Steady-state analytical solutions for the lattice boltzmann equation

• Authors: Gábor Házi
• Languages of publication: EN

Abstracts

EN

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.

Keywords

EN

lattice Boltzmann method; Navier-Stokes equations; analytical solutions; 47.11.+j; 51.10.+y

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2003
• Volume: 1
• Issue: 3
• Pages: 453-462

Dates

published

1 - 9 - 2003

online

1 - 9 - 2003

Contributors

author

Gábor Házi

References

• [1] S. Chen and G.D. Doolen: “Lattice Boltzmann method for fluid flows”, Annual Rev. Fluid Mech., Vol. 30, (1998), pp. 329. http://dx.doi.org/10.1146/annurev.fluid.30.1.329[Crossref]
• [2] G. Házi, A.R. Imre, G. Mayer, I. Farkas: “Lattice Boltzmann methods for two-phase flow modeling”, Ann. Nucl. Energy, Vol. 29, (2002), pp. 1421. http://dx.doi.org/10.1016/S0306-4549(01)00115-3[Crossref]
• [3] D.R. Noble, S. Chen, J.G. Georgiadis, R.O. Buckius: “A consistent hydrodynamic boundary-condition for the lattice Boltzmann method”, Phys. Fluids, Vol. 7, (1995), pp. 203. http://dx.doi.org/10.1063/1.868767[Crossref]
• [4] U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet: “Lattice gas hydrodynamics in two and three dimensions”, Compl. Syst., Vol. 1, (1987), pp. 648.
• [5] Y.H. Qian, D. d'Humieres, P. Lallemand, “Lattice BGK models for Navier-Stokes equation”, Europh. Letters, Vol. 17, (1992), pp. 479.
• [6] Q. Zou, S. Hou, G.D. Doolen: “Analytical solutions of the lattice Boltzmann BGK model”, J. Stat. Phys., Vol. 81, (1995), pp. 319. http://dx.doi.org/10.1007/BF02179981[Crossref]
• [7] B. Legras, B. Villone, U. Frisch: “Dispersive stabilization of the inverse cascade for the Kolmogorov flow”, Phys. Rev. Letters, Vol. 82, (1999), pp. 4440. http://dx.doi.org/10.1103/PhysRevLett.82.4440[Crossref]
• [8] L.S. Luo, H. Chen, S. Chen, G.D. Doolen, Y.C. Lee: “Generalized hydrodynamic transport in lattice-gas automata”, Phys. Rev. A, Vol. 43, (1991), pp. 7097. http://dx.doi.org/10.1103/PhysRevA.43.7097[Crossref]
• [9] L.S. Luo: “Analytic solutions of linearized lattice Boltzmann equation for simple flows”, J. Stat. Phys., Vol. 88, (1997), pp. 913. http://dx.doi.org/10.1023/B:JOSS.0000015178.19008.78[Crossref]
• [10] X. He, Q. Zou, L.S. Luo, M. Dembo: “Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model”, J. Stat. Phys., Vol. 87, (1997), pp. 115. http://dx.doi.org/10.1007/BF02181482[Crossref]
• [11] Q. Zou, S. Hou, S. Chen, G.D. Doolen: “An improved incompressible lattice Boltzmann model for time-independent flows”, J. Stat. Phys., Vol. 81, (1995), pp. 35. http://dx.doi.org/10.1007/BF02179966[Crossref]
• [12] D. d'Humieres and I. Ginzburg: “Multi-reflection boundary conditions for lattice Boltzmann models”, ITWM Report, Nr. 38, (2002).
• [13] G. Házi: “Accuracy of the lattice Boltzmann method based on analytical solutions”, Phys. Rev. E, Vol. 67, (2003), pp. 056705. http://dx.doi.org/10.1103/PhysRevE.67.056705[Crossref]

Identifiers

DOI

10.2478/BF02475856