Hernández-Ortiz Juan P, de Pablo Juan J, Graham Michael D
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA.
J Chem Phys. 2006 Oct 28;125(16):164906. doi: 10.1063/1.2358344.
A Brownian dynamics simulation technique is presented where a Fourier-based N log N approach is used to calculate hydrodynamic interactions in confined flowing polymer systems between two parallel walls. A self-consistent coarse-grained Langevin description of the polymer dynamics is adopted in which the polymer beads are treated as point forces. Hydrodynamic interactions are therefore included in the diffusion tensor through a Green's function formalism. The calculation of Green's function is based on a generalization of a method developed for sedimenting particles by Mucha et al. [J. Fluid Mech. 501, 71 (2004)]. A Fourier series representation of the Stokeslet that satisfies no-slip boundary conditions at the walls is adopted; this representation is arranged in such a way that the total O(N2) contribution of bead-bead interactions is calculated in an O(N log N) algorithm. Brownian terms are calculated using the Chebyshev polynomial approximation proposed by Fixman [Macromolecules 19, 1195 (1986); 19, 1204 (1986)] for the square root of the diffusion tensor. The proposed Brownian dynamics simulation methodology scales as O(N1.25 log N). Results for infinitely dilute systems of dumbbells are presented to verify past predictions and to examine the performance and numerical consistency of the proposed method.
本文提出了一种布朗动力学模拟技术，该技术采用基于傅里叶变换的N log N方法来计算两个平行壁之间受限流动聚合物系统中的流体动力学相互作用。采用了聚合物动力学的自洽粗粒化朗之万描述，其中聚合物珠子被视为点力。因此，流体动力学相互作用通过格林函数形式包含在扩散张量中。格林函数的计算基于Mucha等人[《流体力学杂志》501, 71 (2004)]为沉降颗粒开发的一种方法的推广。采用了斯托克斯子的傅里叶级数表示，该表示在壁处满足无滑移边界条件；这种表示的排列方式使得珠子 - 珠子相互作用的总O(N2)贡献通过O(N log N)算法计算。布朗项使用Fixman[《大分子》19, 1195 (1986); 19, 1204 (1986)]提出的切比雪夫多项式近似来计算扩散张量的平方根。所提出的布朗动力学模拟方法的计算量为O(N1.25 log N)。给出了哑铃无限稀溶液系统的结果，以验证过去的预测，并检验所提方法的性能和数值一致性。
