Advertisement

Application of Lattice Boltzmann Method for Generation of Flow Velocity Field Over River Bed-Forms

  • Mikołaj Karpiński
  • Robert J. Bialik
  • Paweł M. Rowiński
Chapter
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)

Abstract

In this chapter a Lattice Boltzmann Method (LBM) was presented as a relatively simple tool for generation of flow velocity field over river sand waves. The special attention was paid to the way of discretization of the presented equations. The choice of this method was conditioned by its advantages for modeling of complex geometries. Moreover, the computations with use of this method are easy to parallelize in contrast to the widely used models. The numerical results were compared with the available laboratory data and a reasonable agreement was found among the mean fluid velocity over the stoss, crest and trough of the considered fixed, triangular dune.

Keywords

Large Eddy Simulation Lattice Boltzmann Method Collision Operator Sand Wave Discrete Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by the Institute of Geophysics of Polish Academy of Sciences through the project for Young Scientists No. 16/IGF PAN/ 2011/Mł. The authors are also grateful to V. Nikora, A. Rajwa, and A. Sukhodolov for stimulating discussions on this topic and constructive comments on the manuscript.

References

  1. Aberle J, Nikora V, Henning M, Ettmer B, Hentschel B (2010) Statistical characterization of bed roughness due to bed forms: a field study in the Elbe River at Aken. Germany. Water Resour Res 46:W03521CrossRefGoogle Scholar
  2. Bennett SJ, Best JL (1995) Mean flow and turbulence structure over fixed, 2-dimensional dunes - implications for sediment transport and bedform stability. Sedimentology 42(3):491–513CrossRefGoogle Scholar
  3. Best J, Kostaschuk R (2002) An experimental study of turbulent flow over a low-angle dune. J Geophys Res 107(C9):3135Google Scholar
  4. Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems. Phys Rev 94(3):511–525CrossRefGoogle Scholar
  5. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluids flows. Annu Rev Fluid Mech 30:329–364CrossRefGoogle Scholar
  6. Coleman SE, Melville BW (1994) Bed-form development. J Hydraul Eng ASCE 120(4):544–560CrossRefGoogle Scholar
  7. Coleman SE, Melville BW (1996) Initiation of bed forms on a flat sand bed. J Hydraul Eng ASCE 122(6):301–310CrossRefGoogle Scholar
  8. Coleman SE, Nikora VI, Aberle J (2011) Interpretation of alluvial beds through bed-elevation distribution moments. Water Resour Res 47:W11505CrossRefGoogle Scholar
  9. Fernandez R, Best J, Lopez F (2006) Mean flow, turbulence structure, and bed form superimposition across the ripple-dune transition. Water Resour Res 42(5):W05406CrossRefGoogle Scholar
  10. Grigoriadis DGE, Balaras E, Dimas AA (2010) Large-eddy simulations of unidirectional water flow over dunes. J Geophys Res 114:F02022CrossRefGoogle Scholar
  11. Grigoriadis DGE, Dimas AA, Balaras E (2012) Large-eddy simulations of wave turbulent boundary layer over rippled bed. Coast Eng 60:174–189CrossRefGoogle Scholar
  12. Guo Z, Zheng C, Shi B (2002) Discrete lattice effects on the forcing term in the lattice Boltzman method. Phys Rev E 65:046308CrossRefGoogle Scholar
  13. He X, Luo LS (1997) Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys Rev E 56:6811–6817CrossRefGoogle Scholar
  14. Hino M (1968) Equilibrium-range spectra of sand waves formed by flowing water. J Fluid Mech 34(3):565–573CrossRefGoogle Scholar
  15. Julien PY, Klaassen GJ (1995) Sand-dune geometry of large rivers during floods. J Hydraul Eng ASCE 121(9):657–663CrossRefGoogle Scholar
  16. Lyn DA (1993) Turbulence measurements in open-channel flows over artificial bed forms. J Hydraul Eng ASCE 119(3):306–326CrossRefGoogle Scholar
  17. Nelson JM, Smith JD (1989) Mechanics of flow over ripples and dunes. J Geophys Res 94(C6):8146–8162Google Scholar
  18. Nelson JM, McLean SR, Wolfe SR (1993) Mean flow and turbulence fields over 2-dimensional bed forms. Water Resour Res 29(12):3935–3953CrossRefGoogle Scholar
  19. Nikora VI, Sukhodolov AN, Rowinski PM (1997) Statistical sand wave dynamics in one-directional water flows. J Fluid Mech 351:17–39CrossRefGoogle Scholar
  20. Parsons DR, Best JL, Orfeo O, Hardy RJ, Kostaschuk R, Lane SN (2005) Morphology and flow fields of three-dimensional dunes, Rio Parana, Argentina: results from simultaneous multibeam echo sounding and acoustic Doppler current profiling. J Geophys Res 110(F4):F04S03Google Scholar
  21. Qian YH, D’Humieres D, Lallemand P (1992) Lattice BGK models for Navier-Stokes equation. Europhys Lett 17(479)Google Scholar
  22. Singh A, Lanzoni S, Wilcock PR, Foufoula-Georgiou E (2011) Multiscale statistical characterization of migrating bed forms in gravel and sand bed rivers. Water Resour Res 47:W12526CrossRefGoogle Scholar
  23. Sukhodolov AN, Fedele JJ, Rhoads BL (2006) Structure of flow over alluvial bedforms: an experiment on linking field and laboratory methods. Earth Surf Process Landforms 31:1292–1310CrossRefGoogle Scholar
  24. Stoesser T, Braun C, Garcia-Villalba M, Rodi W (2008) Turbulence structures in flow over two-dimensional dunes. J Hydraul Eng ASCE 134(1):42–55CrossRefGoogle Scholar
  25. Yue WS, Lin CL, Patel VC (2005) Large eddy simulation of turbulent open-channel flow with free surface simulated by level set method. Phys Fluids 17(2):025108CrossRefGoogle Scholar
  26. Yue WS, Lin CL, Patel VC (2006) Large-eddy simulation of turbulent flow over a fixed two-dimensional dune. J Hydraul Eng ASCE 132(7):643–651CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mikołaj Karpiński
    • 1
  • Robert J. Bialik
    • 1
  • Paweł M. Rowiński
    • 1
  1. 1.Institute of Geophysics, Polish Academy of SciencesWarsawPoland

Personalised recommendations