Skip to main content
SpringerLink
Log in

Numerical Modelling of Free-Surface Flows with Bottom and Surface-Layer Pressure Treatment

  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

A new non-hydrostatic numerical model with the three-dimensional Navier-Stokes equations on structured grids was constructed and discussed. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. The eddy viscosity coefficient was calculated by the efficient k-ε turbulence model. A new surface-layer non-hydrostatic treatment and a local cell bottom treatment were introduced so that the three-dimensional model is fully non-hydrostatic and is free of any hydrostatic assumption. The developed model is second-order accuracy in both time and space when semi-implicit coefficient is set to 0.5. The validity of the present solution algorithm was demonstrated from its application to the three-dimension channel flow and the wave propagation over a submerged bar problems.

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

Similar content being viewed by others

References

  1. LU Lin, LI Yu-cheng. Numerical simulation of turbulent free surface flow over obstruction[J]. Journal of Hydrodynamics, 2008, 20(4): 414–423.

    Article  Google Scholar 

  2. AI Cong-fang, JIN Sheng. Three-dimensional free-surface flow model for simulating water wave motions[J]. Chinese Journal of Hydrodynamics, 2008, 23(3): 338–347(in Chinese).

    Google Scholar 

  3. PARK J. C., KIM M. H. and MIYATA H. Fully non-linear free-surface simulations by a 3D viscous numerical wave tank[J]. International Journal for Numerical Methods in Fluids, 1999, 29(6): 685–703.

    Article  Google Scholar 

  4. HUR D. S., MIZUTANI N. Numerical estimation of the wave forces acting on a three-dimensional body on submerged breakwater[J]. Coastal Engineering, 2003, 47: 329–345.

    Article  Google Scholar 

  5. HUA Lei-na. Research on ALE fractional-step finite element method and appliance of it to viscous free surface fluid flow[D]. Master Thesis, Tianjin: Tianjin University, 2005(in Chinese).

    Google Scholar 

  6. VINCENZO C., ROY A. W. An unstructured grid, three-dimensional model based on the shallow water equations[J]. International Journal for Numerical Methods in Fluids, 2000, 32: 331–348.

    Article  Google Scholar 

  7. LI Shao-wu, LU Li-feng and SHI Zhong. A quasi-3D numerical model for estuarine tidal bore[J]. Journal of Hydrodynamics, Ser. A, 2004, 19(4): 407–415(in Chinese).

    Google Scholar 

  8. MAHADEVAN A., OLIGER J. and STREET R. A non-hydrostatic meso scale ocean model. part 1: Well posedness and scaling[J]. Journal of Physics and Oceanography, 1996, 26: 1868–1880.

    Article  Google Scholar 

  9. CASULLI V., ZANOLLI P. Semi-implicit numerical modeling of non-hydrostatic free-surface flows for environmental problems[J]. Mathematical and Computer Modeling, 2002, 36(9–10):1131–1149.

    Article  Google Scholar 

  10. CASULLI V. A semi-implicit finite difference method for non-hydrostatic, free-surface flows[J]. International Journal for Numerical Methods in Fluids, 1999, 30: 425–440.

    Article  Google Scholar 

  11. HAM D. A., PIETRZAK J. and STELLING G. S. A streamline tracking algorithm for semi-Lagrangian advection schemes based on the analytic integration of the velocity field[J]. Journal of Computational and Applied Mathematics, 2006, 192(1): 168–174.

    Article  MathSciNet  Google Scholar 

  12. PEYMAN B., MASOUD M. N. and AFSHIN A. A three-dimensional non-hydrostaticvertical boundary fitted model for free-surface flows[J]. International Journal for Numerical Methods in Fluids, 2008, 56(6): 607–627.

    Article  MathSciNet  Google Scholar 

  13. AI Cong-fang, JIN Sheng. Three-dimensional non-hydrostatic model for free-surface flows with unstructured grid[J]. Journal of Hydrodynamics, 2008, 20(1): 108–116.

    Article  Google Scholar 

  14. STANSBY P. K., ZHOU J. G. Shallow water flow solver with non-hydrostatic pressure 2D vertical plane problems[J]. International Journal for Numerical Methods in Fluids, 1998, 28(3): 541–563.

    Article  Google Scholar 

  15. AI Cong-fang. Numerical simulation of free surface flow[D]. Ph. D. Thesis, Dalian: Dalian University of Technology, 2008(in Chinese).

    Google Scholar 

  16. BEJI S., BATTJES J. A. Experimental investigation of wave propagation over a bar[J]. Coastal Engineering, 1993, 19: 151–162.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Kun Wang, Sheng Jin & Gang Liu

Authors
  1. Kun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kun Wang.

Additional information

Biography: WANG Kun (1979-), Female, Ph. D. Candidate

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, K., Jin, S. & Liu, G. Numerical Modelling of Free-Surface Flows with Bottom and Surface-Layer Pressure Treatment. J Hydrodyn 21, 352–359 (2009). https://doi.org/10.1016/S1001-6058(08)60156-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1001-6058(08)60156-0

Key words

Search

Navigation