This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.
S. Chen , H. Chen , D. Martnez and W. Matthaeus , Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett., 67 (1991), 3776.
Y. Qian , D. D’Humiéres and P. Lallemand , Lattice BGK models for Navier-Stokes equation, EPL (Europhysics Letters), 17 (1992), 479.
D. D’Humiéres , Multiplerelaxationtime lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 360 (2002), pp. 437–451.
R. Mei , L.-S. Luo and W. Shyy , An accurate curved boundary treatment in the lattice Boltzmann method, J. Comput. Phys., 155 (1999), pp. 307–330.
Z. Guo , C. Zheng and B. Shi , An extrapolation method for boundary conditions in lattice Boltzmann method, Phys. Fluids, 14 (2002), pp. 2007–2010.
P. Lallemand and L.-S. Luo , Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61 (2000), 6546.
X. He and G. Doolen , Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. Comput. Phys., 134 (1997), pp. 306–315.
H. Chen , S. Chen and W. H. Matthaeus , Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys. Rev. A, 45 (1992), R5339.
S. Chen , D. Martinez and R. Mei , On boundary conditions in lattice Boltzmann methods, Phys. Fluids, 8 (1996), pp. 2527–2536.
Z. Guo , B. Shi and N. Wang , Lattice BGK model for incompressible NavierStokes equation, J. Comput. Phys., 165 (2000), pp. 288–306.
C. Shu , X. Niu and Y. Chew , Taylor series expansion and least squares-based lattice Boltzmann method: three-dimensional formulation and its applications, Int. J. Modern Phys. C, 14 (2003), pp. 925–944.
Z.-G. Feng and E. E. Michaelides , The immersed boundary-lattice Boltzmann method for solving fluidparticles interaction problems, J. Comput. Phys., 195 (2004), pp. 602–628.
Y.-H. Zhang , X.-J. Gu , R. W. Barber and D. R. Emerson , Capturing Knudsen layer phenomena using a lattice Boltzmann model, Phys. Rev. E, 74 (2006), 046704.
C. Lim , C. Shu , X. Niu and Y. Chew , Application of lattice Boltzmann method to simulate microchannel flows, Phys. Fluids, 14 (2002), pp. 2299–2308.
X. He , S. Chen and G. D. Doolen , A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146 (1998), pp. 282–300.
Y. Peng , C. Shu and Y. Chew , Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E, 68 (2003), 026701.
G. Tang , W. Tao and Y. He , Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions, Phys. Fluids, 17 (2005), 058101.
X. He , S. Chen and R. Zhang , A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of RayleighTaylor instability, J. Comput. Phys., 152 (1999), pp. 642–663.
X. Shan and H. Chen , Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47 (1993), 1815.
T. Inamuro , T. Ogata , S. Tajima and N. Konishi , A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys., 198 (2004), pp. 628–644.
X. Shan , Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method, Phys. Rev. E, 55 (1997), 2780.
T. Liszka and J. Orkisz , The finite difference method at arbitrary irregular grids and its application in applied mechanics, Comput. Struct., 11 (1980), pp. 83–95.
C. B. Lee , New features of CS solitons and the formation of vortices, Phys. Lett. A, 247 (1998), pp. 397–402.
C. Lee , Possible universal transitional scenario in a flat plate boundary layer: Measurement and visualization, Phys. Rev. E, 62 (2000), 3659.
C. K. Aidun and J. R. Clausen , Lattice-Boltzmann method for complex flows, Ann. Rev. Fluid Mech., 42 (2010), pp. 439–472.
S. Chen and G. D. Doolen , Lattice Boltzmann method for fluid flows, Ann. Rev. Fluid Mech., 30 (1998), pp. 329–364.
X. He and L.-S. Luo , Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56 (1997), 6811.
G. R. McNamara and G. Zanetti , Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61 (1988), 2332.
Y. Wang , C. Shu and C. Teo , Development of LBGK and incompressible LBGK-based lattice Boltzmann flux solvers for simulation of incompressible flows, Int. J. Numer. Methods Fluids, 75 (2014), pp. 344–364.
Y. Wang , C. Shu and C. Teo , Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows, Comput. Fluids, 94 (2014) pp. 98–111.
Y. Wang , C. Shu , H. Huang and C. Teo , Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio, J. Comput. Phys., 280 (2015), pp. 404–423.
Y. Wang , L. Yang and C. Shu , From lattice Boltzmann method to lattice Boltzmann flux solver, Entropy, 17 (2015), pp. 7713–7735.
F. M. White , Fluid Mechanics, McGraw-Hill, New York, 2003.
R. Benzi , S. Succi and M. Vergassola , The lattice Boltzmann equation: theory and applications, Phys. Reports, 222 (1992), pp. 145–197.
T. Inamuro , M. Yoshino and F. Ogino , Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number, Phys. Fluids, 9 (1997), pp. 3535–3542.
Z. Guo and C. Shu , Lattice Boltzmann Method and Its Applications in Engineering, World Scientific, 2013.
J. Kim and P. Moin , Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), pp. 308–323.
J. D. Sterling , S. Chen , Stability analysis of lattice Boltzmann methods, J. Comput. Phys., 123 (1996), pp. 196–206.
X. Niu , C. Shu , Y. Chew and T. Wang , Investigation of stability and hydrodynamics of different lattice Boltzmann models, J. Stat. Phys., 117 (2004), pp. 665–680.
U. Ghia , K. N. Ghia and C. Shin , High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48 (1982), 387–411.
R. Mei , L.-S. Luo , P. Lallemand and D. D’Humiéres , Consistent initial conditions for lattice Boltzmann simulations, Comput. Fluids, 35 (2006), pp. 855–862.
R. Mei and W. Shyy , On the finite difference-based lattice Boltzmann method in curvilinear coordinates, J. Comput. Phys., 143 (1998), pp. 426–448.
Z. Guo , C. Zheng and B. Shi , Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65 (2002), 046308.