Skip to main content
SpringerLink
Log in
Book cover

Numerical Simulation of Water Waves pp 367–403Cite as

Incompressible Viscous Fluid Model for Simulating Water Waves

  • Chapter
  • First Online:

  • 615 Accesses

Part of the book series: Springer Tracts in Civil Engineering ((SPRTRCIENG))

Abstract

This book focuses on various unsteady gravity flows with a free surface in nature and engineering, i.e., water waves, and introduces the theories, methodologies, and case studies on numerical simulation. This chapter describes Reynolds equation for incompressible viscous fluid as a model for simulating water waves.

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

References

  1. Launder BE, Spalding DB. The numerical computation of turbulent flows. Comput Methods Appl Mech Eng. 1974;3(2):269–89.

    Article  Google Scholar 

  2. Lin P, Liu PL-F. Numerical study of breaking waves in the surf zone. J Fluid Mech. 1998;359:239–64.

    Article  Google Scholar 

  3. Osher SJ, Sethain JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys. 1988;79(1):12–49.

    Article  MathSciNet  Google Scholar 

  4. Sussman M, Smereka P, Osher SJ. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys. 1994;114(1):146–59.

    Article  Google Scholar 

  5. Chen Y, Bi Y. Spatial spline and body-fitted coordinates. In: Proceedings of the 1995 national conference on hydrodynamics; 1995.

    Google Scholar 

  6. Zhu J. The boundary integral equation method for solving the Dirichlet problem of a biharmonic equation. Math Numer Sin. 1984;3:278–88.

    MathSciNet  MATH  Google Scholar 

  7. Yuan D, Tao J. Simulation of the flow with free surface by level set method. Acta Mech Sin. 2000;32(3):264–71.

    Google Scholar 

  8. Xie W, Tao J. Interaction of a solitary wave and a front step simulated by level set method. Appl Math Mech. 2000;21(7):686–92.

    MATH  Google Scholar 

  9. Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys. 1981;39:201–25.

    Article  Google Scholar 

  10. Noh WF, Woodward PR. SLIC (simple line interface method). Lect Notes Phys. 1976;59:273–85.

    MATH  Google Scholar 

  11. Chorin AJ. Flame advection and propagation algorithms. J Comput Phys. 1980;35(1):1–11.

    Article  MathSciNet  Google Scholar 

  12. Barr PK, Ashurst WT. An interface scheme for turbulent flame propagation. Technical Report SAND 82-8773, Sandia National Laboratories; 1984.

    Google Scholar 

  13. Youngs DL. Time-dependent multi-material flow with large fluid distortion. Numerical methods in fluid dynamics. New York: Academic Press; 1982. p. 273–85.

    Google Scholar 

  14. Ashgriz N, Poo JY. FLAIR: flux line-segment model for advection and interface reconstruction. J Comput Phys. 1991;93(2):449–68.

    Article  Google Scholar 

  15. Kim SO, No CH. Second-order model for free surface convection and interface reconstruction. Int J Numer Methods Fluids. 1998;26:79–100.

    Google Scholar 

  16. Pilliod JE, Puckett EG. Second-order accurate volume of fluid algorithms for tracking material interfaces. J Comput Phys. 1997;199(2):465–502.

    Article  MathSciNet  Google Scholar 

  17. Colella P, et al. A numerical study of shock wave refractions at a gas interface. In: Pulliam T, editors. Proceedings of the AIAA ninth computational fluid dynamics conference; 1989. p. 426–39.

    Google Scholar 

  18. Kothe DB, et al. Volume tracking of interfaces having surface tension in two and three dimensions. Technical Report AIAA. 96-0859;1996.

    Google Scholar 

  19. Chorin AJ. Numerical solution of the Navier-Stokes equations. Math Comput. 1968;22.

    Google Scholar 

  20. Liu C. Using unsteady Reynolds Navier-Stokes equations to simulate the water wave interaction with coastal structures. Dissertation for Ph.D. degree, Tianjin: Tianjin University; 2003.

    Google Scholar 

  21. Seabra-Santos FJ, Renouard DP, Temperville AM. Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J Fluid Mech. 1987;176:117–34.

    Article  Google Scholar 

  22. Maxworthy T. Experiments on collisions between solitary waves. J Fluid Mech. 1976;76(1):177–85.

    Article  Google Scholar 

  23. Fei Z, Lee J-J. A viscous rotational model for wave overtopping over marine structure. In: Proceedings of 25th international conference on coastal engineering, ASCE, 1996:2178–91.

    Google Scholar 

  24. French JA. Wave uplift pressure on horizontal platforms, Report No. KH_R_19, W. M. Keck Laboratory of Hydraulics and Water Resources, Pasadena: California Institute of Technology; 1969.

    Google Scholar 

  25. Lai CP, Lee J-J. Interaction of finite amplitude waves with platforms or docks. J Waterw, Port, Coast, Ocean Eng. 1989;115(1):19–39.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tianjin University, Tianjin, China

    Jianhua Tao

Authors
  1. Jianhua Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianhua Tao .

Copyright information

© 2020 Shanghai Jiao Tong University Press, Shanghai and Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tao, J. (2020). Incompressible Viscous Fluid Model for Simulating Water Waves. In: Numerical Simulation of Water Waves . Springer Tracts in Civil Engineering . Springer, Singapore. https://doi.org/10.1007/978-981-15-2841-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-2841-5_9

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2840-8

  • Online ISBN: 978-981-15-2841-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation