Taylor-series expansion and least-squares-based lattice Boltzmann method: Two-dimensional formulation and its applications.
Taylor-series expansion and least-squares-based lattice Boltzmann method: Two-dimensional formulation and its applications.
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DOI：
10.1103/physreve.65.036708
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发表时间：
2002-03
期刊：
影响因子：
--
通讯作者：
Chi-Wang Shu;X. Niu;Y. Chew
中科院分区：
文献类型：
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作者：
Chi-Wang Shu;X. Niu;Y. Chew
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。最终的公式是代数形式，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，LBM 版本可以以二阶精度恢复纳维-斯托克斯方程。进行广义流体动力学分析来研究该方法的剪切粘度的波数依赖性。对方形腔中的二维盖驱动流动和极腔流动以及方形腔中的“无流动”模拟进行了数值模拟。取得了良好的结果，并与文献中的现有数据进行了很好的比较，表明该方法在实际应用中具有良好的前景。
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.