Brownian dynamics without Green's functions

Steven Delong, Florencio Balboa Usabiaga, Rafael Delgado-Buscalioni, Boyce E. Griffith, Aleksandar Donev

Research output: Contribution to journalArticle

Abstract

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

Original languageEnglish (US)
Article number4869866
JournalJournal of Chemical Physics
Volume140
Issue number13
DOIs
StatePublished - Apr 7 2014

Fingerprint

Green's function
Green's functions
Hydrodynamics
Brownian movement
hydrodynamics
Tensors
Suspensions
Stokes flow
integrators
stress tensors
configurations
dynamic characteristics
Fluids
Geometry
divergence
Computer simulation
Diptera
Noise
fluids
matrices

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry
  • Medicine(all)

Cite this

Delong, S., Usabiaga, F. B., Delgado-Buscalioni, R., Griffith, B. E., & Donev, A. (2014). Brownian dynamics without Green's functions. Journal of Chemical Physics, 140(13), [4869866]. https://doi.org/10.1063/1.4869866

Brownian dynamics without Green's functions. / Delong, Steven; Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael; Griffith, Boyce E.; Donev, Aleksandar.

In: Journal of Chemical Physics, Vol. 140, No. 13, 4869866, 07.04.2014.

Research output: Contribution to journalArticle

Delong, S, Usabiaga, FB, Delgado-Buscalioni, R, Griffith, BE & Donev, A 2014, 'Brownian dynamics without Green's functions', Journal of Chemical Physics, vol. 140, no. 13, 4869866. https://doi.org/10.1063/1.4869866
Delong S, Usabiaga FB, Delgado-Buscalioni R, Griffith BE, Donev A. Brownian dynamics without Green's functions. Journal of Chemical Physics. 2014 Apr 7;140(13). 4869866. https://doi.org/10.1063/1.4869866
Delong, Steven ; Usabiaga, Florencio Balboa ; Delgado-Buscalioni, Rafael ; Griffith, Boyce E. ; Donev, Aleksandar. / Brownian dynamics without Green's functions. In: Journal of Chemical Physics. 2014 ; Vol. 140, No. 13.
@article{d24dadeec8d747a8a021d20576db5cc0,
title = "Brownian dynamics without Green's functions",
abstract = "We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions {"}on the fly.{"} Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.",
author = "Steven Delong and Usabiaga, {Florencio Balboa} and Rafael Delgado-Buscalioni and Griffith, {Boyce E.} and Aleksandar Donev",
year = "2014",
month = "4",
day = "7",
doi = "10.1063/1.4869866",
language = "English (US)",
volume = "140",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "13",

}

TY - JOUR

T1 - Brownian dynamics without Green's functions

AU - Delong, Steven

AU - Usabiaga, Florencio Balboa

AU - Delgado-Buscalioni, Rafael

AU - Griffith, Boyce E.

AU - Donev, Aleksandar

PY - 2014/4/7

Y1 - 2014/4/7

N2 - We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

AB - We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

UR - http://www.scopus.com/inward/record.url?scp=84898006895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898006895&partnerID=8YFLogxK

U2 - 10.1063/1.4869866

DO - 10.1063/1.4869866

M3 - Article

VL - 140

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 13

M1 - 4869866

ER -