References
- Agrawal, A., Djenidi, L., and Antonia, R.A., 2005. Simulation of gas flow in microchannels with a sudden expansion or contraction, Journal of Fluid Mechanics 530 (2005), pp. 135–144.
- Ansumali, S., and Karlin, I.V., 2002. Kinetic boundary conditions in the lattice Boltzmann method, Physical Review E 66 (2002), p. 026311.
- Cercignani, C., 1990. Mathematical methods in kinetic theory. New York: Plenum Press; 1990.
- Chen, S.Y., and Doolen, G.D., 1998. Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics 30 (1998), pp. 329–364.
- Chikatamarla, S.S., and Karlin, I.V., 2006. Entropy and Galilean invariance of lattice Boltzmann theories, Physical Review Letters 97 (2006), p. 190601.
- d'Humières, D., 1992. Generalized lattice Boltzmann equations, Progress in Aeronautics and Astronautics 159 (1992), pp. 450–458.
- Ginzburg, I., and d'Humières, D., 2003. Multireflection boundary conditions for lattice Boltzmann models, Physical Review E 68 (2003), p. 066614.
- Guo, Z.L., Zhao, T.S., and Shi, Y., 2006. Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for micro gas flows, Journal of Applied Physics 99 (2006), p. 074903.
- Guo, Z.L., Shi, B.C., Zhao, T.S., and Zheng, C.G., 2007. Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows, Physical Review E 76 (2007), p. 056704.
- Guo, Z.L., Zheng, C.G., and Shi, B.C., 2008. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow, Physical Review E 77 (2008), p. 036707.
- He, X., and Luo, L.‐S., 1997. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Physical Review E 56 (1997), pp. 6811–6817.
- Kim, W.T., Jhon, M.S., Zhou, Y., Staroselsky, I., and Chen, H.D., 2005. Nanoscale air bearing modeling via lattice Boltzmann method, Journal of Applied Physics 97 (2005), p. 10P304.
- Lallemand, P., and Luo, L.‐S., 2000. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E 61 (2000), pp. 6546–6562.
- Lee, T., and Lin, C.L., 2005. Rarefaction and compressibility effects of the lattice Boltzmann equation method in a gas microchannel, Physical Review E 71 (2005), p. 046706.
- Lim, C.Y., Shu, C., Niu, X.D., and Chew, Y.T., 2002. Application of lattice Boltzmann method to simulate microchannel flows, The Physics of Fluids 14 (2002), pp. 2299–2308.
- Luo, L.‐S., 2004. Comment on “Discrete Boltzmann equation for microfluidics”, Physical Review Letters 92 (2004), p. 139401.
- Nie, X., Doolen, G.D., and Chen, S., 2002. Lattice-Boltzmann simulations of fluid flows in MEMS, Journal of Statistical Physics 107 (2002), pp. 279–289.
- Niu, X.D., Shu, C., and Chew, Y.T., 2004. A lattice Boltzmann BGK model for simulation of micro flows, Europhysics Letters 67 (2004), pp. 600–606.
- Sbragaglia, M., and Succi, S., 2005. Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions, The Physics of Fluids 17 (2005), p. 093602.
- Shan, X., and He, X., 1998. Discretization of the velocity space in the solution of the Boltzmann equation, Physical Review Letters 80 (1998), pp. 65–68.
- Shan, X., Yuan, X.‐F., and Chen, H., 2006. Kinetic theory representation of hydrodynamics: A way beyond the Navier–Stokes equation, Journal of Fluid Mechanics 550 (2006), pp. 413–441.
- Shen, C., Tian, D.B., Xie, C., and Fan, J., 2004. Examination of the LBM in simulation of microchannel flow in transitional regime, Microscale Thermophysics Engineering 8 (2004), pp. 423–432.
- Sofonea, V., and Sekerka, R.F., 2005. Boundary conditions for the upwind finite difference lattice Boltzmann model: evidence of slip velocity in micro-channel flow, Journal of Computational Physics 207 (2005), pp. 639–659.
- Sofonea, V., and Sekerka, R.F., 2005. Diffuse reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: evidence of temperature jump and slip velocity in microchannels, Physical Review E 71 (2005), p. 066709.
- Succi, S., 2001. The lattice Boltzmann equation for fluid dynamics and beyond. Oxford: Oxford University Press; 2001.
- Succi, S., 2003. Mesoscopic modeling of slip motion at fluid–solid interfaces with heterogeneous catalysis, Physical Review Letters 89 (2003), p. 064502.
- Tang, G.H., Tao, W.Q., and He, Y.L., 2005. Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions, Physics of Fluids 17 (2005), p. 058101.
- Teixeira, C.M., 2005. Simulation of plane Poiseuille flow of a rarefied gas with an extended lattice Boltzmann method, AIP Conference of Proceedings 762 (2005), pp. 668–676.
- Toschi, F., and Succi, S., 2005. Lattice Boltzmann method at finite Knudsen numbers, Europhysics Letters 69 (2005), pp. 549–555.
- Verhaeghe, F., Luo, L.‐S., and Blanpain, B., 2007. Lattice Boltzmann modeling of microchannel flow in slip flow regime, Journal of Computational Physics (2007), Submitted for publication.
- Yu, D., Mei, R., Luo, L.‐S., and Shyy, W., 2003. Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences 39 (2003), pp. 329–367.
- Zhang, Y.H., Qin, R., and Emerson, D.R., 2005. Lattice Boltzmann simulation of rarefied gas flows in microchannels, Physical Review E 71 (2005), p. 047702.
- Zhang, Y.H., Gu, X.J., Barber, R.W., and Emerson, D.R., 2006. Capturing Knudsen layer phenomena using a lattice Boltzmann model, Physical Review E 74 (2006), p. 046704.
- Zhang, Y.H., Gu, X.J., Barber, R.W., and Emerson, D.R., 2007. Modelling thermal flow in the transition regime using a lattice Boltzmann approach, Europhysics Letters 77 (2007), p. 30003.