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Acceleration of lattice-BGK schemes with grid refinement. (English) Zbl 0990.76070
Summary: The LBGK method with local grid refinement has been shown to be an efficient and accurate tool for the simulation of incompressible, viscous flows over complex geometries. In the present study, we propose a further improvement of this concept, enabling the use of smaller amount of time steps on refined grids without impairing the spatial or temporal accuracy. This extension of the LBGK method is tested by analytical and numerical investigations, and the gain in computational time is found to be significant.

76M28 Particle methods and lattice-gas methods
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI
[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] 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
[8] He, X.; Luo, L.-S., Lattice Boltzmann model for the incompressible navier – stokes equation, J. stat. phys., 88, 927, (1997) · Zbl 0939.82042
[9] Filippova, O.; Hänel, D., A novel lattice BGK approach for low Mach number combustion, J. comput. phys., 158, 139, (2000) · Zbl 0963.76072
[10] O. Filippova, and, D. Hänel, Numerical simulation of gas – particle flow in filters by lattice Bhatnagar-Gross-Krook model, in, Advances in Aerosol Filtration, edited by, K. Spurny, CRC Press, Boca Raton, FL, 1998.
[11] Nannelli, F.; Succi, S., The lattice Boltzmann equation on irregular lattices, J. stat. phys., 68, 401, (1992) · Zbl 0925.82036
[12] 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
[13] He, X.; Doolen, G., Lattice Boltzmann method on a curvilinear coordinate system: vortex shedding behind a circular cylinder, Phys. rev. E, 56, 434, (1997)
[14] 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
[15] Berger, M.J.; Collela, P., Local adaptive mesh refinement for shock hydrodynamics, J. comput. phys., 82, 67, (1989)
[16] Quirk, J.J., An adaptive grid algorithm for computational shock hydrodynamics, (1991) · Zbl 0856.65108
[17] U. Uphoff, D. Hänel, and, P. Roth, A grid refinement study for detonation simulation with detailed chemistry, in, Proc. of 6th Int. Conf. on Num. Combustion, New Orleans, 1996.
[18] Filippova, O.; Hänel, D., Grid refinement for lattice-BGK models, J. comput. phys., 147, 219, (1998) · Zbl 0917.76061
[19] Filippova, O.; Hänel, D., Boundary-Fitting and local grid refinement for lattice-BGK models, Int. J. mod. phys. C, 9, 1271, (1998)
[20] Schäfer, M.; Turek, S., Benchmark computations of laminar flow around a cylinder, Notes in numerical fluid mechanics, 52, 547, (1996) · Zbl 0874.76070
[21] Breuer, M.; Bernsdorf, J.; Zeiser, T.; Durst, F., Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume, Int. J. heat fluid flow, 21, 186, (2000)
[22] Mazzocco, F.; Arrighetti, G.; Bella, G.; Spagnoli, L.; Succi, S., Multiscale lattice Boltzmann schemes: A preliminary application to axial turbomachine flow simulations, Int. J. mod. phys. C, 11, 233, (2000)
[23] K. Dortmann, Computation of viscous unsteady compressible flow about airfoils, in, IC11 NMFD Williamsburg, VA, 1988.
[24] Hänel, D.; Breuer, M., On the computation of transonic viscous flows, Symposium transsonicum III, IUTAM symposium, 75, (1988)
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