Lattice Boltzmann Method and its Applications to Fluid Flow Problems (original) (raw)

Abstract

The main objective of this paper is to demonstrate the validity of lattice Boltzmann method (LBM) for different flows and phase transition process. For the present simulation D2Q9 model has been used. The soundness of LBM has been checked by implementing it on test problems including Plane Poiseuille flow, Planar Couette flow and Lid Driven Cavity flow. The results of these simulations show the capability of present incom-pressible LBM model in handling both steady and unsteady flows. Blood flow simulation has been performed using Casson's Rheology model and lastly, phase transition process has been simulated using Shan and Chen model. The results obtained for blood flow and phase transition process are in excellent agreement with the analytical results and the results present in literature.

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References (38)

  1. G. McNamara and G. Zanetti, Phys. Rev. Lett. 61, 2332,1988
  2. J. Higuera, S. Succi, and R. Benzi, Europhys. Lett. 9, 345,1989
  3. H. Chen, S. Chen, and W. H. Matthaeus, Phys. Rev. A 45, R5339 ,1991
  4. Y. H. Qian, D. d'Humie`res, and P. Lallemand, Europhys. Lett. 17, 479 ,1992
  5. Lattice Gas Methods for Partial Differential Equations, edited by Gary D. Doolen, Addison- Wesley, Redwood City, CA, 1990
  6. Lattice Gas Methods: Theory, Applications, and Hardware, edited by Gary D. Doolen, MIT, Cam-bridge, 1991
  7. Dieter A. Wolf Gladrow, Lattice Gas Cellular Automata and Lattice Boltzmann Models, Lectures Notes in Mathematics, 1st Edition, Springer Verlag Berlin Heidelberg, New York, 2000.
  8. Special issue on lattice-based models and related topics, edited by J. L. Lebowitz, S. A. J. Stat. Phys. 81, 1995
  9. M. Sahimi, Flow phenomena in rocks: from continuum models to fractals, percolation, cellular au-tomata and simulated annealing, Rev. Mod. Phys. 65(4), 1393, 1993.
  10. J. Bear, Dynamics of Fluids in Porous Media, Elsevier, New York, 1972
  11. S. Succi, E. Foti and M. Gramignani, Flow through geometrically irregular media with lattice Gas Automata, Meccanica 25, 253, 1990.
  12. S. Chen, K. Diemer, G. Doolean, K. Eggert, C.Fu, S. Gutman and B. Travis, Lattice gas models for non ideal fluids, Physica D 47, 97, 1991.
  13. R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145, 1992.
  14. E. Foti, S Succi and F. Higuera, Three dimensional flows in complex geometries with the lattice Boltzmann method, Europhys. Lett. 10(5), 433, 1989.
  15. A. Gunstensen, D. Rothman, S. Zaleski and G. Zanetti, Lattice Boltzmann model of immiscible fluids, Phy. Rev. A 43(8),4320, 1991.
  16. D. Rothman and S. Zaleski, lattice gas models of phase seperation, Rev. Mod. Phys.66, 1417, 1994.
  17. A. Gunstensen, and D. Rothman, Lattice Boltzmann studies of immiscible two phase flows through porous media, Phys. Rev. A 43, 4320, 1991
  18. H. Shan and H. Chen, Simulation of non ideal gas and liquid gas phase transitions by the Lattice Boltzmann equations, Phys. Rev. E 49, 2941, 1995.
  19. M. Swift, W. Osborne and J. Yeomans, Lattice Boltzmann simulations of non ideal fluids, Phys. Rev.Lett.75, 830, 1995.
  20. X. Shan, Simualtion of Rayleigh Benard convection using Lattice Boltzmann method, Phys. Rev. E 55, 2780, 1997.
  21. K. Xu and L. S. Luo, Connection between lattice Boltzmann equation and beam scheme. Int. J. Mod. Phys. C 9(8), 1177, 1998.
  22. F. Alexander, S. Chen and J. Sterling, Lattice Boltzmann thermo hydrodynamics, Phys. Rev. E 53, 2298, 1993.
  23. Y. Chen, H. Ohashi and M. Akiyama, Thermal lattice Bhatnagar Gross Krook model without non linear deviations in macrodynamic equations, Phys. Rev. E 50, 2776, 1994.
  24. Y. Chen, Lattice Bhatnagar Gross Krook Methods for Fluid Dynamics: Compressible, Thermal and Multiphase Models, Ph.D. Thesis Dept. of Quantum Engineering and System Science, Uni- versity of Tokyo, 1994.
  25. G. Yan, Y. Chen and S. Hu, Simple lattice Boltzmann for simulating flows with shock waves, Phys. Rev. E 59, 454, 1999.
  26. S. H. Qisu Zou et al, "Simulation of Cavity Flow by the Lattice Boltzmann Method", Journal of Computational Physics, Volume 118 Page 329-347, Nov. 1994
  27. Rafik Ouared and Bastien Chopard, "Lattice Boltzmann Simulations of Blood Flow Non Newto-nian Rheology and Clotting Processes," Journal of Statistical Physics, Vol.121, Nos.112, October 2005.
  28. Shan X and Chen H, "Lattice Boltzmann model for simulating flows with multiple phases and components", Physical Review, Vol.47, No.3 p.1815-1817, 1993
  29. Michael C.Sukop, Daniel T.Thorne, Jr., Lattice Boltzmann Modeling An Introduction for Geo- scientists and Engineers, 1st Edition, Springer Verlag Berlin Heidelberg, 2006
  30. Sauro Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, 1st Edition, Clar-endon Press Oxford, 2001
  31. J. L. Sohn, Int. J. Numer. Methods Fluids , Volume 8, Page1469,1988
  32. Rothman D.H., "Cellular Automata Fluids: A Model for Flow in Porous Media", Geophysics 53: 509-518, 1988
  33. Appert C. and Zaleski S., "Lattice Gas with Liquid Gas Transition", Phys Rev Lett, 64:1-4, 1990.
  34. Swift M.R., Orlandini E, Osborn W. R. and Yeomans J.M., "LB Simulations of Liquid Gas and Binary Fluid", Phys Rev E 54:5041-5052, 1996.
  35. He X, and Doolen G. D., "Thermodynamic foundations of kinetic Theory and LB Models for Multiphase Flows", J Stat Phys 107:309-328, 2002.
  36. Zhang R, and Chen H, "LBM for Liquid Vapor Thermal Flows", Phys Rev E 67, 2003
  37. D. Rothman and S. Zaleski,"Lattice gas models of phase separation", Rev. Mod. Phys. 66, 1417, 1999
  38. Begum, R., Basit, M. A., Chughtai, I.R.," Lattice Boltzmann Simulation of Flow in a Lid Driven Square Cavity", Science International Lahore Pakistan.