Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh

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

Volumn 72, Issue 4, 2005, Pages

  Li, Yusong ^a   Leboeuf, Eugene J ^a   Basu, P K ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRANK-NICOLSON METHOD; INHERENT GEOMETRIC FLEXIBILITY; LATTICE BOLTZMANN METHOD (LBM); UNSTRUCTURED MESH;

CRYSTAL LATTICES; FINITE ELEMENT METHOD; FLOW OF FLUIDS; OPTIMIZATION; PARAMETER ESTIMATION; TIME DOMAIN ANALYSIS;

LEAST SQUARES APPROXIMATIONS;

EID: 28844509238     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.046711     Document Type: Article

References (53)

1. S. Chen and G. D. Doolen, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.30.1.329 30, 329 (1998).
2. R. Benzi, S. Succi, and M. Vergassola, Phys. Rep., Phys. Lett. PRPLCM 0370-1573 10.1016/0370-1573(92)90090-M 222, 145 (1992).
3. G. R. McNamara and G. Zanetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.2332 61, 2332 (1988).
4. F. Higuera, S. Succi, and R. Benzi, Europhys. Lett. EULEEJ 0295-5075 9, 345 (1989).
5. F. J. Higuera and J. Jiménez, Europhys. Lett. EULEEJ 0295-5075 9, 663 (1989).
6. S. Y. Chen, H. D.Chen, D. Martinez, and W. Matthaeus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.3776 67, 3776 (1991).
7. S. Succi, G. Amati, and R. Benzi, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02179964 81, 5 (1995).
8. J. D. Sterling and S. Chen, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1996.0016 123, 196 (1996).
9. X. He, L.-S. Luo, and M. Dembo, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1996.0255 129, 357 (1996).
10. C. Shu, X. D. Niu, and Y. T. Chew, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036708 65, 036708 (2002).
11. T. Imamura, K. Suzuki, T. Nakamura, and M. Yoshida, J. Comput. Phys. JCTPAH 0021-9991 202, 645 (2005).
12. O. Filippova and D. Hanel, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1998.6089 147, 219 (1998).
13. C.-L. Lin and Y. G. Lai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.2219 62, 2219 (2000).
14. A. Dupuis and B. Chopard, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066707 67, 066707 (2003).
15. H. Chen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.3955 58, 3955 (1998).
16. N. Z. Cao, S. Y. Chen, S. Jin, and D. Martinez, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.R21 55, R21 (1997).
17. R. Mei and W. Shyy, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1998.5984 143, 426 (1998).
18. F. Nannelli and S. Succi, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01341755 68, 401 (1992).
19. G. Amati, S. Succi, and R. Benzi, Fluid Dyn. Res. FDRSEH 0169-5983 10.1016/S0169-5983(96)00026-3 19, 289 (1997).
20. G. Peng, H. Xi, and C. Duncan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.R4124 58, R4124 (1998).
21. G. Peng, H. Xi, and C. Duncan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.4675 59, 4675 (1999).
22. H. Xi, G. Peng, and S.-H. Chou, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.6202 59, 6202 (1999).
23. S. Ubertini, G. Bella, and S. Succi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.016701 68, 016701 (2003).
24. S. Ubertini and S. Succi, Comput. Fluid Dyn. J. 0918-6654 5, 85 (2005).
25. T. Lee and C.-L. Lin, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.2001.6791 171, 336 (2001).
26. T. Lee and C.-L. Lin, J. Comput. Phys. JCTPAH 0021-9991 10.1016/S0021-9991(02)00065-7 185, 445 (2003).
27. G. Strang and G. J. Fix, in An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, 1973).
28. B.-n. Jiang, in The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics (Springer, New York, 1998).
29. Y. Li, E. J. LeBoeuf, and P. K. Basu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.065701 69, 065701 (2004).
30. P. Bhatnagar, E. P. Gross, and M. K. Krook, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.94.511 94, 511 (1954).
31. Q. Zou and X. He, Phys. Fluids PHFLE6 1070-6631 10.1063/1.869307 9, 1591 (1997).
32. S. Chen, D. Martinez, and R. Mei, Phys. Fluids PHFLE6 1070-6631 10.1063/1.869035 8, 2527 (1996).
33. R. S. Maier, R. S. Bernard, and D. W. Grunau, Phys. Fluids PHFLE6 1070-6631 10.1063/1.868961 8, 1788 (1996).
34. A. J. Wathen, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/0045-7825(89)90052-2 74, 271 (1989).
35. G. Comini, M. Manzan, and C. Nonino, Int. J. Numer. Methods Fluids IJNFDW 0271-2091 20, 443 (1995).
36. Z. Guo and T. S. Zhao, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066709 67, 066709 (2003).
37. W. M. Deen, in Analysis of Transport Phenomena (Oxford University Press, New York, 1998).
38. X. He and G. D. Doolen, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1997.5709 134, 306 (1997).
39. J. D. Tritton, J. Fluid Mech. JFLSA7 0022-1120 6, 231 (1959).
40. M. Coutanceau and R. Bouard, J. Fluid Mech. JFLSA7 0022-1120 79, 231 (1977).
41. F. Nieuwstadt and H. B. Keller, Comput. Fluids CPFLBI 0045-7930 10.1016/0045-7930(73)90026-1 1, 59 (1973).
42. S. C. R. Dennis and G. Z. Chang, J. Fluid Mech. JFLSA7 0022-1120 42, 471 (1970).
43. S. Chen, K. Diemer, G. D. Doolen, K. Eggert, C. Fu, S. Gutman, and B. J. Travis, Physica D PDNPDT 0167-2789 10.1016/0167-2789(91)90281-D 47, 72 (1991).
44. A. Cancelliere, C. Chang, E. Foti, D. H. Rothman, and S. Succi, Phys. Fluids A PFADEB 0899-8213 12, 2085 (1990).
45. D. H. Rothman, Geophysics GPYSA7 0016-8033 10.1190/1.1442482 53, 509 (1988).
46. L. Talon, J. Martin, N. Rakotomalala, D. Salin, and Y. C. Yortsos, Water Resour. Res. WRERAQ 0043-1397 10.1029/2002WR001392 39, 1135 (2003).
47. D. Zhang and Q. Kang, Geophys. Res. Lett. GPRLAJ 0094-8276 31, L12504 (2004).
48. D. Zhang, R. Y. Zhang, S. Y. Chen, and V. E. Soll, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/1999GL011101 27, 1195 (2000).
49. M. C. Sukop and D. Or, Water Resour. Res. WRERAQ 0043-1397 10.1029/2003WR002333 40, W01509 (2004).
50. M. A. A. Spaid and F. R. Phelan,Jr., Phys. Fluids PHFLE6 1070-6631 10.1063/1.869392 9, 2468 (2004).
51. C. Pan, M. Hilpert, and C. T. Miller, Water Resour. Res. WRERAQ 0043-1397 10.1029/2003WR002120 40, W01501 (2004).
52. Y. Li, E. J. LeBoeuf, P. K. Basu, and S. Madadevan, Adv. Water Resour. AWREDI 0309-1708 28, 835 (2005)
53. B. Fornberg, J. Fluid Mech. JFLSA7 0022-1120 98, 819 (1980).