Improved axisymmetric lattice Boltzmann scheme

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 5, 2010, Pages

  Li, Q ^a   He, Y L ^a   Tang, G H ^a   Tao, W Q ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL SOLUTIONS; AXISYMMETRIC; AXISYMMETRIC FLOW; BENCH-MARK PROBLEMS; CYLINDRICAL CAVITIES; HAGEN-POISEUILLE FLOW; LATTICE BOLTZMANN METHOD; LATTICE-BOLTZMANN SCHEME; NUMERICAL RESULTS; SINGLE-PARTICLE; SINGULARITY PROBLEMS; SOURCE TERMS; VELOCITY GRADIENTS; WOMERSLEY FLOW;

DISTRIBUTION FUNCTIONS; GRAIN BOUNDARIES; NUMERICAL ANALYSIS; PHILOSOPHICAL ASPECTS;

DROP FORMATION;

EID: 77953344925     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.056707     Document Type: Article

References (61)

1. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986). 10.1103/PhysRevLett.56.1505
2. F. Higuera and J. Jiménez, EPL 9, 663 (1989). 10.1209/0295-5075/9/ 7/009
3. F. Higuera, S. Succi, and R. Benzi, EPL 9, 345 (1989). 10.1209/0295-5075/9/4/008
4. J. M. V. A. Koelman, EPL 15, 603 (1991). 10.1209/0295-5075/15/6/007
5. S. Chen, H. Chen, D. Martínez, and W. Matthaeus, Phys. Rev. Lett. 67, 3776 (1991). 10.1103/PhysRevLett.67.3776
6. Y. H. Qian, D. d'Humières, and P. Lallemand, EPL 17, 479 (1992). 10.1209/0295-5075/17/6/001
7. X. He and L.-S. Luo, Phys. Rev. E 56, 6811 (1997). 10.1103/PhysRevE.56. 6811
8. D. d'Humières, in Rarefied Gas Dynamics: Theory and Simulations, Prog. Astronaut. Aeronaut, edited by, B. D. Shizgal, and, D. P. Weaver, (AIAA, Washington, D.C., 1992), Vol. 159.
9. P. Lallemand and L.-S. Luo, Phys. Rev. E 61, 6546 (2000). 10.1103/PhysRevE.61.6546
10. D. d'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L.-S. Luo, Philos. Trans. R. Soc. London, Ser. A 360, 437 (2002). 10.1098/rsta.2001. 0955
11. P. J. Dellar, J. Comput. Phys. 190, 351 (2003). 10.1016/S0021-9991(03) 00279-1 (Pubitemid 37141658)
12. M. E. McCracken and J. Abraham, Phys. Rev. E 71, 036701 (2005). 10.1103/PhysRevE.71.036701 (Pubitemid 40619896)
13. K. N. Premnath and J. Abraham, J. Comput. Phys. 224, 539 (2007). 10.1016/j.jcp.2006.10.023
14. I. Ginzburg, Adv. Water Resour. 28, 1171 (2005). 10.1016/j.advwatres. 2005.03.004 (Pubitemid 41448126)
15. I. Ginzburg, Adv. Water Resour. 28, 1196 (2005). 10.1016/j.advwatres. 2005.03.009 (Pubitemid 41448127)
16. I. Ginzburg, F. Verhaeghe, and D. Humiéres, Comm. Comp. Phys. 3, 427 (2008).
17. S. Succi, Eur. Phys. J. B 64, 471 (2008). 10.1140/epjb/e2008-00067-3
18. R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992). 10.1016/0370-1573(92)90090-M
19. S. Chen and G. D. Doolen, Annu. Rev. Fluid Mech. 30, 329 (1998). 10.1146/annurev.fluid.30.1.329
20. A. J. C. Ladd and R. Verberg, J. Stat. Phys. 104, 1191 (2001). 10.1023/A:1010414013942
21. D. Yu, R. Mei, L.-S. Luo, and W. Shyy, Prog. Aerosp. Sci. 39, 329 (2003). 10.1016/S0376-0421(03)00003-4
22. B. Dünweg and A. J. C. Ladd, Adv. Polym. Sci. 221, 89 (2009).
23. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Clarendon Press, Oxford, 2001).
24. M. C. Sukop and D. T. Thorne Jr., Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers (Springer, Berlin, 2005).
25. I. Halliday, L. A. Hammond, C. M. Care, K. Good, and A. Stevens, Phys. Rev. E 64, 011208 (2001). 10.1103/PhysRevE.64.011208
26. Y. Peng, C. Shu, Y. T. Chew, and J. Qiu, J. Comput. Phys. 186, 295 (2003). 10.1016/S0021-9991(03)00067-6 (Pubitemid 36374163)
27. T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006). 10.1142/S0129183106008923 (Pubitemid 43829827)
28. T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007). 10.1103/PhysRevE.75.056703 (Pubitemid 47001023)
29. T. Reis and T. N. Phillips, Phys. Rev. E 77, 026703 (2008). 10.1103/PhysRevE.77.026703 (Pubitemid 351366304)
30. X. He, X. Shan, and G. D. Doolen, Phys. Rev. E 57, R13 (1998). 10.1103/PhysRevE.57.R13
31. X. He, S. Chen, and G. D. Doolen, J. Comput. Phys. 146, 282 (1998). 10.1006/jcph.1998.6057 (Pubitemid 128347125)
32. Z. Guo, C. Zheng, and B. Shi, Phys. Rev. E 65, 046308 (2002). 10.1103/PhysRevE.65.046308 (Pubitemid 40618993)
33. K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005). 10.1103/PhysRevE.71.056706 (Pubitemid 41481064)
34. K. N. Premnath and J. Abraham, Phys. Fluids 17, 122105 (2005). 10.1063/1.2148987 (Pubitemid 43124985)
35. S. Mukherjee and J. Abraham, Phys. Rev. E 75, 026701 (2007). 10.1103/PhysRevE.75.026701 (Pubitemid 46226233)
36. J. G. Zhou, Phys. Rev. E 78, 036701 (2008). 10.1103/PhysRevE.78.036701
37. S. Chen, J. Tölke, S. Geller, and M. Krafczyk, Phys. Rev. E 78, 046703 (2008). 10.1103/PhysRevE.78.046703
38. S. Chen, J. Tölke, and M. Krafczyk, Phys. Rev. E 79, 016704 (2009). 10.1103/PhysRevE.79.016704
39. Z. Guo, H. Han, B. Shi, and C. Zheng, Phys. Rev. E 79, 046708 (2009). 10.1103/PhysRevE.79.046708
40. F. M. White, Fluid Mechanics, 5th ed. (McGraw-Hill, New York, 2003).
41. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, England, 1970).
42. S. Hou, Q. Zou, S. Chen, G. Doolen, and A. C. Cogley, J. Comput. Phys. 118, 329 (1995). 10.1006/jcph.1995.1103
43. Q. Li, Y. L. He, G. H. Tang, and W. Q. Tao, Phys. Rev. E 80, 037702 (2009). 10.1103/PhysRevE.80.037702
44. X. He and L.-S. Luo, J. Stat. Phys. 88, 927 (1997). 10.1023/B:JOSS. 0000015179.12689.e4
45. R. Du, B. Shi, and X. Chen, Phys. Lett. A 359, 564 (2006). 10.1016/j.physleta.2006.07.074 (Pubitemid 44634231)
46. L. Zheng, B. Shi, and Z. Guo, Phys. Rev. E 78, 026705 (2008). 10.1103/PhysRevE.78.026705
47. S. Chen, Appl. Math. Comput. 193, 266 (2007). 10.1016/j.amc.2007.03.087 (Pubitemid 47562560)
48. Q. Zou and X. He, Phys. Fluids 9, 1591 (1997). 10.1063/1.869307
49. A. M. Artoli, A. G. Hoekstra, and P. M. A. Sloot, Int. J. Mod. Phys. C 13, 1119 (2002). 10.1142/S0129183102003826 (Pubitemid 36047019)
50. A. A. Wheeler, J. Cryst. Growth 102, 691 (1990). 10.1016/0022-0248(90) 90832-6 (Pubitemid 20722591)
51. D. Xu, C. Shu, and B. C. Khoo, J. Cryst. Growth 173, 123 (1997). 10.1016/S0022-0248(96)00791-9
52. H. Huang, T. S. Lee, and C. Shu, Int. J. Numer. Methods Fluids 53, 1707 (2007). 10.1002/fld.1380 (Pubitemid 46613392)
53. K. Hourigan, L. J. W. Graham, and M. C. Thompson, Phys. Fluids 7, 3126 (1995). 10.1063/1.868620
54. K. Fujimura, H. S. Koyama, and J. M. Hyun, ASME Trans. J. Fluids Eng. 119, 450 (1997). 10.1115/1.2819154
55. K. Fujimura, H. Yoshizawa, R. Iwatsu, and H. S. Koyama, J. Fluids Eng. 123, 604 (2001). 10.1115/1.1385834
56. A. Y. Gelfgat, J. M. Bar-Yoseph, and A. Solan, J. Fluid Mech. 311, 1 (1996). 10.1017/S0022112096002492
57. H. M. Blackburn and J. M. Lopez, Phys. Fluids 12, 2698 (2000). 10.1063/1.1313550
58. E. Serre and P. Bontoux, J. Fluid Mech. 459, 347 (2002). 10.1017/S0022112002007875
59. S. K. Bhaumik and K. N. Lakshmisha, Comput. Fluids 36, 1163 (2007). 10.1016/j.compfluid.2007.02.001 (Pubitemid 46746460)
60. Z. L. Guo, C. Zheng, and B. Shi, Chin. Phys. 11, 366 (2002). 10.1088/1009-1963/11/4/310 (Pubitemid 135684623)
61. K. N. Premnath and S. Banerjee, Phys. Rev. E 80, 036702 (2009). 10.1103/PhysRevE.80.036702