Please enter verification code
Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 3, May 2013, Pages: 87-93
Received: May 30, 2013; Published: Jun. 20, 2013
Views 3721      Downloads 374
Anil Kumar, Department of Applied Mathematics, World Institute of Technology Sohna Gurgaon, India
S P Agrawal, Department of Civil Engineering, World Institute of Technology Sohna Gurgaon, India
Article Tools
Follow on us
In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won’t merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.
Cavity Flow, Lattice Boltzmann, Aspect Ratio, Vortex Integration
To cite this article
Anil Kumar, S P Agrawal, Mathematical and Simulation of Lid Driven Cavity Flow at Different Aspect Ratios Using Single Relaxation Time Lattice Boltzmann Technique, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 3, 2013, pp. 87-93. doi: 10.11648/j.ajtas.20130203.17
Chen, S., Doolen, G.D., "Lattice Boltzmann method for fluid flow", Ann Rev Fluid Mech, Vol. 30 (1998), 329-364.
Zou, Q., He, X., "On pressure and velocity boundary conditions for the lattice Boltzmann BGK model", Phys Fluids, Vol. 9 (1997), 1591-1598.
Niu, X.D., Shu, C., Chew, Y.T., "A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows" , Comput Fluids, Vol. 36 (2006), 273-281.
Ho, C.F., Chang, C., Lin, K.H., Lin, C.A., "Consistent boundary conditions for 2D and 3D laminar lattice Boltzmann Simulations", CMES-Comput Model in Eng & Sci Vol. 44 (2009), 137-155.
Liu, C.H., Lin, K.H., Mai, H.C., Lin, C.A., "Thermal boundary conditions for thermal lattice Boltzmann simulations", Comput Math Appl Vol. 59 (2010), 2178-2193.
Hou , S., Zou, Q., Chen, S., Doolen, G., Cogley, A.C., "Simulation of cavity flow by the lattice Boltzmann method", J Comput Phys, Vol. 118 (1995), 329-347.
Guo, Z.L., Shi, B.C., Wang , N., "Lattice BGK model for incompressible Navier–Stokes equation", J Comput Phys, Vol. 165 (2000) 288-306.
Ghia, U., Ghia, K.N., Shin, C.T., "High-Resolutions for incompressible flow using the Navier–tokes equations and a multigrid method", J Comput Phys, Vol. 48 (1982), 387-411.
Erturk, E., Corke, T.C., Gökçöl, C., "Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers", Int. J. Numer. Meth. Fluids, Vol. 48 (2005), 747-774.
Taneda, S., "Visulization of separating Stokes flows", Journal of the Physical Society of Japan, Vol. 46(6) (1979), 1935- 1941.
Shen, C., Floryan, J.M., "Low Reynolds number flows over cavities", Phys Fluids, Vol. 28(11) (1985), 3191-3203.
Patil, D., Lakshmisha, K., Rogg, B., "Lattice Boltzmann simulation of lid-driven flow in deep cavities", Comput Fluids, Vol. 35(10) (2006), 1116-1125.
Pandit, S.K., "On the use of compact streamfunction-velocity formulation of1stready Navier–Stokes equations on geometries beyond rectangular", J Sci Comput, Vol. 36(2) (2008), 219-242.
Lin, L.S., Chen, Y.C., Lin, C.A., "Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios", Computers & Fluids, Vol. 45(1) (2011), 233-240.
Chen, S., Martinez, D., Mei, R., "On boundary conditions in lattice Boltzmann methods", Phys. Fluids, Vol. 8(9) (1996),2527-2537.
JN Reddy : Applied functional analysis and variational methods in Engineering, Mc Graw Hill Book Company New York 1986.
P Fischer, LW; Ho, GE; Karniadakis, EMR and Patera:Recent advanced in parellal spectral element simulation of unsteady incompressible fluid flows, computer and structures, 30, 217-231, 1988.
D. Arumuga Perumal, Anoop K. Dass "Application of lattice Boltzmann method for incompressible viscous flows, Applied Mathematical Modeling vol. 14, 23-39, 2013.
Reyad Omari "CFD simulation of Lid Driven cavity flow at moderate Reynolds Number, European Scientific Journal May 2013 edition vol.9 (15) 45-60.
Anil Kumar , CL Varshney and Sajjan Lal " Analytical study of effect of disorder on dispersionin steady inertial flows in porous effect, Scientific Research and Essays vol. 4(11) 1392-1402. 2009.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186