A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part I, laminar flows
A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part I, laminar flows
复制标题
格子玻尔兹曼法中无滑移边界处理的浸没边界法和插值反弹方案的比较研究：第一部分，层流
DOI：
10.1016/j.compfluid.2019.06.032
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发表时间：
2019
影响因子：
2.8
通讯作者：
Wang, Lian-Ping
中科院分区：
文献类型：
--
作者：
Peng, Cheng;Ayala, Orlando M.;Wang, Lian-Ping
在晶格玻尔兹曼法中，处理曲面无滑移边界最常用的两种算法是插值反弹格式和浸入边界法。虽然这些算法经常在涉及复杂几何形状的数值模拟中实现，例如颗粒负载流，但它们的性能很少在相同环境下的相同局部量上进行系统比较。在本文中，我们基于四个选定的二维和三维层流问题的理论分析和数值模拟，对一些常用的和最先进的插值反弹方案和浸入边界方法进行了系统的比较研究。我们的分析表明，当使用正则三角函数将速度从欧拉网格插值到拉格朗日网格，并将得到的边界力返回到欧拉网格时，浸入式边界方法（IBM）通常产生一阶精度。对于IBM来说，本地速度和流体动力/扭矩的精度都是一阶的，这显然不同于文献中有时声称的二阶精度。浸入边界法的另一个问题是，扩散流固界面内的局部应力往往被严重低估。另一方面，内插式回弹一般在速度、水动力/扭矩和局部应力场方面具有二阶精度。内插式回弹方案的主要缺点是，当固体物体在网格线上移动时，其计算的流体动力/扭矩波动水平较高。为了准确地模拟固体颗粒上的流动，还提供了两种方法中必要的网格分辨率的一般准则。
The interpolated bounce-back schemes and the immersed boundary method are the two most popular algorithms in treating a no-slip boundary on curved surfaces in the lattice Boltzmann method. While those algorithms are frequently implemented in the numerical simulations involving complex geometries, such as particle-laden flows, their performances are seldom compared systematically over the same local quantities within the same context. In this paper, we present a systematic comparative investigation on some frequently used and most state-of-the-art interpolated bounce-back schemes and immersed boundary methods, based on both theoretical analyses and numerical simulations of four selected 2D and 3D laminar flow problems. Our analyses show that immersed boundary methods (IBM) typically yield a first-order accuracy when the regularized delta-function is employed to interpolate velocity from the Eulerian to Lagrangian mesh, and the resulting boundary force back to the Eulerian mesh. This first order in accuracy for IBM is observed for both the local velocity and hydrodynamic force/torque, apparently different from the second-order accuracy sometime claimed in the literature. Another problem of immersed boundary methods is that the local stress within the diffused fluid-solid interface tends to be significantly underestimated. On the other hand, the interpolated bounce-back generally possesses a second-order accuracy for velocity, hydrodynamic force/torque, and local stress field. The main disadvantage of the interpolated bounce-back schemes is its higher level of fluctuations in the calculated hydrodynamic force/torque when a solid object moves across the grid lines. General guidelines are also provided for the necessary grid resolutions in the two approaches in order to accurately simulate flows over a solid particle.