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A multi-block lattice Boltzmann method for viscous fluid flows. (English) Zbl 1036.76051
The authors introduce a D2Q9 lattice Boltzmann algorithm on block-refined grids. At grid interfaces, continuity of density, momentum and viscous stress is used as construction criterion for coupling conditions. The relaxation times on different grids are chosen in such a way that the viscosity is grid-independent. The number of temporal substeps in a refined region is equal to the integer factor between the coarse and fine grid length, thus reflecting a hydrodynamical scaling. Several numerical examples are presented (lid driven cavity, flow around a cylinder, flow over NACA0012 airfoil), and the smooth transition of fields across the grid interfaces is demonstrated.

76M28 Particle methods and lattice-gas methods
76D05 Navier-Stokes equations for incompressible viscous fluids
76N15 Gas dynamics (general theory)
Full Text: DOI
[1] McNamara, Physical Review Letters 61 pp 2332– (1988)
[2] Higuera, Europhysics Letters 9 pp 345– (1989)
[3] Qian, Europhysics Letters 17 pp 479– (1992)
[4] Benzi, Physics Report 222 pp 145– (1992)
[5] Chen, Annual Review of Fluid Mechanics 30 pp 329– (1998)
[6] Computational Techniques for Fluid Dynamics, vol. II. Springer-Verlag: New York, 1983.
[7] Computational Techniques for Fluid Dynamics, vols. I & II. Springer-Verlag: New York, 1988.
[8] Computational Modeling for Fluid Flow and Interfacial Transport, (corrected printing) Elsevier: Amsterdam, 1997.
[9] Bhatnagar, Physical Review 94 pp 511– (1954)
[10] He, Physical Review E 55 pp r6333– (1997)
[11] He, Physical Review E 56 pp 6811– (1997)
[12] Mei, Journal of Computational Physics 155 pp 307– (1999)
[13] Computational Fluid Dynamics With Moving Boundaries. Taylor & Francis: Oxford, 1996.
[14] Ye, Journal of Computational Physics 156 pp 209– (1999)
[15] Filippova, Journal of Computational Physics 147 pp 219– (1998)
[16] Lin, Physical Review E 62 pp 2219– (2000)
[17] Kandhai, Computer Physics Communications 129 pp 100– (2000)
[18] Ghia, Journal of Computational Physics 48 pp 387– (1982)
[19] Computational Techniques for Complex Transport Phenomena. Cambridge University Press: New York, 1999.
[20] Benchmark computations of laminar flow over a cylinder. Notes in Numerical Fluid Mechanics, vol. 52. Vieweg Verlag: Braunschweig, 1996; 547-566. · Zbl 0874.76070
[21] Drela, AIAA Journal 25 pp 1347– (1987)
[22] Evaluation of Powerflow for aerodynamic applications. Preprint, 2000.
[23] Filippova, Journal of Computational Physics 165 pp 407– (2000)
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