文献类型：期刊文献

英文题名：Designing correct fluid hydrodynamics on a rectangular grid using MRT lattice Boltzmann approach

作者：Zong, Yuan[1,2]; Peng, Cheng[2]; Guo, Zhaoli[3]; Wang, Lian-Ping[2,3]

机构：[1] State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, China; [2] Department of Mechanical Engineering, 126 Spencer Laboratory, University of Delaware, Newark, DE, 19716-3140, United States; [3] National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, China

年份：2016

卷号：72

期号：2

起止页码：288

外文期刊名：Computers and Mathematics with Applications

收录：EI(收录号：20152400938907)

语种：英文

外文关键词：Degrees of freedom (mechanics) - Kinetic theory - Viscous flow - Inverse problems - Navier Stokes equations - Numerical methods - Vortex flow - Computational fluid dynamics - Hydrodynamics - Relaxation time

摘要：While the lattice Boltzmann method (LBM) has become a powerful numerical approach for solving complex flows, the standard lattice Boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions. For inhomogeneous and anisotropic flows, it is desirable to have a LBM model that utilizes a rectangular grid. There were two previous attempts to extend the multiple-relaxation-time (MRT) LBM to a rectangular lattice grid in 2D, however, the resulting hydrodynamic momentum equation was not fully consistent with the Navier-Stokes equation, due to anisotropy of the transport coefficients. In the present work, a new MRT model with an additional degree of freedom is developed in order to match precisely the Navier-Stokes equation when a rectangular lattice grid is used. We first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the Chapman-Enskog procedure. Then an additional adjustable parameter that governs the relative orientation in the energy-normal stress subspace is introduced. It is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients, thus the exact Navier-Stokes equation can be derived on a rectangular grid. Our theoretical findings are confirmed by numerical solutions using three two-dimension benchmark problems, i.e. the channel flow, the cavity flow, and the decaying Taylor-Green vortex flow. The numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters. ? 2015 Elsevier Ltd. All rights reserved.