@Article{AAMM-8-2,
author = {Ren, Junjie and Ping, Guo and Zhaoli, Guo},
title = {Rectangular Lattice Boltzmann Equation for Gaseous Microscale Flow},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2016},
volume = {8},
number = {2},
pages = {306--330},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m672},
url = {https://global-sci.com/article/73334/rectangular-lattice-boltzmann-equation-for-gaseous-microscale-flow}
}