A fluctuating boundary integral method for Brownian suspensions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Bao, Yuanxun¹  Rachh, Manas^2,4  Keaveny, Eric E.³  Greengard, Leslie^1,4  Donev, Aleksandar¹ 

[1] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

[2] Yale Univ, Appl Math Program, New Haven, CT 06511 USA

[3] Imperial Coll London, Dept Math, London SW7 2AZ, England

[4] Flatiron Inst, Ctr Computat Biol, New York, NY USA

关键词: Brownian dynamics;    Stokes flow;    Boundary integral equation;    Fluctuating hydrodynamics;    Fast algorithm;    Colloidal suspension;   

DOI  :  10.1016/j.jcp.2018.08.021

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free