Simulating Brownian suspensions with fluctuating hydrodynamics

TL;DR

This paper introduces an efficient computational method combining fluctuating hydrodynamics with a new midpoint time-integration scheme, enabling accurate and cost-effective simulation of Brownian suspensions, including complex phenomena like gelation.

Contribution

It presents the drifter-corrector (DC) scheme combined with fluctuating force-coupling method (FCM) for improved Brownian suspension simulations, reducing computational cost while maintaining accuracy.

Findings

Reproduces equilibrium distributions accurately.

Effectively simulates suspension dynamics in various domains.

Reduces simulation costs to near deterministic levels.

Abstract

Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint need only be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation.