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 dynamic properties of interacting particles in flow.
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Steven
S
Delong
Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049, Spain.
Florencio Balboa
FB
Usabiaga
Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049, Spain.
Rafael
R
Delgado-Buscalioni
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Boyce E
BE
Griffith
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Aleksandar
A
Donev
D000465:Algorithms; D003198:Computer Simulation; D057446:Hydrodynamics; D008956:Models, Chemical; D009038:Motion; D013269:Stochastic Processes; D013535:Suspensions / Q000737:chemistry
D013535:Suspensions