A fluctuating boundary integral method for Brownian suspensions

Yuanxun Bao, Manas Rachh, Eric E. Keaveny, Leslie Greengard, Aleksandar Donev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1094-1119
Number of pages26
JournalJournal of Computational Physics
StatePublished - Dec 1 2018


  • Boundary integral equation
  • Brownian dynamics
  • Colloidal suspension
  • Fast algorithm
  • Fluctuating hydrodynamics
  • Stokes flow

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'A fluctuating boundary integral method for Brownian suspensions'. Together they form a unique fingerprint.

Cite this