zbMATH — the first resource for mathematics

Lattice BGK model for incompressible Navier-Stokes equation. (English) Zbl 0979.76069
Summary: Most of the existing lattice Boltzmann BGK models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper we design a LBGK model without compressible effect for simulating incompressible flows. The incompressible Navier-Stokes equations are exactly recovered from this incompressible LBGK model. Numerical simulations of plane Poiseuille flow, unsteady two-dimensional shear decaying flow, driven cavity flow, and flow around circular cylinder are performed. The results agree well with analytic solutions and with numerical results of previous studies.

76M28 Particle methods and lattice-gas methods
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Reference removed in proofs.
[2] Chen, S.; Doolen, G., Lattice Boltzmann method for fluid flows, Ann. rev. fluid mech., 30, 329, (1998) · Zbl 1398.76180
[3] Chen, S.; Martinez, D.; Mei, R., On boundary conditions in lattice Boltzmann methods, Phys. fluids., 8, 2527, (1996) · Zbl 1027.76630
[4] Coutanceau, M.; Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. 1. steady flow, J. fluid mech., 79, 231, (1977)
[5] E, W.-N.; Liu, J., Essential compact scheme for unsteady viscous incompressible flows, J. comput. phys., 126, 122, (1996)
[6] Filippova, O.; Hänel, D., Grid refinement for lattice-BGK models, J. comput. phys., 147, 219, (1998) · Zbl 0917.76061
[7] Frisch, U.; d’Humiéres, D.; Hasslacher, B.; Lallemand, P.; Pomeau, Y.; Rivet, J.-P., Lattice gas hydrodynamics in two and three dimensions, Complex syst., 1, 649, (1987) · Zbl 0662.76101
[8] Ghia, U.; Ghia, K.N.; Shin, C.T., High-re solutions for incompressible flow using the navier – stokes equations and a multigrid method, J. comput. phys., 48, 387, (1982) · Zbl 0511.76031
[9] He, X.; Luo, L.-S., Lattice Boltzmann model for the incompressible navier – stokes equation, J. stat. phys., 88, 927, (1997) · Zbl 0939.82042
[10] 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
[11] Higuera, F.J.; Succi, S., Simulating the flow around a circular cylinder with a lattice Boltzmann equation, Europhys. lett., 8, 517, (1989)
[12] Hou, S.; Zou, Q., Simulation of cavity flow by the lattice Boltzmann method, J. comput. phys., 118, 329, (1995) · Zbl 0821.76060
[13] Lin, Z.; Fang, H.; Tao, R., Improved lattice Boltzmann model for incompressible two-dimensional steady flows, Phys. rev. E, 54, 6323, (1997)
[14] Martinez, D.O.; Matthaeus, W.H.; Chen, S.; Montgomery, D.C., Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics, Phys. fluids., 6, 1285, (1994) · Zbl 0826.76069
[15] Mei, R.; Shyy, Q., On the finite difference-based lattice Boltzmann method in curvilinear coordinates, J. comput. phys., 143, 426, (1998) · Zbl 0934.76074
[16] Nieuwstadt, F.; Keller, H.B., Viscous flow past circular cylinders, Comput. fluids., 1, 59, (1973) · Zbl 0328.76022
[17] Qian, Y.; d’Humiéres, D.; Lallemand, P., Lattice BGK models for navier – stokes equation, Europhys. lett., 17, 479, (1992) · Zbl 1116.76419
[18] Schreiber, R.; Keller, H., Driven cavity flow by efficient numerical techniques, J. comput. phys., 49, 310, (1983) · Zbl 0503.76040
[19] Vanka, S.P., Block-implicit multigrid solution of navier – stokes equations in primitive variables, J. comput. phys., 65, 138, (1986) · Zbl 0606.76035
[20] Wagner, L., Pressure in lattice Boltzmann simulations of flow around a cylinder, Phys. fluids., 6, 3516, (1994) · Zbl 0832.76079
[21] Wagner, L.; Hayot, F., Lattice Boltzmann simulations of flow past a cylindrical obstacle, J. stat. phys., 81, 63, (1995) · Zbl 1106.82361
[22] 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.