Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows

Fluid Dynamics Research

Volumn 38, Issue 9, 2006, Pages 641-659

  Inamuro, Takaji ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Binary droplet collision; Bubble flow; Lattice Boltzmann method; Lattice kinetic scheme; Two phase flow; Unsteady flow in porous media

Indexed keywords

BUBBLES (IN FLUIDS); COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; NUMERICAL METHODS; POROUS MATERIALS; TWO PHASE FLOW;

BINARY DROPLET COLLISION; BUBBLE FLOW; LATTICE BOLTZMANN METHOD; LATTICE KINETIC SCHEME;

VISCOUS FLOW;

BUBBLES (IN FLUIDS); COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; NUMERICAL METHODS; POROUS MATERIALS; TWO PHASE FLOW; VISCOUS FLOW;

EID: 33746387506     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fluiddyn.2006.02.007     Document Type: Article

References (51)

1. Anderson D.M., McFadden G.B., and Wheeler A.A. Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1998) 139-165
2. Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1998) 329-364
3. Chen S., Chen H., Martinez D., and Mattaeus W.H. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys. Rev. Lett. 67 (1991) 3776-3779
4. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 745-762
5. Chou S.Y., and Baganoff D. Kinetic flux-vector splitting for the Navier-Stokes equations. J. Comput. Phys. 130 (1997) 217-230
6. d'Humières, D., 1992. Generalized lattice-Boltzmann equations. In: Shizgal, B.D., Weaver, D.P. (Eds.), Rarefied Gas Dynamics, Progress in Astronautics and Aeronautics, vol. 159. AIAA, Washington, DC, pp. 450-458.
7. Ginzburg I., and Steiner K. Lattice Boltzmann model for free-surface flow and its application to filling process in casting. J. Comput. Phys. 185 (2003) 61-99
8. Gunstensen A.K., Rothman D.H., Zaleski S., and Zanetti G. Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43 (1991) 4320-4327
9. He, X., Luo, L.-S., 1997a. A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55, 6333-6336.
10. He X., and Luo L.-S. Theory of the lattice Boltzmann equation: from Boltzmann equation to lattice Boltzmann equation. Phys. Rev. E 56 (1997) 6811-6817
11. He X., Chen S., and Doolen G.D. A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 146 (1998) 282-300
12. He X., Chen S., and Zhang R. A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J. Comput. Phys. 152 (1999) 642-663
13. Inamuro T., Yoshino M., and Ogino F. A non-slip boundary condition for lattice Boltzmann simulations. Phys. Fluids 7 (1995) 2928-2930 (Erratum: 8 (1996) 1124)
14. Inamuro T., Yoshino M., and Ogino F. Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number. Phys. Fluids 9 (1997) 3535-3542
15. Inamuro T., Yoshino M., and Ogino F. Lattice Boltzmann simulation of flows in a three-dimensional porous structure. Int. J. Numer. Meth. Fluids 29 (1999) 737-748
16. Inamuro T., Maeba K., and Ogino F. Flow between parallel walls containing the lines of neutrally buoyant circular cylinders. Int. J. Multiphase Flow 26 (2000) 1981-2004
17. Inamuro T., Konishi N., and Ogino F. A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach. Comput. Phys. Commun. 129 (2000) 32-45
18. Inamuro T., Miyahara T., and Ogino F. Lattice Boltzmann simulations of drop deformation and breakup in simple shear flow. In: Satofuka N. (Ed). Computational Fluid Dynamics, 2000 (2001) 499-504
19. Inamuro T., Yoshino M., Inoue H., Mizuno R., and Ogino F. A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat transfer problem. J. Comput. Phys. 179 (2002) 201-215
20. Inamuro, T., Mizuno, R., Ogino, F., 2002b. Lattice Boltzmann simulation of flow and heat- and mass-transfer with a chemical reaction in a porous structure. In: Taine, J. (Ed.), Proceedings of the 12th International Heat Transfer Conference. Elsevier SAS, pp. 519-524.
21. Inamuro T. A lattice kinetic scheme for incompressible viscous flows with heat transfer. Phil. Trans. R. Soc. Lond. A 360 (2002) 477-484
22. Inamuro T., Tomita R., and Ogino F. Lattice Boltzmann simulations of drop deformation and breakup in shear flows. Int. J. Mod. Phys. B 17 (2003) 21-26
23. Inamuro T., and Ogata T. A lattice kinetic scheme for bubble flows. Phil. Trans. R. Soc. Lond. A 362 (2004) 1735-1743
24. Inamuro T., Ogata T., and Ogino F. Numerical simulation of bubble flows by the lattice Boltzmann method. Future Generation Computer Systems 20 (2004) 959-964
25. Inamuro T., Ogata T., Tajima S., and Konishi N. A lattice Boltzmann method for incompressible two-phase flows with large density differences. J. Comput. Phys. 198 (2004) 628-644
26. Inamuro T., Tajima S., and Ogino F. Lattice Boltzmann simulation of droplet collision dynamics. Int. J. Heat Mass Transfer 47 (2004) 4649-4657
27. Jacqmin D. Calculation of two-phase Navier-Stokes using phase-field modeling. J. Comput. Phys. 155 (1999) 96-127
28. Junk M., and Rao S.V. A New discrete velocity method for Navier-Stokes equations. J. Comput. Phys. 151 (1999) 178-198
29. Ladd A.J.C. Sedimentation of homogeneous suspensions of non-Brownian spheres. Phys. Fluids 9 (1997) 491-499
30. Lallemand P., and Luo L.-S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61 (2000) 6546-6562
31. Luo L.S. Unified theory of lattice Boltzmann models for nonideal gases. Phys. Rev. Lett. 81 (1998) 1618-1621
32. Luo L.S. Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases. Phys. Rev. E 62 (2000) 4982-4996
33. Luo L.S., and Girimaji S.S. Lattice Boltzmann model for binary mixtures. Phys. Rev. E 66 (2002) 035301
34. Luo L.S., and Girimaji S.S. Theory of the lattice Boltzmann method: two-fluid model for binary mixtures. Phys. Rev. E 67 (2003) 036302
35. Peng Y., Shu C., Chew Y.T., and Inamuro T. A lattice kinetic scheme for the incompressible viscous thermal flows on arbitrary meshes. Phys. Rev. E 69 (2004) 016703
36. Qian Y., d'Humières D., and Lallemand P. Lattice BGK models for the Navier-Stokes equation. Europhys. Lett. 17 (1992) 479-484
37. Rothman D.H., and Zaleski S. Lattice-Gas Cellular Automata (1997), Cambridge University Press, Cambridge
38. Rowlinson, J.S., Widom, B., 1989. Molecular Theory of Capillarity. Clarendon, Oxford, pp. 50-68 (Chapter 3).
39. Shan X. Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method. Phys. Rev. E 55 (1997) 2780-2788
40. Shan X., and Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47 (1993) 1815-1819
41. Sone, Y., 1971. Asymptotic theory of flow of rarefied gas over a smooth boundary II. In: Dini, D. (Ed.), Rarefied Gas Dynamics, vol. 2. Editrice Tecnico Scientifica, Pisa, pp. 737-749.
42. Sone Y. Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers. In: Gatignol R., and Soubbaramayer R. (Eds). Advances in Kinetic Theory and Continuum Mechanics (1991), Springer, Berlin 19-31
43. Sone, Y., 2000. Notes on kinetic-equation approach of fluid-dynamic equations. Mekanik-KTH 2000:09, Department of Mechanics, Royal Institute of Technology, Stockholm.
44. Sone, Y., 2002. Kinetic Theory and Fluid Dynamics, Appendix C. Birkhäuser, Boston, pp. 315-326.
45. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (2001), Oxford University Press, Oxford
46. Swift M.R., Osborn W.R., and Yeomans J.M. Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett. 75 (1995) 830-833
47. Teng S., Chen Y., and Ohashi H. Lattice Boltzmann simulation of multiphase fluid flows through the total variation diminishing artificial compression scheme. Int. J. Heat Fluid Flow 21 (2000) 112-121
48. Wolf-Gladrow D.A. Lattice-Gas Cellular Automata and Lattice Boltzmann Models (2000), Springer, Berlin
49. Xu K., and Prendergast K.H. Numerical Navier-Stokes solutions from gas kinetic theory. J. Comput. Phys. 114 (1994) 9-17
50. Yoshino M., and Inamuro T. Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three-dimensional porous structure. Int. J. Numer. Meth. Fluids 43 (2003) 183-198
51. Yu D., Mei R., Luo L.-S., and Shyy W. Viscous flow computation with the method of lattice Boltzmann equation. Progress in Aerospace Sciences 39 (2003) 329-367