Boundary conditions for thermal lattice Boltzmann equation method

Journal of Computational Physics

Volumn 237, Issue , 2013, Pages 366-395

  Li, Like ^a   Mei, Renwei ^a   Klausner, James F ^a  

^a J Crayton Pruitt Family Department of Biomedical Engineering   (United States)

Author keywords

Convection diffusion equation; Curved boundary; Dirichlet boundary condition; Lattice Boltzmann equation (LBE); Neumann boundary condition

Indexed keywords

BOLTZMANN EQUATION; BOUNDARY CONDITIONS; HEAT CONDUCTION; HEAT FLUX; STEADY FLOW; TEMPERATURE;

CONVECTION-DIFFUSION EQUATIONS; CURVED BOUNDARY; DIRICHLET BOUNDARY CONDITION; DIRICHLET CONDITION; DISTRIBUTION-FUNCTIONS; LATTICE BOLTZMANN EQUATION; LATTICE BOLTZMANN EQUATIONS; NEUMANN BOUNDARY CONDITION; NEUMANN CONDITION; THERMAL LATTICE BOLTZMANN EQUATION;

DISTRIBUTION FUNCTIONS;

EID: 84873116791     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.11.027     Document Type: Article

References (49)

1. Qian Y.H., d'Humières D., Lallemand P. Lattice BGK models for Navior Stokes equation. Europhys. Lett. 1992, 17:479-484.
2. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 1998, 30:329-364.
3. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond 2001, Oxford University Press, New York.
4. Yu D., Mei R., Luo L.-S., Shyy W. Viscous flow computations with the method of lattice Boltzmann equation. Prog. Aerosp. Sci. 2003, 39:329-367.
5. Zheng H.W., Shu C., Chew Y.T. A lattice Boltzmann model for multiphase flows with large density ratio. J. Comput. Phys. 2006, 218:353-371.
6. Premnath K.N., Abraham J. Three-dimensional multi-relaxation-time (MRT) lattice-Boltzmann models for multiphase flow. J. Comput. Phys. 2007, 224:539-559.
7. Luo L.-S., Girimaji S.S. Theory of the lattice Boltzmann method: two-fluid model for binary mixtures. Phys. Rev. E 2003, 67:036302.
8. Asinari P. Asymptotic analysis of multiple-relaxation-time lattice Boltzmann schemes for mixture modeling. Comput. Math. Appl. 2008, 55:1392-1407.
9. Aidun C.K., Clausen J.R. Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 2010, 42:439-472.
10. Lätt J., Chopard B., Succi S., Toschi F. Numerical analysis of the averaged flow field in a turbulent lattice Boltzmann simulation. Physica A 2006, 362:6-10.
11. Yu H., Luo L.-S., Girimaji S.S. LES of turbulent square jet flow using an MRT lattice Boltzmann model. Comput. Fluids 2006, 35:957-965.
12. Guo Z., Zhao T.S., Shi Y. Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows. J. Appl. Phys. 2006, 99:074903.
13. Guo Z., Zhao T.S. Lattice Boltzmann model for incompressible flows through porous media. Phys. Rev. E 2002, 66:036304.
14. Pan C., Luo L.-S., Miller C.T. An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 2006, 35:898-909.
15. Chen H., Chen S., Matthaeus W.H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A 1992, 45:R5339.
16. Bhatnagar P.L., Gross E.P., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 1954, 94:511-525.
17. D. d'Humières, Generalized lattice Boltzmann equations. In rarefied gas dynamics: theory and simulations, Prog. Aeronaut. Astronaut. 159 (1992) 450-458.
18. d'Humières D., Ginzburg I., Krafczyk M., Lallemand P., Luo L.-S. Multiple-relaxtion-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc. Lond. A 2002, 360:437-451.
19. Lallemand P., Luo L.-S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 2000, 61:6546-6562.
20. Alexander F.J., Chen S., Sterling J.D. Lattice Boltzmann thermohydrodynamics. Phys. Rev. E 1993, 47:R2249.
21. Shan X. Solution of Rayleigh-Benard convection using a lattice Boltzmann method. Phys. Rev. E 1997, 55:2780.
22. Chen Y., Ohashi H., Akiyama M. Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations. Phys. Rev. E 1994, 50:2776.
23. Lallemand P., Luo L.-S. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys. Rev. E 2003, 68:036706.
24. He X., Chen S., Doolen G.D. A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 1998, 146:282-300.
25. Guo Z., Zheng C., Shi B. Thermal lattice Boltzmann equation for low Mach number flows: decoupling model. Phys. Rev. E 2007, 75:036704.
26. Shi B., Guo Z. Lattice Boltzmann model for nonlinear convection-diffusion equations. Phys. Rev. E 2009, 79:016701.
27. Mezrhab A., Moussaoui M.A., Jami M., Naji H., Bouzidi M. Double MRT thermal lattice Boltzmann method for simulating convective flows. Phys. Lett. A 2010, 374:3499-3507.
28. Yoshida H., Nagaoka M. Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comput. Phys. 2010, 229:7774-7795.
29. Ziegler D.P. Boundary conditions for lattice Boltzmann simulations. J. Stat. Phys. 1993, 71:1171-1177.
30. Noble D.R., Chen S., Georgiadis J.G., Buckius R.O. A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Phys. Fluids 1995, 7:203-209.
31. Ginzbourg I., d'Humières D. Local second-order boundary methods for lattice Boltzmann models. J. Stat. Phys. 1996, 84:927-971.
32. Ginzburg I., d'Humières D. Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 2003, 68:066614.
33. Chen S., Martinez D., Mei R. On boundary conditions in lattice Boltzmann method. Phys. Fluids 1996, 8:2527-2536.
34. He X., Zou Q., Luo L.-S., Dembo M. Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model. J. Stat. Phys. 1997, 87:115-136.
35. Zou Q., He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 1997, 9:1591-1598.
36. Filippova O., Hänel D. Grid refinement for lattice-BGK model. J. Comput. Phys. 1998, 147:219-228.
37. Mei R., Luo L.-S., Shyy W. An accurate curved boundary treatment in the lattice Boltzmann method. J. Comput. Phys. 1999, 155:307-330.
38. Mei R., Shyy W., Yu D., Luo L.-S. Lattice Boltzmann method for 3-D flows with curved boundary. J. Comput. Phys. 2000, 161:680-699.
39. Bouzidi M., Firdaouss M., Lallemand P. Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 2001, 13:3452-3459.
40. Guo Z., Zheng C., Shi B. An extrapolation method for boundary conditions in lattice Boltzmann method. Phys. Fluids 2002, 14:2007-2010.
41. Tang G.H., Tao W.Q., He Y.L. Thermal boundary condition for the thermal lattice Boltzmann equation. Phys. Rev. E 2005, 72:016703.
42. Huang H., Lee T.S., Shu S. Thermal curved boundary treatment for the thermal lattice Boltzmann equation. Int. J. Modern Phys. C 2006, 17:631-643.
43. Jeong H.K., Yoon H.S., Ha M.Y., Tsutahara M. An immersed boundary-thermal lattice Boltzmann method using an equilibrium internal energy density approach for the simulation of flows with heat transfer. J. Comput. Phys. 2010, 229:2526-2543.
44. Liu C.H., Lin K.H., Mai H.C., Lin C.A. Thermal boundary conditions for thermal lattice Boltzmann simulations. Comput. Math. Appl. 2010, 59:2178-2193.
45. Ho C.F., Chang C., Lin K.H., Lin C.A. Consistent boundary conditions for 2D and 3D laminar lattice Boltzmann simulations. CMES - Comput. Model. Eng. Sci. 2009, 44:137.
46. D'Orazio A., Succi S., Arrighettic C. Lattice Boltzmann simulation of open flows with heat transfer. Phys. Fluids 2003, 15:2778-2781.
47. Kuo L.-S., Chen P.H. Numerical implementation of thermal boundary conditions in the lattice Boltzmann method. Int. J. Heat Mass Transfer 2009, 52:529-532.
48. Ginzburg I. Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations. Adv. Water Resour. 2005, 28:1196-1216.
49. Hahn D.W., Ozisik M.N. Heat Conduction 2012, John Wiley & Sons, New York. third ed.