- Chen, S, and Doolen, GD, 1998. Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30 (1998), pp. 329–364.
- Chen, S, Chen, H, Martínez, D, and Matthaeus, WH, 1991. Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett. 67 (1991), pp. 3776–3779.
- Fromm, JE, 1969. Practical investigation of convective difference approximations of reduced dispersion, Phys. Fluids Suppl. II (1969), pp. 3–12.
- Ghia, U, Ghia, KN, and Shin, CT, 1982. High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method, J. Comput. Phys. 48 (1982), pp. 387–411.
- Higuera, FJ, and Jimenez, J, 1989. Boltzmann approach to lattice gas simulations, Europhys. Lett. 9 (1989), pp. 663–668.
- Hortmann, M, Perić, M, and Scheuerer, G, 1990. Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions, Int. J. Numer. Meth. Fluids 11 (1990), pp. 189–207.
- Inamuro, T, 2002. A lattice kinetic scheme for incompressible viscous flows with heat transfer, Phil. Trans. R. Soc. Lond. A 360 (2002), pp. 477–484.
- Inamuro, T, Yoshino, M, and Ogino, F, 1995. A non-slip boundary condition for lattice Boltzmann simulations, Phys. Fluids 7 (1995), pp. 2928–2930, Erratum: 8.
- Inamuro, T, Yoshino, M, and Ogino, F, 1997. Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number, Phys. Fluids 9 (1997), pp. 3535–3542.
- Inamuro, T, Yoshino, M, Inoue, H, Mizuno, R, and Ogino, F, 2002. A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat-transfer problem, J. Comput. Phys. 179 (2002), pp. 201–215.
- Matsuda, Y, 1990. A new formulation by the finite element method and finite difference method for the one-dimensional convection–diffusion equation, Trans. Jpn Soc. Mech. Eng. B56 (1990), pp. 441–447, in Japanese.
- Matsuda, Y, and Miki, H, 1994. Two-dimensional viscous fluid flow analysis using the fourth-order finite difference method (Approach by the error analysis technique), Trans. Jpn Soc. Mech. Eng. B60 (1994), pp. 3032–3038, in Japanese.
- McNamara, GR, and Zanetti, G, 1988. Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett. 61 (1988), pp. 2332–2335.
- Nadiga, BT, 1992. "A study of multi-speed discrete-velocity gases". 1992, Ph. D. Thesis, California Institute of Technology.
- Patankar, SV, 1980. "Numerical Heat Transfer and Fluid Flow". In: McGraw-Hill. New York. 1980.
- Qian, YH, d'Humières, D, and Lallemand, P, 1992. Lattice BGK models for Navier–Stokes equation, Europhys. Lett. 17 (1992), pp. 479–484.
- Shao, C, Matsuda, Y, and Wakabayashi, T, 2000. Two-dimensional natural convection analysis by the fourth-order finite difference method (2nd Report, in case of high Rayleigh numbers), Trans. Jpn Soc. Mech. Eng. B66 (2000), pp. 332–338, .
- Shao, C, Matsuda, Y, and Nakanishi, I, 2001. Backward-facing step flow analysis using the fourth-order finite-difference method, Trans. Jpn Soc. Mech. Eng. B67 (2001), pp. 2151–2158, .
- Sone, Y, and Dini, D, , 1971. "Asymptotic theory of flow of rarefied gas over a smooth boundary II". In: Editrice Tecnico Scientifica. Pisa. 1971. pp. 737–749, Vol. 2.
- Succi, S, 2001. "The Lattice Boltzmann Equation for Fluid Dynamics and Beyond". In: Oxford University Press. 2001.
Comparison of Accuracy and Efficiency between the Lattice Boltzmann Method and the Finite Difference Method in Viscous/Thermal Fluid Flows
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.