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Grid refinement for lattice-BGK models. (English) Zbl 0917.76061
We propose a local second-order grid refinement scheme for the lattice-BGK model. The refinement scheme and a boundary-fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel at small and moderate Reynolds numbers. \(\copyright\) Academic Press.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical 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.; Succi, S.; Benzi, R., Lattice gas dynamics with enhanced collisions, Europhys. lett., 9, 345, (1989)
[3] Chen, S.; Chen, H.; Martinez, D.; Matthaeus, W., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. rev. lett., 67, 3776, (1991)
[4] Chen, H.; Chen, S.; Matthaeus, W., Recovery of the navier – stokes equations through a lattice gas Boltzmann equation method, Phys. rev. A, 45, R5339, (1992)
[5] Qian, Y.H.; d’Humieres, D.; Lallemand, P., Lattice BGK models for navier – stokes equation, Europhys. lett., 17, 479, (1992) · Zbl 1116.76419
[6] Chen, S.; Wang, Z.; Shan, X.; Doolen, G.D., Lattice Boltzmann computational fluid dynamics in three dimensions, J. stat. phys., 68, 379, (1992) · Zbl 0925.76516
[7] Filippova, O.; Hänel, D., Lattice Boltzmann simulation of gas-particle flow in filters, Comput. fluids, 26, 697, (1997) · Zbl 0902.76077
[8] He, X.; Doolen, G., Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. comput. phys., 134, 306, (1997) · Zbl 0886.76072
[9] He, X.; Doolen, G., Lattice Boltzmann method on a curvilinear coordinate system: vortex shedding behind a circular cylinder, Phys. rev. E, 56, 434, (1997)
[10] He, X.; Luo, L.-S.; Dembo, M., Some progress in lattice Boltzmann method. part 1. nonuniform mesh grids, J. comput. phys., 129, 357, (1996) · Zbl 0868.76068
[11] Berger, M.J.; Collela, P., Local adaptive mesh refinement for shock hydrodynamics, J. comput. phys., 82, 67, (1989)
[12] J. J. Quirk, An adaptive grid algorithm for computational shock hydrodynamics, Cranfield Inst. of Technology, UK, 1991
[13] Uphoff, U.; H\"{a}nel, D.; Roth, P., Influence of reactive particles on the structure of detonation waves, Comb. in sci. technol., 110-111, 419, (1995)
[14] 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
[15] He, X.; Luo, L.-S., Lattice Boltzmann model for the incompressible navier – stokes equation, J. stat. phys., 88, 927, (1997) · Zbl 0939.82042
[16] Ziegler, D.P., Boundary conditions for lattice Boltzmann simulations, J. stat. phys., 71, 1171, (1993) · Zbl 0943.82552
[17] Ginzbourg, I.; Adler, P.M., Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. phys. II France, 4, 191, (1994)
[18] Chen, S.; Martinez, D.; Mei, R., On boundary conditions in lattice Boltzmann methods, Phys. fluids, 8, 2527, (1996) · Zbl 1027.76630
[19] Noble, D.R.; Chen, S.; Georgiadis, J.G.; Buckius, R.O., A consistent hydrodynamical boundary conditions for the lattice Boltzmann method, Phys. fluids, 7, 203, (1995) · Zbl 0846.76086
[20] O. Filippova, D. Hänel, Boundary-fitting and grid refinement in Lattice-BGK models, Proceedings of 7th International Symposium on CFD, Bejing, China, Int. Acad. Publishers, 192, 1997
[21] Schäfer, M.; Turek, S., Benchmark computations of laminar flow around a cylinder, Notes in numerical fluid mechanics, 52, 547, (1996) · Zbl 0874.76070
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