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Rectangular Lattice Boltzmann Equation for Gaseous Microscale Flow

Part of: Basic methods in fluid mechanics Rarefied gas flows, Boltzmann equation Incompressible viscous fluids

Published online by Cambridge University Press:  27 January 2016

Junjie Ren ,
Ping Guo  and
Zhaoli Guo
Junjie Ren
Affiliation:
School of Sciences, Southwest Petroleum University, Chengdu 610500, China
Ping Guo
Affiliation:
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
Zhaoli Guo*
Affiliation:
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
*
*Corresponding author. Email: renjunjie1900@126.com (J. Ren), guopingswpi@vip.sina.com (P. Guo), zlguo@hust.edu.cn (Z. Guo)
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Abstract

The lattice Boltzmann equation (LBE) is considered as a promising approach for simulating flows of liquid and gas. Most of LBE studies have been devoted to regular square LBE and few works have focused on the rectangular LBE in the simulation of gaseous microscale flows. In fact, the rectangular LBE, as an alternative and efficient method, has some advantages over the square LBE in simulating flows with certain computational domains of large aspect ratio (e.g., long micro channels). Therefore, in this paper we expand the application scopes of the rectangular LBE to gaseous microscale flow. The kinetic boundary conditions for the rectangular LBE with a multiple-relaxation-time (MRT) collision operator, i.e., the combined bounce-back/specular-reflection (CBBSR) boundary condition and the discrete Maxwell's diffuse-reflection (DMDR) boundary condition, are studied in detail. We observe some discrete effects in both the CBBSR and DMDR boundary conditions for the rectangular LBE and present a reasonable approach to overcome these discrete effects in the two boundary conditions. It is found that the DMDR boundary condition for the square MRT-LBE can not realize the real fully diffusive boundary condition, while the DMDR boundary condition for the rectangular MRT-LBE with the grid aspect ratio a≠1 can do it well. Some numerical tests are implemented to validate the presented theoretical analysis. In addition, the computational efficiency and relative difference between the rectangular LBE and the square LBE are analyzed in detail. The rectangular LBE is found to be an efficient method for simulating the gaseous microscale flows in domains with large aspect ratios.

Keywords

Lattice Boltzmann equationgaseous microscale flowrectangular latticeboundary conditionsmultiple-relaxation time

MSC classification

Secondary: 76M28: Particle methods and lattice-gas methods 76D05: Navier-Stokes equations 76P05: Rarefied gas flows, Boltzmann equation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 306 - 330
Copyright
Copyright © Global-Science Press 2014 

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