A fluctuating boundary integral method for Brownian suspensions
File(s)
Accepted version
Author(s)
Bao, Yuanxun
Rachh, Manas
Keaveny, Eric
Greengard, Leslie
Donev, Aleksandar
Type
Journal Article
Abstract
We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation–dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method Fiore et al. (2017) [24], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.
Date Issued
2018-12-01
Date Acceptance
2018-08-13
Citation
Journal of Computational Physics, 2018, 374, pp.1094-1119
ISSN
0021-9991
Publisher
Elsevier
Start Page
1094
End Page
1119
Journal / Book Title
Journal of Computational Physics
Volume
374
Copyright Statement
© 2018 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://arxiv.org/abs/1709.01480v2
Grant Number
EP/P013651/1
Subjects
math.NA
math.NA
Publication Status
Published
Date Publish Online
2018-08-16