Discrete effects on boundary conditions of the lattice Boltzmann method for fluid flows with curved no-slip walls

作     者：Liang Wang Shi Tao Xuhui Meng Kai Zhang Gui Lu 

作者机构：Beijing Key Laboratory of Emission Surveillance and Control for Thermal Power Generation North China Electric Power University Beijing 102206 China School of Energy Power and Mechanical Engineering North China Electric Power University Beijing 102206 China Guangdong Provincial Key Laboratory of Distributed Energy Systems Dongguan University of Technology Dongguan 523808 China Division of Applied Mathematics Brown University Providence Rhode Island 02912 USA Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education North China Electric Power University Beijing 102206 China 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2020年第101卷第6期

页      面：063307-063307页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基　　金：National Natural Science Foundation of China, NSFC, (51606064, 51776068, 51906044) National Natural Science Foundation of China, NSFC Fundamental Research Funds for the Central Universities, (2018MS060) Fundamental Research Funds for the Central Universities 

主　　题：Slip boundary effects Wall slip 

摘      要：The lattice Boltzmann method (LBM) has been formulated as a powerful numerical tool to simulate incompressible fluid flows. However, it is still a critical issue for the LBM to overcome the discrete effects on boundary conditions successfully for curved no-slip walls. In this paper, we focus on the discrete effects of curved boundary conditions within the framework of the multiple-relaxation-time (MRT) model. We analyze in detail a single-node curved boundary condition [Zhao et al., Multiscale Model. Simul. 17, 854 (2019)] for predicting the Poiseuille flow and derive the numerical slip at the boundary dependent on a free parameter as well as the distance ratio and the relaxation times. An approach by virtue of the free parameter is then proposed to eliminate the slip velocity while with uniform relaxation parameters. The theoretical analysis also indicates that for previous curved boundary schemes only with the distance ratio and the halfway bounce-back (HBB) boundary scheme, the numerical slip cannot be removed with uniform relaxation times virtually. We further carried out some simulations to validate our theoretical derivations, and the numerical results for the case of straight and curved boundaries confirm our theoretical analysis. Finally, for fluid flows with curved boundary geometries, resorting to more degrees of freedom from the boundary scheme may have more potential to eliminate the discrete effect at the boundary with uniform relaxation times.