Comparison of accuracy and efficiency between the lattice Boltzmann method and the finite difference method in viscous/thermal fluid flows

International Journal of Computational Fluid Dynamics

Volumn 18, Issue 4, 2004, Pages 333-345

  Yoshino, M ^a   Matsuda, Y ^a   Shao, C ^a,b  

^a SHINSHU UNIVERSITY   (Japan)

^b AW Engineering Co Ltd   (Japan)

Author keywords

Cavity flow; Finite difference method (FDM); Incompressible viscous flow; Lattice Boltzmann method (LBM); Natural convection; Porous structure

Indexed keywords

CAVITY FLOW; INCOMPRESSIBLE VISCOUS FLOW; LATTICE BOLTZMANN METHOD (LBM); POROUS STRUCTURE;

COMPUTATIONAL COMPLEXITY; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NATURAL CONVECTION; POISSON EQUATION; PROBLEM SOLVING; VISCOUS FLOW;

MECHANICAL ENGINEERING;

EID: 2942603506     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: 10.1080/1061856031000154775     Document Type: Conference Paper

References (20)

1. Chen, S. and Doolen, G.D. (1998) "Lattice Boltzmann method for fluid flows", Annu. Rev. Fluid Mech. 30, 329-364.
2. Chen, S., Chen, H., Martínez, D. and Matthaeus, W.H. (1991) "Lattice Boltzmann model for simulation of magnetohydrodynamics", Phys. Rev. Lett. 67, 3776-3779.
3. Fromm, J.E. (1969) "Practical investigation of convective difference approximations of reduced dispersion", Phys. Fluids Suppl. II, 3-12.
4. Ghia, U., Ghia, K.N. and Shin, C.T. (1982) "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method", J. Comput. Phys. 48, 387-411.
5. Higuera, F.J. and Jimenez, J. (1989) "Boltzmann approach to lattice gas simulations", Europhys. Lett. 9, 663-668.
6. 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, 189-207.
7. Inamuro, T. (2002) "A lattice kinetic scheme for incompressible viscous flows with heat transfer", Phil. Trans. R. Soc. Lond. A 360, 477-484.
8. Inamuro, T., Yosbino, M. and Ogino, F. (1995) "A non-slip boundary condition for lattice Boltzmann simulations", Phys. Fluids 7, 2928-2930, Erratum: 8, 1124.
9. Inamuro, T., Yoshino, M. and Ogino, F. (1997) "Accuracy of the lattice Boltzmann method for small Rnudsen number with finite Reynolds number", Phys. Fluids 9, 3535-3542.
10. 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, 201-215.
11. 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, 441-447 (in Japanese).
12. 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, 3032-3038 (in Japanese).
13. McNamara, G.R. and Zanetti, G. (1988) "Use of the Boltzmann equation to simulate lattice-gas automata", Phys. Rev. Lett. 61, 2332-2335.
14. Nadiga, B.T. (1992) "A study of multi-speed discrete-velocity gases", Ph. D. Thesis, California Institute of Technology.
15. Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow (McGraw-Hill, New York).
16. Qian, Y.H., d'Humières, D. and Lallemand, P. (1992) "Lattice BGK models for Navier-Stokes equation", Europhys. Lett. 17, 479-484.
17. 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, 332-338 (in Japanese).
18. 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, 2151-2158 (in Japanese).
19. Sone, Y. (1971) "Asymptotic theory of flow of rarefied gas over a smooth boundary JJ", In: Dini, D., ed, Rarefied Gas Dynamics (Editrice Tecnico Scientifica, Pisa) Vol. 2, pp 737-749.
20. Succi, S. (2001) The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press).