Viscous flow computations with the method of lattice Boltzmann equation

Progress in Aerospace Sciences

Volumn 39, Issue 5, 2003, Pages 329-367

  Yu, Dazhi ^a   Mei, Renwei ^a   Luo, Li Shi ^b,c   Shyy, Wei ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b NASA LANGLEY RESEARCH CENTER   (United States)

^c NATIONAL INSTITUTE OF AEROSPACE   (United States)

Author keywords

Boundary condition; Force evaluation; Grid refinement; Lattice Boltzmann equation; Multi block; Multi relaxation time; Single relaxation time

Indexed keywords

BOUNDARY CONDITIONS; RELAXATION PROCESSES; REYNOLDS NUMBER; TURBULENCE; VISCOSITY OF LIQUIDS;

LATTICE BOLTZMANN EQUATION;

FLOW OF FLUIDS;

EID: 0038359301     PISSN: 03760421     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0376-0421(03)00003-4     Document Type: Review

References (215)

1. Alves AS, editor. Discrete models of fluid dynamics, Figueira da Foz, Portugal, September 19-22, 1990. Singapore: World Scientific, 1991.
2. Verheggen TMM, editor. Numerical methods for the simulation of multi-phase and complex flow. Proceedings of a Workshop held at Koninklijke/Shell-Laboratorium, Amsterdam, The Netherlands, May 30-June 1, 1990. Berlin: Springer, 1992.
3. Lebowitz JL, Orszag SA, Qian YH, editors. Proceedings of the Fifth International Conference on Discrete Models for Fluid Mechanics. Princeton, NJ, June 27-29, 1994. J Stat Phys 1995;81(1/2):1-538.
4. Lebowitz JL, Orszag SA, Qian YH, editors. Proceedings of the Fifth International Conference on Discrete Models for Fluid Mechanics. Princeton, NJ, June 27-29, 1994. J Stat Phys 1995;81(1/2):1-538.
5. Boghosian BM, Alexander FJ, Coveney PV, editors. Proceedings of the 1996 Conference on Discrete Models for Fluid Mechanics, Boston, MA, August 26-28, 1996. Int J Mod Phys C 1997;8(4):637-1011.
6. Boghosian BM, Alexander FJ, Coveney PV, editors. Proceedings of the 1996 Conference on Discrete Models for Fluid Mechanics, Boston, MA, August 26-28, 1996. Int J Mod Phys C 1997;8(4):637-1011.
7. Boghosian BM, editor. Proceedings of the Seventh International Conference on the Discrete Simulation of Fluids, Oxford, UK, July 14-18, 1998. Int J Mod Phys C 1998;9(8):1123-617.
8. Boghosian BM, editor. Proceedings of the Seventh International Conference on the Discrete Simulation of Fluids, Oxford, UK, July 14-18, 1998. Int J Mod Phys C 1998;9(8):1123-617.
9. Ohashi H, Chen Y, editors. Proceedings of the Eighth International Symposium on the Discrete Simulation of Fluid Dynamics, Tokyo, Japan, July 28-30, 1999. Comp Phys Commun 2000;129(1-3):1-291.
10. Ohashi H, Chen Y, editors. Proceedings of the Eighth International Symposium on the Discrete Simulation of Fluid Dynamics, Tokyo, Japan, July 28-30, 1999. Comp Phys Commun 2000;129(1-3):1-291.
11. Lebowitz JL, editor. Special Issue Based on the Ninth Annual International Conference on Discrete Simulation of Fluid Dynamics, Santa Fe, NM, August 21-24, 2000. J Stat Phys 2002;107(1/2):1-598.
12. Lebowitz JL, editor. Special Issue Based on the Ninth Annual International Conference on Discrete Simulation of Fluid Dynamics, Santa Fe, NM, August 21-24, 2000. J Stat Phys 2002;107(1/2):1-598.
13. Coveney PV, Succi S, editors. Discrete modelling and simulation of fluid dynamics, the 10th International Conference on Discrete Simulation of Fluid Dynamics, Cargese, July 2-6, 2001. Philos Trans R Soc London A 2002;360(1792):1-573.
14. Coveney PV, Succi S, editors. Discrete modelling and simulation of fluid dynamics, the 10th International Conference on Discrete Simulation of Fluid Dynamics, Cargese, July 2-6, 2001. Philos Trans R Soc London A 2002;360(1792):1-573.
15. Monaco R., Preziosi L. Fluid dynamic applications of the discrete Boltzmann equation. 1991;World Scientific, Singapore.
16. Chopard B., Droz M. Cellular automata modeling of physical systems. 1998;Cambridge University Press, Cambridge, UK.
17. Wolf-Gladrow D.A. Lattice-gas cellular automata and lattice Boltzmann models. 2000;Springer, Berlin.
18. Succi S. The lattice Boltzmann equation for fluid dynamics and beyond. 2001;Oxford University Press, New York.
19. Benzi R., Succi S., Vergassola M. The lattice Boltzmann equation theory and applications. Phys Rep. 222:1992;45-197.
20. Qian Y.H., Succi S., Orszag S.A. Recent advances in lattice Boltzmann computing. Stauffer D. Annual reviews of computational physics III. 1996;World Scientific, Singapore.
21. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech. 30:1998;329-364.
22. Luo L-S, Future of LGA. LBE methods. In: Salas MA, Anderson WK, editors. Computational aerosciences in the 21st century. Dordrecht: Kluwer, 2000. p. 165-87. (Available at http://www.icase.edu/∼luo/publications.html ).
23. Luo L-S. The lattice-gas and lattice Boltzmann methods: past, present, and future. In: Wu J-H, Zhu Z-J, editors. Proceedings of the International Conference on Applied Computational Fluid Dynamics, Beijing, China, 2000. p. 52-83.
24. Hardy J., de Pazzis O., Pomeau Y. Molecular dynamics of a classical lattice gas. transport properties and time correlation functions Phys Rev A. 13:1976;1949-1961.
25. Frisch U., Hasslacher B., Pomeau Y. Lattice-gas automata for the Navier-Stokes equations. Phys Rev Lett. 56:1986;1505-1508.
26. Frisch U., d'Humieres D., Hasslacher B., Lallemand P., Pomeau Y., Rivet J-P. Lattice gas hydrodynamics in two and three dimensions. Complex System. 1:1987;649-707.
27. Wolfram S. Cellular automata and complexity. collected papers:1994;Addison-Wesley, New York.
28. Rivet J-P., Boon J.P. Lattice Gas Hydrodynamics. 2001;Cambridge University Press, Cambridge, UK.
29. Peyret R, Taylor TD. Computational technique for fluid dynamics, vol. II. New York: Springer, 1983.
30. Fletcher CAJ. Computational techniques for fluid dynamics, vols. I and II. New York: Springer, 1988.
31. McNamara G., Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett. 61:1988;2332-2335.
32. Higuera F.J., Jiménez J. Boltzmann approach to lattice gas simulations. Europhys Lett. 9:1989;663-668.
33. Koelman J.M.V.A. A simple lattice Boltzmann scheme for Navier-Stokes fluid flow. Europhys Lett. 15:1991;603-607.
34. Qian Y.H., d'Humières D., Lallemand P. Lattice BGK models for Navier Stokes equation. Europhys Lett. 17:1992;479-484.
35. Chen H., Chen S., Matthaeus W.H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys Rev A. 45:1992;R5339-R5342.
36. d'Humières D. Generalized lattice Boltzmann equations. In: Shizgal D, Weaver DP, editors. Rarefied Gas Dynamics: theory and simulations. Prog Astronaut Aeronaut 1992;159:450-8.
37. 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 system. Phys Rev. 94:1954;511-525.
38. He X., Luo L-S. A priori derivation of the lattice Boltzmann equation. Phys Rev E. 55:1997;R6333-R6336.
39. He X., Luo L-S. Theory of the lattice Boltzmann equation. from Boltzmann equation to lattice Boltzmann equation Phys Rev E. 56:1997;6811-6817.
40. Broadwell J.E. Study of rarefied shear flow by the discrete velocity method. J Fluid Mech. 19:1964;401-404.
41. Broadwell J.E. Shock structure in a simple discrete velocity gas. Phys Fluids. 7:1964;1243-1247.
42. Gatignol R. Théorie Cinétique des Gaz à Répartition Discrète des Vitesses. Lecture Notes in Physics, vol. 36. Berlin: Springer, 1975.
43. Goldstein D, Sturtevant B, Broadwell JE. Investigations of the motion of discrete-velocity gases. In: Muntz R, Weaver DP, Campbell DH, editors. Rarefied gas dynamics: theoretical and computational techniques. Prog Astronaut Aeronaut 1989;118:100-117.
44. Inamuro T., Sturtevant B. Numerical study of discrete-velocity gases. Phys Fluids A. 2:1990;2196-2203.
45. Bobylev AV. Relationships between discrete and continuous kinetic theories. In: Brun R, Campargue R, Gatignol R, Lengrand JC, editors. Rarefied Gas Dynamics: Proceedings of the 21st International Symposium on Rarefied Gas Dynamics, Marseille, France, July 26-31, 1998. Toulouse: CEPAD, 1999. p. 19-30.
46. Mieussens L. Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics. Math Models Methods Appl Sci. 10:2000;1121-1149.
47. Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J Comput Phys. 162:2000;429-466.
48. Mieussens L. Convergence of a discrete-velocity model for the Boltzmann-BGK equation. Comp Math Appl. 41:2001;83-96.
49. Luo L-S. Some recent results on discrete velocity models and ramifications for lattice Boltzmann equation. Comp Phys Commun. 129:2000;63-74.
50. Cao N., Chen S., Jin S., Martinez D. Physical symmetry and lattice symmetry in lattice Boltzmann method. Phys Rev E. 55:1997;R21-R24.
51. Mei R., Shyy W. On the finite difference-based lattice Boltzmann method in curvilinear coordinates. J Comput Phys. 143:1998;426-448.
52. Tölke J., Krafczyk M., Schulz M., Rank E. Implicit discretization and nonuniform mesh refinement approaches for FD discretization of LBGK models. Int J Mod Phys C. 9(8):1998;1143-1157.
53. Kandhai D., Soll W., Chen S., Hoekstra A., Sloot P. Finite-difference lattice-BGK methods on nested grids. Comput Phys Commun. 129:2000;100-109.
54. Chapman S., Cowling T.G. The mathematical theory of nonuniform gases. 1970;Cambridge University Press, Cambridge.
55. Strumolo G., Viswanathan B. New directions in computational aerodynamics. Phys World. 10:1997;45-49.
56. He X., Zhang R., Chen S., Doolen G. On the three-dimensional Rayleigh-Taylor instability. Phys Fluids. 11:1999;1143-1152.
57. Martys N.S., Chen H. Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys Rev E. 53:1996;743-750.
58. Ladd A.J.C. Numerical simulation of particular suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J Fluid Mech. 271:1994;285-309.
59. Ladd A.J.C. Numerical simulation of particular suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J Fluid Mech. 271:1994;311-339.
60. Ladd A.J.C., Verberg R. Lattice Boltzmann simulations of particle fluid suspensions. J Stat Phys. 104:2001;1191-1251.
61. Nguyen N-Q., Ladd A.J.C. Lubrication corrections for lattice Boltzmann simulations of particle suspensions. Phys Rev E. 66:2002;046708.
62. Ladd A.J.C. Effects of container walls on the velocity fluctuations of sedimenting spheres. Phys Rev Lett. 88:2002;048301.
63. Heemels M.N., Hagen M.H.J., Lowe C.P. Simulating solid colloidal particles using the lattice-Boltzmann method. J Comput Phys. 164:2000;48-61.
64. Horbach J., Frenkel D. Lattice-Boltzmann method for the simulation of transport phenomena in charged colloids. Phys Rev E. 64:2001;061507.
65. Qi D. Non-spherical colloidal suspensions in three-dimensional space. Int J Mod Phys C. 8:1997;985-997.
66. Qi D. Lattice Boltzmann simulation of particles in non-zero-Reynolds-number flows. J Fluid Mech. 385:1999;41-62.
67. Qi D. Lattice-Boltzmann simulations of fluidization of rectangular particles. Int J Multiph Flow. 26:2000;421-433.
68. Qi D. Simulations of fluidization of cylindrical multiparticles in a three-dimensional space. Int J Multiph Flow. 27:2000;107-118.
69. Qi D., Luo L-S., Aravamuthan R., Strieder W. Lateral migration and orientation of elliptical particles in Poiseuille flows. J Stat Phys. 107:2002;101-120.
70. Qi D., Luo L-S. Rotational and orientational behaviour of a three-dimensional spheroidal particles in Couette flow. J Fluid Mech. 447:2003;201-203.
71. Qi D., Luo L-S. Transitions in rotations of a non-spherical particle in a three-dimensional moderate Reynolds number Couette flow. Phys Fluids. 12:2002;4440-4443.
72. Aidun C.K., Lu Y.N., Ding E.J. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J Fluid Mech. 373:1998;287-311.
73. Ding E.J., Aidun C.K. The dynamics and scaling law for particles suspended in shear flow with inertia. J Fluid Mech. 423:2000;317-344.
74. Ding EJ, Aidun CK. Extension of the lattice-Boltzmann method for direct simulation of suspended particles near contact. J Stat Phys 2002, to appear.
75. Feng Z.G., Michaelides E.E. Interparticle forces and lift on a particle attached to a solid boundary in suspension flow. Phys Fluids. 14:2002;49-60.
76. Clague D.S., Cornelius P.J. The hydrodynamic force and torque on a bounded sphere in Poiseuille flow. Int J Numer Methods Fluids. 35:2002;55-70.
77. Chen S., Dawson S.P., Doolen G.D., Janecky D.R., Lawniczak A. Lattice methods and their applications to reacting systems. Comput Chem Eng. 19:1995;617-646.
78. Yu H., Luo L-S., Girimaji S.S. Scalar mixing and chemical reaction simulations using lattice Boltzmann method. Int J Computat Eng Sci. 3:2002;73-87.
79. Chen S., Chen H., Martínez D., Matthaeus W.H. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys Rev Lett. 67:1991;3776-3779.
80. Miller W., Succi S., Mansutti D. A lattice Boltzmann model for anisotropic liquid/solid phase transition. Phys Rev Lett. 86:2001;3578-3581.
81. Miller W., Succi S. A lattice Boltzmann model for anisotropic crystal growth from melt. J Stat Phys. 107:2002;173-186.
82. Hou S., Zou Q., Chen S., Doolen G., Cogley A.C. Simulation of cavity flow by the lattice Boltzmann method. J Comput Phys. 118:1995;329-347.
83. Luo L-.S. Symmetry breaking of flow in 2D symmetric channels. simulations by lattice-Boltzmann method Int J Mod Phys. 8:1997;859-867.
84. He X., Doolen G. Lattice Boltzmann method on a curvilinear coordinate system. vortex shedding behind a circular cylinder Phys Rev E. 56:1997;434-440.
85. He X., Doolen D. Lattice Boltzmann method on curvilinear coordinates systems. flow around a circular cylinder J Comput Phys. 134:1997;306-315.
86. Amati G., Succi S., Piva R. Massively parallel lattice-Boltzmann simulation of turbulent channel flow. Int J Mod Phys C. 8:1997;869-877.
87. Amati G., Benzi R., Succi S. Extended self-similarity in boundary-layer turbulence. Phys Rev E. 55:1997;6985-6988.
88. He X., Zou Q., Luo L-S., Dembo M. Some progress in the lattice Boltzmann method. Part I, non-uniform mesh grids. J Comput Phys. 129:1996;357-363.
89. Filippova O., Hänel D. Grid refinement for lattice-BGK models. J Comput Phys. 147:1998;219-228.
90. Yu D., Mei R., Shyy W. A multi-block lattice Boltzmann method for viscous fluid flows. Int J Numer Methods Fluids. 39:2002;99-120.
91. Ziegler D.P. Boundary conditions for lattice Boltzmann simulations. J Stat Phys. 71:1993;1171-1177.
92. Ginzbourg I., Alder P.M. Boundary flow condition analysis for the three-dimensional lattice Boltzmann model. J Phys II France. 4:1994;191-214.
93. Mei R., Luo L-S., Shyy W. An accurate curved boundary treatment in the lattice Boltzmann method. J Comput Phys. 155:1999;307-330.
94. Bouzidi M., Firdaouss M., Lallemand P. Momentum transfer of a lattice Boltzmann fluid with boundaries. Phys Fluids. 13:2001;3452-3459.
95. Yu D, Mei R, Shyy W. A unified boundary treatment in lattice Boltzmann method. New York: AIAA 2003-0953, 2003.
96. Cornubert R., d'Humières D., Levermore D. A Knudsen layer theory for lattice gases. Physica D. 47:1991;241-259.
97. Behrend Q. Solid-fluid boundaries in particle suspension simulation via the lattice Boltzmann method. Phys Rev E. 52:1995;1164-1175.
98. Ginzbourg I. Boundary condition problems in lattice gas methods for single and multiple phases. PhD thesis, Université Paris VI, 1994.
99. Lallemand P., Luo L-S. Theory of the lattice Boltzmann method. dispersion, dissipation, isotropy, Galilean invariance, and stability Phys Rev E. 61:2000;6546-6562.
100. Dellar PJ. Bulk and shear viscosities in lattice Boltzmann equations. Phys Rev E 2001;64:031203.
101. Mei R, Yu D, Shyy W. Assessment of the multi-relaxation-time and single-relaxation-time models in the lattice Boltzmann equation method. New York: AIAA paper 2001-2666, 2001.
102. Mei R, Yu D, Shyy W, Luo L-S. Force evaluation in the lattice Boltzmann method involving curved geometry. Phys Rev E 2002;65:041203.
103. Shyy W., Liu J., Wright J. Pressure-based viscous flow computation using multiblock overlapping curvilinear grid. Numer Heat Transfer. 25:1994;39-59.
104. Shyy W. Computational modeling for fluid flow and interfacial transport, corrected printing. 1997;Elsevier, Amsterdam.
105. Shyy W., Thakur S.S., Ouyang H., Liu J., Blosch E. Computational techniques for complex transport phenomena. 1999;Cambridge University Press, New York.
106. Fornberg B. Steady incompressible flow past a row of circular cylinder. J Fluid Mech. 225:1991;655-671.
107. Mei R., Shyy W., Yu D., Luo L-.S. Lattice Boltzmann method for 3-D flows with curved boundary. J Comput Phys. 161:2000;680-699.
108. Bouzidi M., d'Humières D., Lallemand P., Luo L-S. Lattice Boltzmann equation on a two-dimensional rectangular grid. J Comput Phys. 172:2001;704-717.
109. Schäfer M, Turek S. Benchmark computations of laminar flow around a cylinder. In: Hirshel H, editor. Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics, vol. 52. Braunschweig: Vieweg, 1996. p. 547-66.
110. Lin C.L., Lai Y.G. Lattice Boltzmann method on composite grids. Phys Rev E. 62:2000;2219-2225.
111. Ghia U., Ghia K.N., Shin C.T. High-Re solution for incompressible flow using the Navier-Stokes equations and a multigrid method. J Comput Phys. 48:1982;387-411.
112. Drela M., Giles M.B. Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25:1987;1347-1355.
113. Lockard D.P., Luo L-S., Milder S.D., Singer B.A. Evaluation of powerflow for aerodynamic applications. J Stat Phys. 107:2002;423-478.
114. Wolfram S. Cellular automaton fluids. 1. basic theory J Stat Phys. 45:1986;471-526.
115. Lavallee P., Boon J.P., Noullez A. Boundaries in lattice gas flows. Physica D. 47:1991;233-240.
116. Noble D.R., Chen S., Georgiadis J.G., Buckius R.O. A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Phys Fluids. 7:1995;203-209.
117. Inamuro T., Yoshino M., Ogino F. A non-slip boundary condition for lattice Boltzmann simulations. Phys Fluids. 7:1995;2928-2930.
118. Maier R.S., Bernard R.S., Grunau D.W. Boundary conditions for the lattice Boltzmann methods. Phys Fluids. 8:1996;1788-1801.
119. Chen S., Martínez D., Mei R. On boundary conditions in lattice Boltzmann method. Phys Fluids. 8:1996;2527-2536.
120. Zou Q., He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. 9:1997;1591-1598.
121. He X., Zou Q., Luo L-S., Dembo M. Analytic solutions and analysis on non-slip boundary condition for the lattice Boltzmann BGK model. J Stat Phys. 87:1997;115-136.
122. Yu D. Viscous flow computations with the lattice Boltzmann equation method. PhD dissertation, University of Florida, 2002.
123. Grunau DW. Lattice methods for modeling hydrodynamics. PhD dissertation, Colorado State University, 1993.
124. Skordos P.A. Initial and boundary conditions for the lattice Boltzmann method. Phys Rev E. 48:1992;4823-4842.
125. He X., Luo L-.S. Lattice Boltzmann model for the incompressible Navier-Stokes equation. J Stat Phys. 88:1997;927-944.
126. d'Humières D., Ginzburg I., Krafczyk M., Lallemand P., Luo L-S. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans R Soc London A. 360:2002;437-451.
127. Eggels J.G.M., Sommers J.A. Numerical simulation of free convective flow using the lattice-Boltzmann scheme. Int J Heat Fluid Flow. 16:1996;357-364.
128. Shan X. Simulation of Rayleigh-Benard convection using a lattice Boltzmann method. Phys Rev E. 55:1997;2780-2788.
129. Succi S., Bella G., Papetti F. Lattice kinetic theory for numerical combustion. J Sci Comput. 12:1997;395-408.
130. Yan G., Chen Y., Hu S. Simple lattice Boltzmann model for simulating flows with shock wave. Phys Rev E. 59:1999;454-459.
131. Hinton F.L., Rosenbluth M.N., Wong S.K., Lin-Liu Y.R., Miller R.L. Modified lattice Boltzmann method for compressible fluid simulations. Phys Rev E. 63:2001;061212.
132. Shi W., Shyy W., Mei R. Finite-difference-based lattice Boltzmann method for inviscid compressible flows. Numer Heat Transfer. B40:2001;1-20.
133. Huang J., Xu F., Vallieres M., Feng D.H., Qian Y.H., Fryxell B., Strayer M.R. A thermal LBGK model for large density and temperature difference. Int J Mod Phys C. 8:1997;827-841.
134. Renda A., Bella G., Succi S., Karlin I.V. Thermohydrodynamic lattice BGK schemes with non-perturbative equilibria. Europhys Lett. 41:1998;279-283.
135. Sun C. Simulations of compressible flows with strong shocks by an adaptive lattice Boltzmann model. J Comput Phys. 161:2000;70-84.
136. Mason R.J. A multi-speed compressible lattice-Boltzmann model. J Stat Phys. 107:2002;385-400.
137. Alexander F.J., Chen S., Sterling J.D. Lattice Boltzmann thermohydrodynamics. Phys Rev E. 47:1993;R2249-R2252.
138. Qian Y.H. Simulating thermohydrodynamics with lattice BGK models. J Sci Comput. 8:1993;231-242.
139. McNamara G., Alder B.J. Analysis of the lattice Boltzmann treatment of hydrodynamics. Physica A. 194:1993;218-228.
140. McNamara G., Garcia A., Alder B.J. Stabilization of thermal lattice Boltzmann models. J Stat Phys. 81:1995;395-408.
141. McNamara G., Garcia A., Alder B.J. A hydrodynamically correct thermal lattice Boltzmann model. J Stat Phys. 87:1997;1111-1121.
142. He X., Chen S., Doolen G.D. A novel thermal model for the lattice Boltzmann method in incompressible limit. J Comput Phys. 146:1998;282-300.
143. Palmer B.J., Rector D.R. Lattice Boltzmann algorithm for simulating thermal flow in compressible fluids. J Comput Phys. 161:2000;1-19.
144. Ihle T., Kroll D.M. Thermal lattice-Boltzmann method for non-ideal gases with potential energy. Computer Phys Comm. 129:2000;1-12.
145. Inamuro T. A lattice kinetic scheme for incompressible viscous flows with heat transfer. Philos Trans R Soc London A. 360:2002;477-484.
146. Pavlo P., Vahala G., Vahala L., Soe M. Linear stability analysis of thermo-lattice Boltzmann models. J Comput Phys. 139:1998;79-91.
147. Pavlo P., Vahala G., Vahala L. Preliminary results in the use of energy-dependent octagonal lattices for thermal lattice Boltzmann simulations. J Stat Phys. 107:2002;499-519.
148. Filippova O., Hänel D. A novel lattice BGK approach for low mach number combustion. J Comput Phys. 158:2002;139-160.
149. Nadiga B.T. An Euler solver based on locally adaptive discrete velocities. J Stat Phys. 81:1995;129-146.
150. Lallemand P, Luo L-S. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 2002, submitted for publication.
151. Lallemand P., Luo L-S. Hybrid finite-difference thermal lattice Boltzmann equation. Int J Mod Phys B. 17:2003;41-47.
152. Mezrhab A, Bouzidi M, Lallemand P. Hybrid lattice-Boltzmann finite-difference simulation of convective flows. Comput Fluids 2002, to appear.
153. Luo L-S. Unified theory of the lattice Boltzmann models for nonideal gases. Phys Rev Lett. 81:1998;1618-1621.
154. Luo L-S. Theory of the lattice Boltzmann method. lattice Boltzmann models for nonideal gases Phys Rev E. 62:2000;4982-4996.
155. Luo L-S., Girimaji S.S. Lattice Boltzmann model for binary mixtures. Phys Rev E. 66:2002;035301.
156. Luo L-S., Girimaji S.S. Theory of the lattice Boltzmann method. Two-Huid model for binary mixtures Phys Rev E. 67:2003;036302.
157. Sankaranarayanan K., Shan X., Devrekidis I.G., Sundaresan S. Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J Fluid Mech. 452:2002;61-96.
158. Sankaranarayanan K., Kevrekidis I.G., Sundaresan S., Lu J., Tryggvason G. A comparative study of lattice Boltz-mann and front-tracking finite-difference methods for bubble simulations. Int J Multiphase Flow. 29:2003;109-116.
159. Ahlrichs P., Dunweg B. Lattice-Boltzmann simulation of polymer-solvent systems. Int J Mod Phys C. 9:1998;1429-1438.
160. Ahlrichs P., Dunweg B. Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics. J Chem Phys. 111:1999;8225-8239.
161. Ahlrichs P., Everaers R., Dunweg B. Screening of hydrodynamic interactions in semi-dilute polymer solutions. a computer simulation study Phys Rev E. 64:2002;040501.
162. Schelkle M., Frohn A. Three-dimensional lattice Boltzmann simulations of binary collisions between equal droplets. J Aerosal Sci. 26:1995;S145-S146.
163. Frohn A., Roth N. Dynamics of droplets. 2000;Springer, Berlin.
164. Sehgal B.R., Nourgaliev R.R., Dinh T.N. Numerical simulation of droplet deformation and break-up by lattice-Boltzmann method. Prog Nucl Energy. 34:1999;471-488.
165. Xi H.W., Duncan C. Lattice Boltzmann simulations of three-dimensional single droplet deformation and breakup under simple shear flow. Phys Rev E. 59:1999;3022-3026.
166. Kang Q.J., Zhang D.X., Chen S.Y. Displacement of a two-dimensional immiscible droplet in a channel. Phys Fluids. 12:2002;3203-3214.
167. van Kats F.M., Egberts P.J.P. Spreading dynamics modeled by lattice-Boltzmann techniques. J Colloid Interface Sci. 205:1998;166-177.
168. Raiskinmaki P., Koponen A., Merikoski J., Timonen J. Spreading dynamics of three dimensional droplets by the lattice-Boltzmann method. Comp Mater Sci. 18:2000;7-12.
169. Ginzburg I, Steiner K. Lattice Boltzmann model for free-surface flow and its application to filling process in casting. (Also ITWM Report (34)-2002, (available at http://www.itwm.fhg.de ). J Comput Phys 2003;185:61-99.
170. He X., Chen S.Y., Zhang R.Y. A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J Comput Phys. 152:1999;642-663.
171. Nie X., Qian Y.H., Doolen G.D., Chen S. Lattice Boltzmann simulation of the two-dimensional Rayleigh-Taylor instability. Phys Rev E. 58:1998;6861-6864.
172. Clark TT. A numerical study of the statistics of a two-dimensional Rayleigh-Taylor mixing layer. Los Alamos National Laboratory Unclassified Report LA-UR-01-3875, Phys Fluids 2001, also submitted for publication.
173. Gunstensen A.K., Rothman D.H. Lattice-Boltzmann studies of immiscible 2-phase flow through porous-media. J Geophys Res-Solid Earth. 98:1993;6431-6441.
174. Ferréol B., Rothman D.H. Lattice-Boltzmann simulations of flow-through Fontainebleau sandstone. Transp Porous Media. 20:1995;3-20.
175. Hill R.J., Koch D.L., Ladd A.J.C. Moderate-Reynolds-number flows in ordered and random arrays of spheres. J Fluid Mech. 448:2001;243-278.
176. Angelopoulos A.D., Paunov V.N., Burganos V.N., Payatakes A.C. Lattice Boltzmann simulation of nonideal vapor-liquid flow in porous media. Phys Rev E. 57:1998;3237-3245.
177. Hazlett R.D., Chen S.Y., Soll W.E. Wettability and rate effects on immiscible displacement. lattice Boltzmann simulation in microtomographic images of reservoir rocks J Pet Sci Eng. 20:1998;167-175.
178. Spaid M.A.A., Phelan F.R. Modeling void formation dynamics in fibrous porous media with the lattice Boltzmann method. Compos Part A-Appl Sci Manuf. 29:1998;749-755.
179. Bekri S., Vizika O., Thovert J.F., Adler P.M. Binary two-phase flow with phase change in porous media. Int J Multiph Flow. 27:2001;477-526.
180. Mantle M.D., Sederman A.J., Gladden L.F. Single- and two-phase flow in fixed-bed reactors. MRI flow visualisation and lattice-Boltzmann simulations Chem Eng Sci. 56:2001;523-529.
181. Tölke J., Krafczyk M., Schulz M., Rank E. Lattice Boltzmann simulations of binary fluid flow through porous media. Philos Trans R Soc London A. 360:2002;535-545.
182. Ginzburg I., d'Humieres D. Local second-order boundary methods for lattice Boltzmann models. J Stat Phys. 84:1996;927-971.
183. Lallemand P., Luo L-S. Lattice Boltzmann method for moving boundaries. J Comput Phys. 184:2003;406-421.
184. d'Humieres D, Ginzburg I. Multi-reflection boundary conditions for lattice Boltzmann models. ITWM Report (38)-2002 (available at http://www.itwm.fhg.de/ ).
185. Verberg R., Ladd A.J.C. Lattice Boltzmann model with sub-grid-scale boundary conditions. Phys Rev Lett. 84:2000;2148-2151.
186. Breuer M., Bernsdorf J., Zeiser T., Durst F. Accurate computations of the laminar flow past a square cylinder based on two different methods. lattice-Boltzmann and finite volume Int J Heat Fluid Flows. 21:2000;186-196.
187. d'Humieres D., Bouzidi M., Lallemand P. Thirteen-velocity three-dimensional lattice Boltzmann model. Phys Rev E. 63:2001;066702.
188. Junk M., Klar A. Discretizations for the incompressible Navier-Stokes equations based on the lattice-Boltzmann method. SIAM J Sci Comp. 22:2000;1-19.
189. Junk M. A finite difference interpretation of the lattice Boltzmann method. Numer Methods Partial Differential Equations. 17:2002;383-402.
190. Junk M, Klar A, Luo L-S. Theory of the lattice Boltzmann method: mathematical analysis of the lattice Boltzmann equation. J Comput Phys 2002, submitted for publication.
191. Martínez D.O., Matthaeus W.H., Chen S., Montgomery D.C. Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics. Phys Fluids. 6:1994;1285-1298.
192. Trevino C., Higuera F. Lattice Boltzmann and spectral simulations of non-linear stability of Kolmogorov flows. Rev Mex Fis. 40:1994;878-890.
193. Vergassola M., Benzi R., Succi S. On the hydrodynamic behavior of the lattice Boltzmann-equation. Europhys Lett. 13:1990;411-416.
194. Chen S., Wang Z., Shan X.W., Doolen G.D. Lattice Boltzmann computational fluid dynamics in three dimensions. J Stat Phys. 68:1992;379-400.
195. Benzi R., Struglia M.V., Tripiccione R. Extended self-similarity in numerical simulations of three-dimensional anisotropic turbulence. Phys Rev E. 53:1996;R5565-R5568.
196. Luo L-S, Wang L-P, Qi DW. Applications of the lattice Boltzmann method to complex and turbulent flows. In: Breuer M, Durst F, Zenger C, editors. High Performance Scientific and Engineering Computing. Proceedings of the 3rd International FORTWIHR Conference on HPSEC, Erlangen, March 12-14, 2001. Lecture Notes in Computational Science and Engineering, vol. 21. Berlin: Springer, 2002. pp. 123-30.
197. Eggels J.M.G. Direct and large-eddy simulation of turbulent fluid flow using the lattice-Boltzmann scheme. Int J Heat Fluid Flow. 17:1996;307-323.
198. Hou S, Sterling J, Chen S, Doolen GD. A lattice Boltzmann subgrid model for high Reynolds number flows. In: Lawniczak AT, Kapral R, editors. Pattern formation and lattice gas automata. Fields Institute Communications 6, Providence, RI: AMS, 1996. p. 151-66.
199. Derksen J., Van den Akker H.E.A. Parallel simulation of turbulent fluid flow in a mixing tank. LNCS. 1401:1998;96-104.
200. Derksen J., Van den Akker H.E.A. Large eddy simulations on the flow driven by a Rushton turbine. AICHE J. 45:1999;209-221.
201. Derksen J., Van den Akker H.E.A. Simulation of vortex core precession in a reverse-flow cyclone. AICHE J. 46:2000;1317-1331.
202. Krafczyk M. Gitter-Boltzmann-Methoden: Von der Theorie zur Anwendung. Habilitation Thesis, Techische Universitat Munchen, Munchen, 2001.
203. Lu Z.Y., Liao Y., Qian D.Y., McLaughlin J.B., Derksen J.J., Kontomaris K. Large eddy simulations of a stirred tank using the lattice Boltzmann method on a nonuniform grid. J Comput Phys. 181:2002;675-704.
204. Krafczyk M., Tölke J., Luo L-S. Large-eddy simulations with a multiple-relaxation-time LBE model. Int J Mod Phys B. 17:2003;33-39.
205. Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev. 91:1963;99-164.
206. Martinuzzi R., Tropea C. The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow. ASME J Fluids Eng. 115:1993;85-92.
207. Rodi W., Ferziger J.H., Breuer M., Pourquie M. Status of large-eddy simulation. results of a workshop ASME J Fluids Eng. 119:1997;248-262.
208. Karniadakis EmG, Beskok A. Micro flows. 2002;Springer, New York.
209. Kuksenok O., Yeomans J.M., Balazs A.C. Creating localized mixing stations within micro fluidic channels. Langmuir. 17(23):2001;7186-7190.
210. Lim C.Y., Shu C., Niu X.D., Chew Y.T. Application of lattice Boltzmann method to simulate microchannel flows. Phys Fluids. 14(7):2002;2299-2308.
211. Thamida S.K., Chang H.C. Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges. Phys Fluids. 14(12):2002;4315-4328.
212. Kuksenok O., Yeomans J.M., Balazs A.C. Using patterned substrates to promote mixing in microchannels. Phys Rev E. 65(3):2002;031502.
213. Berger M.J., Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. J Comput Phys. 53:1984;484-512.
214. Baker T.J. Mesh adaptation strategies for problems in fluid dynamics. Finite Elements Anal Design. 25:1997;243-273.
215. Steinthorsen E, Modiano E, Crutchfield WY, Bell LB, ColellaP. An adaptive semi-implicit scheme for simulations of unsteady viscous compressible flow. In: AIAA Paper 95-1727-CP, Proceedings of the 12th AIAA CFD Conference, 1995.