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Lattice Boltzmann method on curvilinear coordinates system: Flow around a circular cylinder. (English) Zbl 0886.76072
Using an interpolation-based strategy, the lattice Boltzmann method is extended to general curvilinear coordinate systems. As an example, a cylindrical coordinate system is used to simulate two-dimensional flow around a circular cylinder. Numerical simulations are carried out for impulsive initial conditions with Reynolds numbers up to \(10^4\). The agreement of our results with previous computational and experimental results is satisfactory.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D99 Incompressible viscous fluids
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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[1] McNamara, G.; Zanetti, G., Use of the Boltzmann equation to simulate lattice-gas automata, Phys. rev. lett., 61, 2332, (1988)
[2] Higuera, F.J.; Jeménez, J., Boltzmann approach to lattice gas simulations, Europhys. lett., 9, 663, (1989)
[3] Frisch, U.; Hasslacher, B.; Pomeau, Y., Lattice-gas automata for the navier – stokes equation, Phys. rev. lett., 56, 1505, (1986)
[4] Wolfram, S., Cellular automaton fluid 1: basic theory, J. stat. phys., 45, 471, (1986) · Zbl 0629.76002
[5] Xu, K., On the construction of BGK-type schemes for compressible flow simulations, AIAA paper, 96-0525, (1996)
[6] Bhatnagar, P.L.; Gross, E.P.; Krook, M., A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component system, Phys. rev., 94, 511, (1954) · Zbl 0055.23609
[7] Chen, H.; Chen, S.; Matthaeus, W.H., Recovery of the navier – stokes equations using a lattice Boltzmann method, Phys. rev. A., 45, R5339, (1991)
[8] Qian, Y.H.; d’Humières, D.; Lallemand, P., Lattice BGK models for the navier – stokes equation, Europhys. lett., 17, 479, (1992) · Zbl 1116.76419
[9] Ladd, A.J.C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part I. theoretical foundation, J. fluid mech., 271, 285, (1994) · Zbl 0815.76085
[10] Ladd, A.J.C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part II. numerical results, J. fluid mech., 271, 311, (1994)
[11] Hou, S.; Zou, Q.; Chen, S.; Doolen, G.D.; Cogley, A., Simulation of cavity flow by the lattice Boltzmann method, J. comput. phys., 118, 329, (1995) · Zbl 0821.76060
[12] He, X.; Luo, L.S.; Dembo, M., Some progress in lattice Boltzmann method: part I. nonuniform mesh grids, J. comput. phys., 129, 357, (1996) · Zbl 0868.76068
[13] Nannelli, F.; Succi, S., The lattice Boltzmann equation on irregular lattices, J. stat. phys., 68, 401, (1992) · Zbl 0925.82036
[14] Succi, S.; Amati, G.; Benzi, R., Challenges in lattice Boltzmann computing, J. stat. phys., 81, 5, (1995) · Zbl 1106.82376
[15] Chapman, S.; Cowling, T.G., The mathematical theory of non-uniform gases, (1970), Cambridge Univ. Press Cambridge · Zbl 0098.39702
[16] Grad, H., On the kinetic theory of rarefied gases, Commun. pure appl. math., 2, 331, (1949) · Zbl 0037.13104
[17] Pekeris, C.L., Solution of the boltzmann – hilbert integral equation, Proc. nat. acad. soc., 41, 661, (1955) · Zbl 0065.09202
[18] Zou, Q.; Hou, S.; Chen, S.; Doolen, G., An improved incompressible lattice Boltzmann model for time-independent flows, J. stat. phys., 81, 35, (1995) · Zbl 1106.82366
[19] X. He, L. S. Luo, Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys. · Zbl 0939.82042
[20] Dennis, S.C.R.; Chang, G.Z., Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100, J. fluid mech., 42, 471, (1980) · Zbl 0193.26202
[21] Fornberg, B., A numerical study of steady viscous flow past a circular cylinder, J. fluid mech., 98, 819, (1980) · Zbl 0428.76032
[22] Ginzbourg, I.; Alder, P.M., Boundary condition analysis for the three-dimensional lattice Boltzmann model, J. phys. II France, 4, 191, (1994)
[23] Chang, C.C.; Chern, R.L., A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method, J. fluid mech., 233, 243, (1991) · Zbl 0739.76048
[24] Koumoutsakos, P.; Leonard, A., High-resolution simulations of the flow around an impulsively started cylinder using vortex method, J. fluid mech., 296, 1, (1995) · Zbl 0849.76061
[25] Coutanceau, M.; Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. part 1. steady flow, J. fluid mech., 79, 231, (1977)
[26] Coutanceau, M.; Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. part 2. unsteady flow, J. fluid mech., 79, 257, (1977)
[27] Collins, W.M.; Dennis, S.C.R., Flow past an impulsively started circular cylinder, Fluid mech., 60, 105, (1973) · Zbl 0266.76022
[28] Collins, W.M.; Dennis, S.C.R., The initial flow past an impulsively started circular cylinder, Q. J. mech. appl. math., 26, 53, (1973) · Zbl 0267.76016
[29] Nieuwstadt, F.; Keller, H.B., Viscous flow past circular cylinders, Comput. & fluids, 1, 59, (1973) · Zbl 0328.76022
[30] Bouard, R.; Coutanceau, M., The early stage of development of the wake behind an impulsively stated cylinder for 40 < re < 10^{4}, J. fluid mech., 101, 583, (1980)
[31] Loc, Ta Phuoc, Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder, J. fluid mech., 100, 111, (1980) · Zbl 0441.76034
[32] Loc, T.P.; Bouard, R., Numerical solution of the early stage of the unsteady viscious flow around a cylinder: A comparison with experimental visualization and measurement, J. fluid mech., 160, 93, (1985)
[33] Higuera, F.J.; Succi, S., Simulating the flow around a circular cylinder with a lattice Boltzmann equation, Europhys. lett., 8, 517, (1989)
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