Two Dimensional Simulation of Incompressible Fluid Flow Using Lattice Boltzmann Method


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Abstract


We present the mains of the new method of modeling and simulation lattice Boltzmann methods for fluid flows. Showing some comparisons between classical computations in fluid mechanics based on the resolution of the Navier-Stokes equations and this method. The two dimensional square lattice model with 9 velocities (d2q9) and a simple relaxation time are presented and applied to simulate a laminar flow over backward facing step. The results obtained are in good agreement with those published in the literature.
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Keywords


CFD; Lattice Boltzmann Method; Incompressible Fluid Flow

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References


U. Frisch, B Hasslacher and Y. Pomeau , Lattice gas automata for the Navier-Stokes Equation. Phys.Rev. Lett., 56(14), pp. 1505-1508, 1986.

U. Frisch, D. d’Humi`eres, B. Hasslacher, et al., Lattice gas hydrodynamics in two and three dimensions, Complex Syst. 1, 649, 1987.

G. Zenetti, The hydrodynamics of lattice gas automata. Phys. Rev. A40, pp. 1539-1548, 1989.

P. Clavin, P. Lallemand, Y. Pomeau and G. Searby, Simulation of free boundaries in flow systems by lattice-gas models. J. Fluid Mech. vol.188, pp. 437-464, 1988.

McNamara G, Zanetti GUse of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett;61 pp. 2332–2335. 1988.

Y. H. Qian, D. D'Humieres, & P. Lallemand, Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17, pp. 479-484, 1992.

X. He & L. Luo, Lattice Boltzmann model the incompressible Navier Stokes equation, journal of statistical physics 88, pp. 927-944., 1997.

X. He & L. Luo, Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E 56, pp.6811-6817, 1997.

S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30, pp.329-364, 1998.

CAJ. Fletcher Computational techniques for fluid dynamics, vols.I and II. ( New York: Springer 1988).

P Wesseling Principles of Computational Fluid Dynamics (Springer, 2001).

FJ. Higuera, J. Jimienez Boltzmann Approach to lattice gas simulations. Europhys Lett 9, pp. 663–668. . 1989.

Koelman JMVA, A simple lattice Boltzmann scheme for Navier–Stokes fluid flow. Europhys Lett1, 5, pp. 603–607, 1991.

S. Chen, SP. Dawson, GD Doolen, DR. Janecky, A. Lawniczak. Lattice metods and their applications to reacting systems. Comput Chem Eng ,19, PP. 617-646, 1995.

NS. Martys, H. Chen, Simulation of multi-component fluids in complex three-dimensional geometries by lattice Boltzmann method. Phys. Rev. E 53, pp. 743-750,1996.

H.Yu, L-S. Luo, SS. Girimaji. Scalar mixing and chemical reaction simulations using lattice Boltzmann method. Int. J. Computat Eng Sci 3, pp. 73-87, 2002

W. Miller, S. Succi, D. Mansutti, A lattice Boltzmann model for anisotropic liquid/solid phase transition. Phys. Rev. Lett 86, pp. 3578-3581, 2001.

W. Miller, S. Succi, D. A lattice Boltzmann model for anisotropic crystal growth from melt. J Stat Phys 107, pp. 173-186, 2002.

S. Chen, H. Chen D. Martinez, WH. Matthaeus. Lattice Boltzmann model for simulation of magneto hydrodynamics, phys. Rev. Lett 67, pp.3776-3779, 1991.

S. Succi, The lattice Boltzmann equation for fluid dynamics and beyond. (New York: Oxford University press, 2001).

John D Anderson Computational Fluid Dynamics The Basics With Applications (McGraw Hill, Inc NeyYork 1995).

P.L. Bhatnagar, E.P. Gross and M. Krook A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component system, Phys. Rev. 94, pp. 511-525, 1954.

Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids 9, pp. 1591-1598,1997.

J. Bernsdorf, Stromungsbereshnungen mit Lattice Boltzmann automaten. Kunrzlehrgang NUMET, LSTM, Universitat Erlangen-Nrnberg, 2000.

T. Inamuro, M. Yoshineand F. Ogine, A non-slip boundary condition for lattice Boltzmann simulation. Phys. Fluids, Vol.7, pp.2928-2930, 1995.

B.F. Armaly, F. Durst, J. C.F. Pereira and B.Schonung. Experimental and theorical investigation of backward-facing step flow, Journ. Fluid. Mech., Vol. 127, pp. 473-4961, 1983.

K. Morgan, J. Periaux, F. Thomasset, Analysis of laminar flow over a backward step. In notes on numerical fluid mechanics, (Vol. 9, Vieweg 1984).

J. Kim, P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comp. Phys. 59, pp. 308-323, 1985.

P. Orlandi, Vorticity-Velocity formulation for high Re flows, Computers & Fluids, 15, pp. 137-149, 1987.

S. Patankar, K. C. Karki, H. C. Monia, Development and evaluation of improved numerical schemes for recirculating flows. Proc. AIAA 25th Aerospace Sciences Meeting (Reno, NV), AIAA, New York, 1987, pp. 87-91.

G. Guj, F. Stella, Numerical solutions of high-Re recirculating flows in vorticity-velocity formulation. Int. J. Numer. Meth. Fluids, 8, pp. 405-416, 1988.

J. L. Shon, Evaluation of FIDAP on some classical laminar and turbulent benchmarks. Int. J. Numer. Meth. Fluids, 8, pp.1469-1490, 1988.

S. Thangam, D. D, Knight, Effect of step height on the separated flow past a backward-facing. Phys. Fluids, 1, pp. 604-606, 1989.

S. Thangam, D. D. Knight, A computational scheme in generalized coordinates for viscous incompressible flows. Computers & Fluids, 18 pp. 317-327, 1990.

T.H. Le, B. Troff, P. Sagault, K. Dang-Tra, L. Ta Phuoc, PEGASE: A Navier-Stokes solver for direct numerical simulation of incompressible flows, Int. Jour. Num. Meth. Fluids, Vol. 24, 833-861, 1997.


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