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A coupled lattice BGK model for the Boussinesq equations. (English) Zbl 1014.76071
Summary: We develop a thermal lattice BGK model for Boussinesq incompressible fluids. The basic idea is to solve velocity field and temperature field using two independent lattice BGK equations, and then combine them into one coupled model for the whole system. The porous plate problem and two-dimensional natural convection flow in square cavity with \(\text{Pr}=0.71\) and various Rayleigh numbers are simulated using the model. The numerical results are in good agreement with analytical solutions of previous studies.

MSC:
76M28 Particle methods and lattice-gas methods
76R10 Free convection
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Chen, Annual Review of Fluid Mechanics 30 pp 329– (1998) · Zbl 1398.76180 · doi:10.1146/annurev.fluid.30.1.329
[2] Alexander, Physics Review E 47 pp r2249– (1993) · doi:10.1103/PhysRevE.47.R2249
[3] Qian, Journal of Science and Computation 8 pp 231– (1993) · Zbl 0783.76004 · doi:10.1007/BF01060932
[4] Chen, Physics Review E 50 pp 2776– (1994) · doi:10.1103/PhysRevE.50.2776
[5] Bartoloni, International Journal for Modular Physics C 4 pp 993– (1993) · doi:10.1142/S012918319300077X
[6] Eggles, International Journal of Heat and Fluid Flow 16 pp 357– (1995) · doi:10.1016/0142-727X(95)00052-R
[7] Shan, Physics Review E 55 pp 2780– (1997) · doi:10.1103/PhysRevE.55.2780
[8] He, Journal of Computational Physics 146 pp 282– (1998) · Zbl 0919.76068 · doi:10.1006/jcph.1998.6057
[9] Martinez, Physics of Fluids 6 pp 1285– (1994) · Zbl 0826.76069 · doi:10.1063/1.868296
[10] Zou, Journal of Statistical Physics 81 pp 35– (1995) · Zbl 1106.82366 · doi:10.1007/BF02179966
[11] Lin, Physics Review E 54 pp 6323– (1997) · doi:10.1103/PhysRevE.54.6323
[12] He, Journal of Statistical Physics 88 pp 927– (1997) · Zbl 0939.82042 · doi:10.1023/B:JOSS.0000015179.12689.e4
[13] Guo, Journal of Computational Physics 165 pp 288– (2000) · Zbl 0979.76069 · doi:10.1006/jcph.2000.6616
[14] Qian, Europhysics Letters 17 pp 479– (1992) · Zbl 1116.76419 · doi:10.1209/0295-5075/17/6/001
[15] Ancona, Journal of Computational Physics 115 pp 107– (1994) · Zbl 0808.65087 · doi:10.1006/jcph.1994.1181
[16] Swift, Physics Review E 75 pp 830–
[17] Qian, Annual Reviews of Computational Physics III 3 pp 195– (1995) · doi:10.1142/9789812830647_0006
[18] Gallivan, International Journal for Numerical Methods in Fluids 25 pp 249– (1997) · Zbl 0889.76061 · doi:10.1002/(SICI)1097-0363(19970815)25:3<249::AID-FLD546>3.0.CO;2-7
[19] Zou, Physics of Fluids 9 pp 1591– (1997) · Zbl 1185.76873 · doi:10.1063/1.869307
[20] An extrapolation method for pressure and velocity boundary conditions in lattice Boltzmann method. Proceedings of the International Conference on Applied Computational Fluid Dynamics, Beijing, 2000, pp. 198-202.
[21] Noble, Physics of Fluids 7 pp 203– (1995) · Zbl 0846.76086 · doi:10.1063/1.868767
[22] de Vahl Davis, International Journal for Numerical Methods in Fluids 3 pp 249– (1983) · doi:10.1002/fld.1650030305
[23] Hortmann, International Journal for Numerical Methods in Fluids 11 pp 189– (1990) · Zbl 0711.76072 · doi:10.1002/fld.1650110206
[24] Barakos, International Journal for Numerical Methods in Fluids 18 pp 695– (1994) · Zbl 0806.76055 · doi:10.1002/fld.1650180705
[25] Markatos, International Journal of Heat Mass Transfer 27 pp 755– (1984) · Zbl 0542.76112 · doi:10.1016/0017-9310(84)90145-5
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