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Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast

J. Y. Shao1, C. Shu1,*, H. B. Huang2, and Y. T. Chew1

  • 1Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
  • 2Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China

  • *Corresponding author: mpeshuc@nus.edu.sg
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Phys. Rev. E 89, 033309 – Published 19 March, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.033309

Abstract

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

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References (49)

  1. R. R. Nourgaliev, T. N. Dinh, T. G. Theofanous, and D. Joseph, Int. J. Multiphase Flow 29, 117 (2003).
  2. C. K. Aidun and J. R. Clausen, Annu. Rev. Fluid Mech. 42, 439 (2010).
  3. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991).
  4. X. W. Shan and H. D. Chen, Phys. Rev. E 47, 1815 (1993).
  5. X. W. Shan and H. D. Chen, Phys. Rev. E 49, 2941 (1994).
  6. X. Y. He, X. W. Shan, and G. D. Doolen, Phys. Rev. E 57, R13 (1998).
  7. X. Y. He, S. Y. Chen, and R. Y. Zhang, J. Comput. Phys. 152, 642 (1999).
  8. M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett. 75, 830 (1995).
  9. M. R. Swift, E. Orlandini, W. R. Osborn, and J. M. Yeomans, Phys. Rev. E 54, 5041 (1996).
  10. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28, 258 (1958).
  11. D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998).
  12. D. Jacqmin, J. Comput. Phys. 155, 96 (1999).
  13. D. Grunau, S. Y. Chen, and K. Eggert, Phys. Fluids A 5, 2557 (1993).
  14. U. D’Ortona, D. Salin, M. Cieplak, R. B. Rybka, and J. R. Banavar, Phys. Rev. E 51, 3718 (1995).
  15. M. Latva-Kokko and D. H. Rothman, Phys. Rev. E 71, 056702 (2005).
  16. T. Reis and T. N. Phillips, J. Phys. A: Math. Theor. 40, 4033 (2007).
  17. S. Leclaire, M. Reggio, and J. Y. Trepanier, Appl. Math. Modell. 36, 2237 (2012).
  18. S. Leclaire, M. Reggio, and J. Y. Trepanier, J. Comput. Phys. 246, 318 (2013).
  19. P. Yuan and L. Schaefer, Phys. Fluids 18, 042101 (2006).
  20. M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, and F. Toschi, Phys. Rev. E 75, 026702 (2007).
  21. X. W. Shan, Phys. Rev. E 73, 047701 (2006).
  22. X. W. Shan, Phys. Rev. E 81, 045701 (2010).
  23. G. Y. Liang, Z. Zeng, Y. Chen, J. Onishi, H. Ohashi, and S. Y. Chen, J. Comput. Phys. 248 323 (2013).
  24. X. Y. He, R. Y. Zhang, S. Y. Chen, and G. D. Doolen, Phys. Fluids 11, 1143 (1999).
  25. T. Lee and C. L. Lin, J. Comput. Phys. 206, 16 (2005).
  26. T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010).
  27. K. Connington and T. Lee, J. Comput. Phys. 250, 601 (2013).
  28. T. Lee, C. L. Lin, and L. D. Chen, J. Comput. Phys. 215, 133 (2006).
  29. A. Fakhari and T. Lee, Phys. Rev. E 87, 023304 (2013).
  30. L. Baroudi, M. Kawaji, and T. Lee, Comput. Math. Appl. 67, 282 (2014).
  31. T. Lee and P. F. Fischer, Phys. Rev. E 74, 046709 (2006).
  32. D. Holdych, D. Rovas, J. Georgiadis, and R. Buckius, Int. J. Mod. Phys. C 9, 1393 (1998).
  33. T. Inamuro, T. Ogata, S. Tajima, and N. Konishi, J. Comput. Phys. 198, 628 (2004).
  34. H. W. Zheng, C. Shu, and Y. T. Chew, J. Comput. Phys. 218, 353 (2006).
  35. H. Ding, P. D. M. Spelt, and C. Shu, J. Comput. Phys. 226, 2078 (2007).
  36. F. Uriel, D. Dominique, H. Brosl, L. Pierre, P. Yves, and P. R. Jean, Complex syst. 1, 649 (1987).
  37. Z. L. Guo, B. C. Shi, and N. C. Wang, J. Comput. Phys. 165, 288 (2000).
  38. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 31, 688 (1959).
  39. H. W. Zheng, C. Shu, and Y. T. Chew, Phys. Rev. E 72, 056705 (2005).
  40. H. W. Zheng, C. Shu, Y. T. Chew, and J. H. Sun, Int. J. Numer. Meth. Fluids 56, 1653 (2008).
  41. A. Fakhari and M. H. Rahimian, Phys. Rev. E 81, 036707 (2010).
  42. Z. L. Guo, C. G. Zheng, and B. C. Shi, Phys. Rev. E 83, 036707 (2011).
  43. H. B. Huang and X. Y. Lu, Phys. Fluids 21, 092104 (2009).
  44. D. H. Sharp, Physica D 12, 3 (1984).
  45. G. Tryggvason, J. Comput. Phys. 75, 253 (1988).
  46. P. Lallemand and L. S. Luo, Phys. Rev. E 61, 6546 (2000).
  47. N. Ashgriz and J. Y. Poo, J. Fluid Mech. 221, 183 (1990).
  48. K. N. Premnath and J. Abraham, Phys. Fluids 17, 122105 (2005).
  49. J. Qian and C. K. Law, J. Fluid Mech. 331, 59 (1997).

Outline

Information

Phys. Rev. E 89, 033309– Published 19 March, 2014
  • Received 10 July 2013
  • Revised 13 November 2013

©2014 American Physical Society

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