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Journal
2003 | 1 | 3 | 453-462
Article title

Steady-state analytical solutions for the lattice boltzmann equation

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Content
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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.
Publisher

Journal
Year
Volume
1
Issue
3
Pages
453-462
Physical description
Dates
published
1 - 9 - 2003
online
1 - 9 - 2003
Contributors
References
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  • [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]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_BF02475856
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