Investigation of the Lattice Boltzmann SRT and MRT Stability for Lid Driven Cavity Flow

Abstract—The Lattice Boltzmann Method (LBM) is applied to incompressible, steady, laminar flow high Reynolds numbers varying in a range from 200 to 2000 for determining stability limits of the LBM Single Relaxation Time (LBM-SRT) and the LBM Multiple Relaxation Time (LBM-MRT). The lid driven cavity flow is analyzed. The effect of the model Mach number on accuracy is investigated by performing computations at different Mach numbers in the range 0.09 – 0.54 and comparing the results with the finite-volume predictions of the incompressible Navier-Stokes equations. It is observed that the Mach number does not affect the results too much within this range, and the results agree well with the finite volume solution of the incompressible Navier-Stokes equation. LBM-MRT is more stable than LBM-SRT especially for low Mach and high Reynolds numbers. For the LBM-SRT solutions, collision frequency (ɷ) decreases with increasing Reynolds and Mach numbers, however, for the LBM-MRT solutions, 7th and 8th relaxation rates ( s ₇=s₈) decrease with decreasing Reynolds numbers and with increasing Mach numbers. Within its stability range, the convergence  speed of the LBM-SRT is higher (approximately %10) than that of LBM-MRT, while the convergence speed of the finite volume method is much lower than the both LBM formulations (the LBM-SRT and the LBM-MRT).

Index Terms—Lid driven cavity flow, lattice Boltzmann method, single relaxation time, multiple relaxation time.

E. Aslan is with the Department of the Mechanical Engineering, Istanbul University, 34320, Istanbul, Turkey (e-mail: erman.aslan@istanbul.edu.tr).
I. Taymaz is with the Department of the Mechanical Engineering, Sakarya University, 54187, Sakarya, Turkey (e-mail: taymaz@sakarya.edu.tr).
A.C. Benim is with the CFD Lab., Department of Mechanical and Process Engineering, Duesseldorf University of Applied Sciences, Josef-Gocklen Str.9, 40474, Duesseldorf, Germany (e-mail: alicemal.benim@fh-duesseldorf.de).

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Cite: E. Aslan, I. Taymaz, and A. C. Benim, "Investigation of the Lattice Boltzmann SRT and MRT Stability for Lid Driven Cavity Flow," International Journal of Materials, Mechanics and Manufacturing vol. 2, no. 4, pp. 317-324, 2014.