$NlogN$ method for hydrodynamic interactions of confined polymer systems: Brownian dynamics

A Brownian dynamics simulation technique is presented where a Fourier-based $NlogN$ 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 $O(NlogN)$ 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 $O(N1.25logN)$⁠. 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.