A fluctuating boundary integral method for Brownian suspensions

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Title: A fluctuating boundary integral method for Brownian suspensions
Authors: Bao, Y
Rachh, M
Keaveny, E
Greengard, L
Donev, A
Item 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.
Issue Date: 31-Dec-2018
Date of Acceptance: 13-Aug-2018
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
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P013651/1
Keywords: math.NA
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-08-16
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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