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Title: Brownian dynamics without Green's functions

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 dynamicmore » properties of interacting particles in flow.« less
Authors:
;  [1] ; ;  [2] ;  [1] ;  [3]
  1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
  2. Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049 (Spain)
  3. (United States)
Publication Date:
OSTI Identifier:
22253301
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 13; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; BROWNIAN MOVEMENT; EQUATIONS; FLUIDS; GREEN FUNCTION; HYDRODYNAMICS; INTERACTIONS; PARTICLES; RESPONSE FUNCTIONS; SIMULATION; STRESSES; SUSPENSIONS