Computing hydrodynamic interactions in confined doubly periodic geometries in linear time
Computing hydrodynamic interactions in confined doubly periodic geometries in linear time
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DOI：
10.1063/5.0141371
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发表时间：
2023-04-21
影响因子：
4.4
通讯作者：
Donev, Aleksandar
中科院分区：
文献类型：
--
作者：
Hashemi, Aref;Pelaez, Raul P.;Donev, Aleksandar
我们开发了一种力耦合方法的线性缩放变体[K]。杨建军，刘建军，刘建军，等。非周期方向上具有单底壁或双壁（狭缝通道）的双周期几何粒子间流体动力相互作用的计算[j] .流体力学学报，2016,36(4):559 - 559（2010）。我们的光谱精确Stokes解算器在周期性的xy平面上使用快速傅里叶变换，在非周期性的z方向上使用切比雪夫多项式，这些方向垂直于壁面(s)。我们把这个问题分解成两个问题。第一个是在z方向上具有自由空间边界条件的粒子（源项）存在的双周期子问题，我们通过借用最近用于快速评估双周期几何中的静电相互作用的方法来解决这个问题[Maxian et al.， J. Chem.]。物理学报，2004,26(3):555 - 557。第二是修正子问题，将边界条件施加到壁面上。与传统的高斯核不同，我们使用半圆核的指数来模拟由于粒子存在而产生的源项（体力），并为核参数提供最佳值，以确保给定的流体动力半径具有至少两位数的精度以及旋转和平移不变性。我们的求解器的计算时间，它是在图形处理单元中实现的，与粒子的数量成线性比例，并且允许在不到一秒的时间内计算大约一百万个粒子的胶体微辊沉积层。我们发现，在狭缝通道中，微辊驱动的密集悬架保持了与单壁上相同的两层结构，但由于增加了约束，其集体速度大大降低。
We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.