A many-component lattice Boltzmann equation simulation for transport of deformable particles

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 362, Issue 1822, 2004, Pages 1885-1914

  Dupin, M M ^a   Spencer, T J ^a   Halliday, I ^a   Care, C M ^a  

^a SHEFFIELD HALLAM UNIVERSITY   (United Kingdom)

Author keywords

Blunting; Lattice Boltzmann; N component flow; Pressure driven flow

Indexed keywords

EID: 4544224993     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2004.1422     Document Type: Review

References (82)

1. Abe, T. 1966 J. Comput. Phys. 131, 241-246.
2. Alexander, F. J., Chen, S. & Sterling, J. D. 1993 Phys. Rev. E 47, 2249-2252.
3. Allen, M. P. & Tildesley, D. J. 1997 Computer simulation of liquids. Oxford: Clarendon.
4. Anderson, J. D. 1995 Computation fluid dynamics: the basics with applications. McGraw-Hill.
5. Armely, B. F., Durst, F., Pereira, J. C. F. & Schönung, B. 1983 J. Fluid Mech. 127, 473-496.
6. Benzi, R., Succi, S. & Vergassola, M. 1992 Phys. Rep. 222, 145-197.
7. Bhatnagar, P. E., Gross, P. E. & Krook, M. 1954 Phys. Rev. A 94, 511-525.
8. Boghosian, B. & Taylor, W. 1997 Int. J. Mod. Phys. C 8, 705-716.
9. Broadwell, J. E. 1964 Phys. Fluids 7, 1243-1247.
10. Cali, A., Luo, L. S., Cancelliere, A., Benzi, R. & Gramignani, M. 1992 Phys. Rev. A 45, 5771-5774.
11. Caro, C. G., Pedeley, T. J., Schroter, R. C. & Seed, W. A. 1998 The mechanics of the circulation. Oxford Medical Publications.
12. Chapman, S. & Cowling, T. G. 1970 The mathematical theory of non-uniform gases, 3rd edn. Cambridge University Press.
13. Chen, H., Chen, S. & Matthaeus, W. H. 1992 Phys. Rev. A 45(8), 5339-5342.
14. Chen, S. & Doolen, G. D. 1998 A. Rev. Fluid Mech. 30, 329-364.
15. Chen, S., Chen, H., Martinez, C. & Matthaeus, W. 1991 Phys. Rev. Lett. 67(27), 3776-3779.
16. Chen, Y., Ohashi, H. & Akiyama, M. 1997 JSME Int. J. B 40(1), 25-32.
17. Chen, Y., Ohashi, H. & Akiyama, M. 1994 Phys. Rev. E 50(4), 2776-2783.
18. Conner, J. & Brebbia, C. 1976 Finite element techniques for fluid flow. Woburn, MA: Newnes-Butterworth.
19. Denham, M. K. & Patrick, M. A. 1974 Trans. IChE 52, 361-367.
20. D'Humières, D., Lallemand, P. & Qian, Y. H. 1989 Review of flow simulations using lattice gases. Lecture Notes in Mathematics, vol. 1402, pp. 56-58. Springer.
21. Do-Quang, M., Aurell, E. & Vergassola, M. 2000 An inventory of lattice Boltzmann models of multiphase flows. Technical Report, ISSN 0348-467X. (Available at http://www.psci.kth.se/Activities/Reports/Results/R_2000_03/ psci2000_03.pdf.)
22. Dupin, M. M., Halliday, I. & Care, C. M. 2003 Multi-component lattice Boltzmann equation for mesoscale blood flow J. Phys. A 36, 8517-8534.
23. Dupin, M. M., Halliday, I. & Care, C. M. 2004 A lattice Boltzmann model of flow blunting. Phil. Trans. R. Soc. Lond. A 362, 1755-1761.
24. Español, P. 2002 SIMU Newsletter, issue 4, ch. III, pp. 59-77. (Available at http://simu.ulb.ac.be/newsletters/N4III.pdf.)
25. Ferreol, B. & Rothman, D. H. 1995 Transport Porous Media 20, 3-20.
26. Filippova, O. & Hanel, D. 1998 Grid refinement for lattice-BGK models. J. Comput. Phys. 147, 219-228.
27. Frank, M., Anderson, D., Weeks, E. R. & Morris, J. F. 2003 J. Fluid Mech. 493, 363-378.
28. Frisch, U., Hasslacher, B. & Pomeau, Y. 1986 Phys. Rev. Lett. 56, 1505-1508.
29. Goodfellow, J. 1991 Molecular dynamics. London: Macmillan.
30. Groot, R. D. & Warren, P. B. 1997 J. Chem. Phys. 107, 4423-4435.
31. Gunstensen, A. K., Rothmann, D. H., Zaleski, S. & Zanetti, G. 1991 Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320-4327.
32. Halliday, I., Care, C. M. & Thompson, S. P. 1998 Macroscopic surface tension in a lattice Bhatnagar-Gross-Krook model of two immiscible fluids. Phys. Rev. E 57, 514-523.
33. Halliday, I., Hammond, L. A., Care, C. M., Good, K. & Stevens, A. 2001 Lattice Boltzmann equation hydrodynamics. Phys. Rev. E 64, 011208.
34. Halliday, I., Hammond, L. A. & Care, C. M. 2002 J. Phys. A 35, 157-166.
35. Hardy, J., Pomeau, Y. & De Pazzis, O. 1973 J. Math. Phys. 14, 1746-1759.
36. Hardy, J., De Pazzis, O. & Pomeau, Y. 1976 Phys. Rev. A 13, 1949-1961.
37. He, X. & Doolen, G. D. 1997a Phys. Rev. E 56, 434-440.
38. He, X. & Doolen, G. D. 1997b J. Comput. Phys. 134(2), 306-315.
39. He, X. & Luo, L. S. 1997a Phys. Rev. E 55(6), 6333-6336.
40. He, X. & Luo, L. S. 1997b Phys. Rev. E 56(6), 6811-6817.
41. He, X., Zou, Q., Luo, L. S. & Dembo, M. 1997a J. Stat. Phys. 87, 115-136.
42. He, X., Luo, L. S. & Dembo, M. 1997b Physica A 239, 276-285.
43. Higuera, F. & Luo, L. S. 1989 Europhys. Lett. 8, 517-521.
44. Hoogerbrugge, P. J. & Koelman, J. M. V. A. 1992 Europhys. Lett. 19, 155-160.
45. Hou, S. 1995 PhD thesis, Kansas State University, Manhatten, KS, USA.
46. Hou, S., Zou, Q., Chen, S. & Doolen, G. D. A. C. 1995 J. Comput. Phys. 118, 329-347.
47. Hou, S., Sterling, S. & Doolen, G. D. 1996 Fields Inst. Commun. 6, 151-166.
48. Kadanoff, L. P., McNamara, G. R. & Zanetti, G. 1989 Phys. Rev. A 40(8), 4527-4541.
49. Kueny, L. J. & Binder, G. 1984 Viscous flow over backward facing steps: an experimental investigation, analysis of laminar flow over a backward facing step. Not. Fluid Mech. 9, 32-42.
50. Ladd, A. J. C. 1994 J. Fluid Mech. 271, 311-339.
51. Landau, L. D. & Lifshitz, E. M. 1995 Fluid mechanics. Course in Theoretical Physics, 2nd edn, vol. 6. Oxford: Butterworth-Heinemann.
52. Liboff, R. C., Herman, J. & Liboff, R. L. 2003 Kineic theory, 2nd edn. Springer.
53. Lin, Z., Fang, H. & Tao, R. 1996 Phys. Rev. E 54(6), 6323-6330.
54. Lishchuk, S. V., Care, C. M. & Halliday, I. 2003 Phys. Rev. E 67, 036701.
55. Luo, L. S. 1998 Phys. Rev. Lett. 81(8), 1618-1621.
56. Luo, L. S., Wang, J. & Qian, Y. H. 1997 Int. J. Mod. Phys. C 8(4), 999-1008.
57. Luo, L. S. 2000 Phys. Rev. E 64(4), 4982-4996.
58. McNamara, G. R. & Zanetti, G. 1988 Phys. Rev. Lett. 61(20), 2332-2335.
59. Maier, R. S., Bernard, R. S. & Grunau, D. W. 1996 Phys. Fluids 8(7), 1788-1801.
60. Martinez, D. O., Chen, S. & Matthaeus, W. H. 1994 Phys. Plasmas 1, 1850-1867.
61. Mei, R., Shyy, S., Yu, D. & Luo, L. S. 2000 J. Comput. Phys. 161, 680-699.
62. Noble, D. R., Georgiadis, J. G. & Buckius, R. O. 1995 J. Stat. Phys. 81, 17-33.
63. Qian, Y. H. & Zhou, Y. 1998 Europhys. Lett. 42(4), 359-364.
64. Qian, Y. H., D'Humières, D. & Lallemand, P. 1992 Europhys. Lett. 17(6), 479-484.
65. Qian, Y. H., Luo, L. S., Massaioli, F. & Orszag, S. A. 1996 Fields Inst. Commun. 6, 207-215.
66. Reider, M. B. & Sterling, J. D. 1995 Comput. Fluids 24, 459-467.
67. Rothmann, D. H. & Zaleski, S. 1994 Rev. Mod. Phys. 66(4), 1417-1479.
68. Shan, X. W. & Chen, H. D. 1994 Phys. Rev. E 49(4), 2941-2948.
69. Skordos, P. A. 1993 Phys. Rev. E 48(6), 4823-4842.
70. Spencer, T. J., Dupin, M. M., Halliday, I. & Care, C. M. 2004 An incompressible Lattice BGK scheme with enhanced stability. (In preparation.)
71. Succi, S. 2001 The lattice Boltzmann equation. Oxford: Clarendon.
72. Succi, S. 2002 Phil. Trans. R. Soc. Lond. A 360, 429-436.
73. Succi, S., Foti, E. & Higuera, F. 1989 Europhys. Lett. 10, 433-438.
74. Succi, S., Benzi, R. & Higuera, F. 1991 Physica D 47, 219-230.
75. Swift, M. R., Osborn, W. R. & Yoemans, J. M. 1995 Phys. Rev. Lett. 75(5), 830-833.
76. Thompson, S. P., Halliday, I. & Care, C. M. 1999 Mesoscopic hydrodynamics of diphasic lattice Bhatnagar-Gross-Krook fluid interfaces. Phys. Chem. Chem. Phys. 1, 2183-2190.
77. Tölke, J., Krafczyk, M., Schultz, M., Rank, E. & Berrios, R. 1998 Int. J. Mod. Phys. C 9, 1143-1157.
78. von Neumann, J. 1966 Theory of self-reproducting automata. University of Illinois Press.
79. Wagner, L. 1994 Phys. Fluids 6, 3516-3518.
80. Wolfram, S. 1986 Rev. Mod. Phys. 55, 601-644.
81. Yang, Z. L., Dinh, T. N., Nourgaliev, R. R. & Sehgal, B. R. 2001 Int. J. Heat Mass Transfer 44, 195-206.
82. Zou, Q., Hou, S., Chen, S. & Doolen, G. D. 1995 Analytical solutions of the lattice Boltzmann BGK model. J. Stat. Phys. 81, 319-334.