Abstract
Lattice Boltzmann method is implemented to study two and three dimensional flows in a square cavity. D2Q9 is used to predict the velocity field in a two dimensional cavity while both D3Q15 and D3Q19 lattice arrangements are employed to predict three dimensional flows in a cavity. The second order and non-equilibrium type of boundary conditions are used to discretize the conditions imposed on the velocity field at both moving and stationary walls. Multi-relaxation time method is applied for two dimensional lattice arrangements while single relaxation time method is employed for three dimensional arrangements. Multi relaxation time provides an accurate and stable simulations at high Re flows. The velocity field predicted here for both two and three dimensional cavity flows agrees well with those documented by previous investigators. It has been shown here that the Lattice Boltzmann method is an effective computational fluid dynamics tool to study high Re flows.
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Chai, Z.-H., Shi, B-C., Lin, Z.: Simulating high Reynolds number flow in two-dimensional lid-driven cavity by MRT Lattice Boltzmann method. Chin. Phys. 15, 1855. doi: 10.1088/1009-1963/15/8/038 (2006)
Almalowi, S.J., Oztekin, A.: Flow simulations using two dimensional thermal Lattice Boltzmann method. J. Appl. Math. 2012, 12 (2012)
He Y., Li Q., Wang Y, Tang G.: Lattice Boltzmann Method and its Applications in Engineering Thermo-Physics. Science in China Press, Beijing (2009)
Ho, C.-F., Chang, C., Lin, K.-H., Lin, C.-A.: Consistent Boundary Conditions for 2D and 3D Lattice Boltzmann Simulations, vol. 44, no. 2, pp. 137–155. CMES Tech Science Press, Duluth (2009)
Hou, S., Zou, Q., Chen, S., et al.: Simulation of cavity flow by the Lattice Boltzmann method. J. Compt. Phys. 118, 329–347 (1995)
Barragy, E., Carey, G.F.: Stream function-vorticity driven cavity solutions using p finite elements. Comput. Fluids 26, 453–468 (1997)
Botella, O., Peyret, R.: Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27:421–433 (1988)
Erturk, E., Corke, T.C., Gokcol, C.: Numerical solutions of 2-D steady incompressible driven cavity flow at high reynolds numbers. Int. J. Numer. Meth. Fluids 48, 747 (2005)
Mei, R., Shy, W., Yu, D., Luo, L.-S.: Lattice Boltzmann method for 3-D flows with curved boundary: NASA, ICASE report no. 2002-17 (2002)
D’Humieres, D., Ginzburg, I., et al.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc Lond. A 360, 437–451 (2002)
He, X., Luo, L.-S.: Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation. Plenum Publishing Corporation, New York (1997)
Wolfram, S.: Cellular automaton fluids 1: basic theory. J. Stat. Phys. 45, 471–526 (1986)
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The author, SJA, would like to thank Saudi Arabia government and the College of Engineering at Taibah University—KSA for their support.
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Almalowi, S.J., Oztekin, D.E., Oztekin, A. (2015). Numerical Simulations of Lid-Driven Cavity Flows Using Multi-relaxation Time Lattice Boltzmann Method. In: Shaari, K., Awang, M. (eds) Engineering Applications of Computational Fluid Dynamics. Advanced Structured Materials, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-02836-1_3
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DOI: https://doi.org/10.1007/978-3-319-02836-1_3
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