Open Access

ARTICLE

On the Multiple-Relaxation-Time Micro-Flow Lattice Boltzmann Method for Complex Flows

by Kazuhiko Suga¹, Takahiko Ito¹

1 Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
2 Corresponding author: suga@me.osakafu-u.ac.jp

Computer Modeling in Engineering & Sciences 2011, 75(2), 141-172. https://doi.org/10.3970/cmes.2011.075.141

Abstract

The multiple-relaxation-time lattice Boltzmann method for micro-scale flows (MRT µ-flow LBM) is extensively evaluated in this study. Following the study of Chai, Shi, Guo and Lu (2010), the diffusive bounce-back wall boundary condition and the collision matrix are modeled. To determine the model parameters, the first-order, 1.5-order and second-order slip-flow models are discussed. Since the mean free path of gas molecules is considered to be influenced by the wall in micro flow systems, the effects of a correction function after Stops (1970) are also evaluated. As the increase of the Knudsen number (Kn), it is necessary to introduce the regularization procedure to remove oscillations from the results, particularly for complex flows. The model combination thus includes the regularization procedure as well. The model validation is firstly performed in canonical force-driven Poiseuille flows at 0.01≤Kn≤ 10. Then, 2-D complex flows around an obstacle such as a triangular- and a square-cylinder at Kn≈0.1 are discussed. Finally, a flow in a 3-D bumpy wall channel at Kn=0.1 is considered. For the 2-D and 3-D flow cases, the two dimensional nine discrete velocity (D2Q9) and the three dimensional 19 discrete velocity (D3Q19) models are applied, respectively. To describe complex shapes of wall surfaces, a linear interpolation scheme is applied to the diffusive bounce-back wall boundary condition. For providing the reference data, simulations by the molecular dynamics (MD) method using the Lennard-Jones potential are also performed for the obstacle and the bumpy channel flows. It is confirmed that the near wall correction of the molecular mean free path is important at Kn>1. With the regularization procedure, the MRT LBM reproduces the reference data very satisfactorily irrespective of the order of the slip-flow model incorporated.

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