Breakdown of Chapman-Enskog expansion and the anisotropic effect for lattice-Boltzmann models of porous flow

Physics of Fluids

Volumn 19, Issue 1, 2007, Pages

  Nie, Xiaobo ^a,b   Martys, Nicos S ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Boltzmann equation; Flow through porous media; Lattice theory; Permeability; Shear flow; Viscosity

Indexed keywords

ANISOTROPY; BOLTZMANN EQUATION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; VISCOSITY;

CHAPMAN-ENSKOG EXPANSION; LATTICE-BOLTZMANN MODEL;

SHEAR FLOW;

ANISOTROPY; BOLTZMANN EQUATION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; SHEAR FLOW; VISCOSITY;

EID: 33847780086     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2432153     Document Type: Article

References (24)

1. R. Benzi, S. Succi, and M. Vergassola, "The lattice Boltzmann equation: Theory and applications" Phys. Rep. 222, 145 (1992). prp PRPLCM 0370-1573 10.1016/0370-1573(92)90090-M
2. S. Y. Chen and G. D. Doolen, "Lattice Boltzmann method for fluid flows" Annu. Rev. Fluid Mech. 30, 329 (1998). arf ARVFA3 0066-4189 10.1146/annurev.fluid.30.1.329
3. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, "Lattice Boltzmann model of immiscible fluids" Phys. Rev. A 43, 4320 (1991). pra PLRAAN 1050-2947 10.1103/PhysRevA.43.4320
4. X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows with multiple phases and components" Phys. Rev. E 47, 1815 (1993). pre PLEEE8 1063-651X 10.1103/PhysRevE.47.1815
5. X. B. Nie, Y. H. Qian, G. D. Doolen, and S. Y. Chen, "Lattice Boltzmann simulation of the two-dimensional Rayleigh-Taylor instability" Phys. Rev. E 58, 6861 (1998). pre PLEEE8 1063-651X 10.1103/PhysRevE.58.6861
6. A. Beskok, G. E. Karniadakis, and W. Trimmer, "Rarefaction and compressibility effects in gas micro-flows" J. Fluids Eng. 118, 448 (1996). jfg JFEGA4 0098-2202
7. X. B. Nie, G. Doolen, and S. Chen, "Lattice Boltzmann simulations of fluid flows in MEMS" J. Stat. Phys. 107, 29 (2002). jst JSTPBS 0022-4715 10.1023/A:1014523007427
8. F. Toschi and S. Succi, "Lattice Boltzmann method at finite Knudsen numbers" Europhys. Lett. 69, 549 (2005). eul EULEEJ 0295-5075 10.1209/epl/i2004-10393-0
9. N. S. Martys and H. D. Chen, "Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method" Phys. Rev. E 53, 743 (1996). pre PLEEE8 1063-651X 10.1103/ PhysRevE.53.743
10. Y. H. Qian, D. d'Humiéres, and P. Lallemand, "Lattice BGK models for Navier-Stokes equation" Europhys. Lett. 17, 479 (1992). eul EULEEJ 0295-5075
11. H. Chen, S. Chen, and W. H. Matthaeus, "Recovery of the Navier-Stokes equations using a lattice gas Boltzmann method" Phys. Rev. A 45, R5339 (1992). pra PLRAAN 1050-2947 10.1103/PhysRevA.45.R5339
12. F. A. L. Dullien, Porous Media: Fluid Transport and Pore Structure (Academic, San Diego, 1992).
13. A. Cancelliere, C. Chang, E. Foti, D. H. Rothman, and S. Succi, "The permeability of a random medium: Comparison of simulation with theory" Phys. Fluids A 2, 2085 (1990). pfa PFADEB 0899-8213 10.1063/ 1.857793
14. N. Martys, D. P. Bentz, and E. J. Garboczi, "Computer simulation study of the effective viscosity in Brinkman's equation" Phys. Fluids 6, 1434 (1994). phf PHFLE6 1070-6631 10.1063/1.868258
15. M.A.A. Spaid and F.R. Phelan, Jr., "Lattice Boltzmann methods for modeling microscale flow in fibrous porous media" Phys. Fluids 9, 2468 (1997). phf PHFLE6 1070-6631 10.1063/1.869392
16. N. S. Martys, "Improved approximation of the Brinkman equation using a lattice Boltzmann method" Phys. Fluids 6, 1807 (2001). phf PHFLE6 1070-6631 10.1063/1.1368846
17. D. M. Freed, "Lattice-Boltzmann method for macroscopic porous media modeling" Int. J. Mod. Phys. C 9, 1491 (1998). imc IJMPEO 0129-1831 10.1142/S0129183198001357
18. Z. L. Guo and T. S. Zhao, "Lattice Boltzmann model for incompressible flows through porous media" Phys. Rev. E 66, 036304 (2002). pre PLEEE8 1063-651X 10.1103/PhysRevE.66.036304
19. Q.J. Kang, D. X. Zhang, and S. Y. Chen, "Unified lattice Boltzmann method for flow in multiscale porous media" Phys. Rev. E 66, 056307 (2002). pre PLEEE8 1063-651X 10.1103/PhysRevE.66.056307
20. J. M. Buick and C. A. Greated, "Gravity in a lattice Boltzmann model" Phys. Rev. E 61, 5307 (2000). pre PLEEE8 1063-651X 10.1103/ PhysRevE.61.5307
21. Z. L. Guo, C. G. Zheng, and B. C. Shi, "Discrete lattice effects on the forcing term in the lattice Boltzmann method" Phys. Rev. E 65, 046308 (2002). pre PLEEE8 1063-651X 10.1103/PhysRevE.65.046308
22. C. Cercignani, Theory and Application of the Boltzmann Equation (Plenum, New York, 1990).
23. H. C. Brinkman, "A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles" Appl. Sci. Res., Sect. A 1, 27 (1947). asd ASRAA9 0365-7132 10.1063/1.1312272
24. X. Y. He, Q. S. Zhou, L. S. Luo, and M. Dembo, "Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model" J. Stat. Phys. 87, 115 (1997). jst JSTPBS 0022-4715 10.1007/BF02181482