Shu C, Niu X D, Chew Y T
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117576.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2B):036708. doi: 10.1103/PhysRevE.65.036708. Epub 2002 Mar 6.
An explicit lattice Boltzmann method (LBM) is developed in this paper to simulate flows in an arbitrary geometry. The method is based on the standard LBM, Taylor-series expansion, and the least-squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Theoretical analysis for the one-dimensional (1D) case showed that the version of the LBM could recover the Navier-Stokes equations with second order accuracy. A generalized hydrodynamic analysis is conducted to study the wave-number dependence of shear viscosity for the method. Numerical simulations of the 2D lid-driven flow in a square cavity and a polar cavity flow as well as the "no flow" simulation in a square cavity have been carried out. Favorable results were obtained and compared well with available data in the literature, indicating that the present method has good prospects in practical applications.
本文开发了一种显式格子玻尔兹曼方法（LBM）来模拟任意几何形状中的流动。该方法基于标准LBM、泰勒级数展开和最小二乘法。最终公式为代数形式，本质上对网格结构和晶格模型没有限制。一维（1D）情况的理论分析表明，该版本的LBM可以以二阶精度恢复纳维-斯托克斯方程。进行了广义流体动力学分析以研究该方法剪切粘度的波数依赖性。对方形腔体内的二维顶盖驱动流、极腔流以及方腔内的“无流动”模拟进行了数值模拟。获得了良好的结果，并与文献中的现有数据进行了很好的比较，表明本方法在实际应用中具有良好的前景。
