesq-type equations gravity waves: derivation and analysis. Phil Trans Roy Soc, London A, 1998, 356: 3123–3184

    Article  MATH  MathSciNet  Google Scholar 

  7. Gobbi M F, Kirby J T, Wei G. A fully nonlinear Boussinesq model for surface wave—II: Extension to 0(kh)4. J Fluid Mech, 2000, 405: 181–210

    Article  MATH  MathSciNet  Google Scholar 

  8. Hong G W. Higher order model of nonlinear and dispersive wave in water of varying depth with arbitrary sloping bottom. China Ocean Eng, 1999, 11(3): 243–260

    Google Scholar 

  9. Wang B L, Liu H. Higher order Boussinesq-type equations for water waves on uneven bottom. Appl Math Mech, 2005, 26(6): 774–784

    Article  MATH  Google Scholar 

  10. Zou Z L. Higher-order Boussinesq equations. Sci China Ser E-Tech Sci, 1997, 27(3): 460–473

    Google Scholar 

  11. Takagi K, Naito S, Hirota K. Hydrodynamic force acting on a floating body in a habour of arbitrary geometry. Proc 3rd Int Offshore Polar Eng Conf, 1993. 192–199

  12. Jiang T. Investigation of waves generated by ships in shallow water. Proc 22nd Symp Nav Hydrodyn, Washington DC, 1998

  13. Bingham H B. A hybrid Boussinesq-panel method for predicting the motion of a moored ship. Coast Eng, 2000, 40: 21–38

    Article  Google Scholar 

  14. Qi P, Zou Z L, Wang Y X. A 3-D composite model for numerical simulation of nonlinear waves. Proc 10th Int Offshore Polar Eng Conf, Seattle, 2000. 68–73

  15. Wang D G, Zou Z L. Time stepping solutions of nonlinear wave forces on moored ship in harbor (in Chinese). Acta Oceanol Sin, 2004, 26(2): 104–117

    MathSciNet  Google Scholar 

  16. Wang D G, Zou Z L, Tang C A. Time stepping solutions of nonlinear wave forces on a three-dimensional box-shaped ship in a harbor (in Chinese). J Ship Mech, 2007, 11(4): 533–644

    Google Scholar 

  17. Wang D G, Zou Z L, Tang C A. Study of nonlinear wave motions and wave forces on ship sections against vertical quay in a harbor (in Chinese). Chinese J Theor Appl Mech, 2006, 38(6): 767–775

    Google Scholar 

  18. Wang D G, Zou Z L, Tang C A. The coupled numerical model of non-linear wave in harbour (in Chinese). Chin J Theor Appl Mech, 2007, 39(5): 587–594

    Google Scholar 

  19. Zou Z L, Xu B H. Numerical model for solving Boussinesq-type equations: comparison and validation. Acta Oceanol Sin, 1998, 17(3): 375–386

    Google Scholar 

  20. Wang D G, Zou Z L, Tang C A. Fully nonlinear three-dimensional numerical wave tank simulation (in Chinese). Acta Oceanol Sin, 2006, 28(4): 138–144

    MATH  MathSciNet  Google Scholar 

  21. Zou Z L. Higher order Boussinesq equations. Ocean Eng, 1999, 26: 767–792

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to DaGuo Wang.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 59979002, 50809008), the Hong Kong Research Grants Council (Grant No. HKU 7171/06E), the China Postdoctoral Science Foundation (Grant No. 20060400972), the Project of the Educational Department of Liaoning Province (Grant No. 2005058) and the Dalian Science and Technology Foundation (Grant No. 2007J23JH027)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, D., Zou, Z., Tham, L. et al. A three-dimensional coupled numerical model of nonlinear waves in a harbor. Sci. China Ser. E-Technol. Sci. 51, 2195–2206 (2008). https://doi.org/10.1007/s11431-008-0241-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-008-0241-3

Keywords