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Localized Parallel Algorithm for Bubble Coalescence in Free Surface Lattice-Boltzmann Method

  • Stefan Donath
  • Christian Feichtinger
  • Thomas Pohl
  • Jan Götz
  • Ulrich Rüde
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5704)

Abstract

The lattice Boltzmann method is a popular method from computational fluid dynamics. An extension of this method handling liquid flows with free surfaces can be used to simulate bubbly flows. It is based on a volume-of-fluids approach and an explicit tracking of the interface, including a reconstruction of the curvature to model surface tension. When this algorithm is parallelized, complicated data exchange is required, in particular when bubbles extend across several subdomains and when topological changes occur through coalescence of bubbles. In a previous implementation this was handled by using all-to-all MPI communication in each time step, restricting the scalability of the simulations to a moderate parallelism on a small number of processors. In this paper, a new parallel bubble merge algorithm will be introduced that communicates updates of the bubble status only locally in a restricted neighborhood. This results in better scalability and is suitable for massive parallelism. The algorithm has been implemented in the lattice Boltzmann software framework waLBerla, resulting in parallel efficiency of 90% on up to 4080 cores.

Keywords

Lattice Boltzmann Method Interface Cell Lattice Boltzmann Model Bubble Coalescence Lattice Boltzmann Simulation 
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.

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References

  1. 1.
    Mashayek, F., Ashgriz, N.: A hybrid finite-element-volume-of-fluid method for simulating free surface flows and interfaces. Int. J. Num. Meth. Fluids 20, 1363–1380 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ghidersa, B.: Finite Volume-based Volume-of-Fluid method for the simulation of two-phase flows in small rectangular channels. PhD thesis, University of Karlsruhe (2003)Google Scholar
  3. 3.
    Gueyffier, D., Li, J., Nadim, A., Scardovelli, S., Zaleski, S.: Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comp. Phys. 152, 423–456 (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Aulisa, E., Manservisi, S., Scardovelli, R., Zaleski, S.: A geometrical area-preserving volume-of-fluid method. J. Comp. Phys. 192, 355–364 (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Chang, Y., Hou, T., Merriam, B., Osher, S.: A level set formulation of Eularian interface capturing methods for incompressible fluid flows. J. Comp. Phys. 124, 449–464 (1996)CrossRefGoogle Scholar
  6. 6.
    Sussman, M., Fatemi, E., Smereka, P., Osher, S.: An improved level set method for incompressible two-phase flows. Comp. & Fl 27(5–6), 663–680 (1998)CrossRefzbMATHGoogle Scholar
  7. 7.
    Osher, S., Fedkiw, R.P.: Level set methods: an overview and some recent results. J. Comp. Phys. 169(2), 463–502 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zinchenko, A.Z., Rother, M.A., Davis, R.H.: Cusping, capture and breakup of interacting drops by a curvatureless boundary-integral algorithm. J. Fluid Mech. 391, 249 (1999)CrossRefzbMATHGoogle Scholar
  9. 9.
    Hou, T., Lowengrub, J., Shelley, M.: Boundary integral methods for multicomponent fluids and multiphase materials. J. Comp. Phys. 169, 302–362 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gunstensen, A.K., Rothman, D.H., Zaleski, S., Zanetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320–4327 (1991)CrossRefGoogle Scholar
  11. 11.
    Rothmann, D., Keller, J.: Immiscible cellular automaton fluids. J. Stat. Phys. 52, 1119–1127 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Tölke, J.: Gitter-Boltzmann-Verfahren zur Simulation von Zweiphasenströmungen. PhD thesis, Technical University of Munich (2001)Google Scholar
  13. 13.
    Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47(3), 1815–1820 (1993)CrossRefGoogle Scholar
  14. 14.
    Inamuro, T., Tomita, R., Ogino, F.: Lattice Boltzmann simulations of drop deformation and breakup in shear flows. Int. J. Mod. Phys. B 17, 21–26 (2003)CrossRefGoogle Scholar
  15. 15.
    Orlandini, E., Swift, M.R., Yeomans, J.M.: A lattice Boltzmann model of binary-fluid mixtures. Europhys. Lett. 32, 463–468 (1995)CrossRefGoogle Scholar
  16. 16.
    Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54(5), 5041–5052 (1996)CrossRefGoogle Scholar
  17. 17.
    He, X., Chen, S., Zhang, R.: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J. Comp. Phys. 152, 642–663 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Ginzburg, I., Steiner, K.: Lattice Boltzmann model for free-surface flow and its application to filling process in casting. J. Comp. Phys. 185, 61–99 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Körner, C., Thies, M., Hofmann, T., Thürey, N., Rüde, U.: Lattice Boltzmann model for free surface flow for modeling foaming. J. Stat. Phys. 121(1–2), 179–196 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Thürey, N.: Physically based Animation of Free Surface Flows with the Lattice Boltzmann Method. PhD thesis, Univ. of Erlangen (2007)Google Scholar
  21. 21.
    Thürey, N., Pohl, T., Rüde, U., Oechsner, M., Körner, C.: Optimization and stabilization of LBM free surface flow simulations using adaptive parameterization. Comp. & Fl. 35(8–9), 934–939 (2006)CrossRefzbMATHGoogle Scholar
  22. 22.
    Thürey, N., Rüde, U.: Free surface lattice-Boltzmann fluid simulations with and without level sets. In: VMV, pp. 199–208. IOS Press, Amsterdam (2004)Google Scholar
  23. 23.
    Xing, X.Q., Butler, D.L., Ng, S.H., Wang, Z., Danyluk, S., Yang, C.: Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model. J. Coll. Int. Sci. 311, 609–618 (2007)CrossRefGoogle Scholar
  24. 24.
    Pohl, T.: High Performance Simulation of Free Surface Flows Using the Lattice Boltzmann Method. PhD thesis, Univ. of Erlangen (2008)Google Scholar
  25. 25.
    Pohl, T., Thürey, N., Deserno, F., Rüde, U., Lammers, P., Wellein, G., Zeiser, T.: Performance evaluation of parallel large-scale lattice Boltzmann applications on three supercomputing architectures. In: SC 2004: Proceedings of the 2004 ACM/IEEE conference on Supercomputing (2004)Google Scholar
  26. 26.
    Körner, C., Pohl, T., Rüde, U., Thürey, N., Zeiser, T.: Parallel lattice Boltzmann methods for CFD applications. In: Bruaset, A., Tveito, A. (eds.) Numerical Solution of Partial Differential Equations on Parallel Computers. Lecture Notes for Computational Science and Engineering, vol. 51, pp. 439–465. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Körner, C., Thies, M., Singer, R.F.: Modeling of metal foaming with lattice Boltzmann automata. Adv. Eng. Mat. 4, 765–769 (2002)CrossRefGoogle Scholar
  28. 28.
    Succi, S.: The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford (2001)zbMATHGoogle Scholar
  29. 29.
    Parker, B.J., Youngs, D.L.: Two and three dimensional Eulerian simulation of fluid flow with material interfaces. Technical Report 01/92, UK Atomic Weapons Establishment, Berkshire (1992)Google Scholar
  30. 30.
    Feichtiner, C., Götz, J., Donath, S., Iglberger, K., Rüde, U.: Concepts of waLBerla Prototype 0.1. Technical Report 07-10, Chair for System Simulation, Univ. of Erlangen (2007)Google Scholar
  31. 31.
    Feichtinger, C., Götz, J., Donath, S., Iglberger, K., Rüde, U.: WaLBerla: Exploiting massively parallel systems for lattice Boltzmann simulations. In: Trobec, R., Vajteršic, M., Zinterhof, P. (eds.) Parallel Computing: Numerics, Applications, and Trends. Springer, UK (2009)Google Scholar
  32. 32.
  33. 33.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Stefan Donath
    • 1
  • Christian Feichtinger
    • 1
  • Thomas Pohl
    • 1
  • Jan Götz
    • 1
  • Ulrich Rüde
    • 1
  1. 1.Friedrich-Alexander University Erlangen-Nuremberg, Chair for System Simulation (LSS)ErlangenGermany

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