Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
J Chem Phys. 2017 Jun 28;146(24):244114. doi: 10.1063/1.4989545.
An efficient parallel Stokes' solver has been developed for complete description of hydrodynamic interactions between Brownian particles in bulk and confined geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green's function formalism. A scalable parallel computational approach is presented, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. Our approach employs a highly efficient iterative finite-element Stokes' solver for the accurate treatment of long-range hydrodynamic interactions in arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes' solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an O(N) parallel algorithm. We illustrate the new algorithm in the context of the dynamics of confined polymer solutions under equilibrium and non-equilibrium conditions. The method is then extended to treat suspended finite size particles of arbitrary shape in any geometry using an immersed boundary approach.
已经开发出一种高效的并行 Stokes 求解器，用于全面描述体相和受限几何形状中布朗粒子之间的流体动力相互作用。采用 Langevin 描述粒子动力学，其中使用格林函数形式主义来包含长程相互作用。提出了一种可扩展的并行计算方法，其中使用无矩阵算法根据广义几何型埃尔德类似方法计算通用几何型 Stokeslet。我们的方法采用高效的迭代有限元 Stokes 求解器，可在任意受限几何形状中准确处理长程流体动力相互作用。布朗随机微分方程的中点时间积分、并行 Stokes 求解器以及 Fluctuation-Dissipation 定理的切比雪夫多项式逼近的组合导致了 O(N) 并行算法。我们在平衡和非平衡条件下受限聚合物溶液动力学的背景下说明了新算法。然后，使用浸入边界方法将该方法扩展到处理任何几何形状中任意形状的悬浮有限尺寸颗粒。
