论文标题
晶格Boltzmann方法中的壁功能方法：使用湍流流量的算法和验证
A wall function approach in lattice Boltzmann method: algorithm and validation using turbulent channel flow
论文作者
论文摘要
在晶格玻尔兹曼方法（LBM）中，广泛使用的壁边界是反弹（bb）边界，它对应于无滑动边界。 BB边界可防止LBM使用粗网格系统来解决高雷诺数流时捕获墙壁上的精确剪切阻力。在这项研究中，我们提出了一个“壁功能弹跳（WFB）”边界，该边界将壁函数纳入LBM的边界条件并克服了BB的限制。 WFB边界使用墙函数模型计算墙上的适当剪切阻力，然后修改分布功能以反映剪切阻力。 Spalding定律被用作WFB中的壁功能。使用基于LBM的大型模拟（LBM-LE）对$re_τ$ = 640和2003的湍流流量进行模拟，以验证提出的边界条件的有效性。结果表明，BB边界低估了$re_τ$ = 640的缓冲层中的时间平均速度，并且在使用粗网格系统时，整个域中的平均速度为$re_τ$ = 2003。但是，WFB在壁上获得了适当的剪切阻力，因此补偿了低估，并与实验或DNS数据更好地达成了同意，尤其是在第一层网格上。此外，WFB在一定程度上改善了近壁区域的雷诺正常应力。 WFB对壁上的剪切应力的分布类似于有限体积方法中壁模型函数的分布。
In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, which corresponds to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when addressing high Reynolds number flows using coarse-grid systems. In this study, we proposed a "wall-function bounce (WFB)" boundary that incorporates a wall function into the LBM's boundary condition and overcomes the limitation of the BB. The WFB boundary calculates the appropriate shear drag on the wall using a wall function model, and thereafter modifies distribution functions to reflect the shear drag. The Spalding's law was utilized as the wall function in WFB. Simulations of turbulent channel flow at $Re_τ$=640 and 2003 using the LBM-based large-eddy simulation (LBM-LES) were conducted to validate the effectiveness of the proposed boundary condition. The results indicate that the BB boundary underestimated the time-averaged velocity in the buffer layer at $Re_τ$=640, and the averaged velocity in the entire domain at $Re_τ$=2003, when using coarse-grid systems. However, WFB obtained the proper shear drag on the wall and thus, compensated for the underestimation and agreed better with the experimental or DNS data, especially at the first-layer grid. In addition, WFB improved the Reynolds normal stress in the near-wall region to some extent. The distributions of shear stress on the wall by WFB was analogous to those by the wall model function in the finite volume method.
