A generalised drift-correcting time integration scheme for Brownian suspensions of rigid particles with arbitrary shape

TL;DR

This paper introduces a generalised drift-correcting scheme for simulating Brownian suspensions of arbitrarily shaped rigid particles, improving computational efficiency while maintaining accuracy in modeling particle dynamics.

Contribution

The paper presents a novel, efficient time-integration scheme that accurately accounts for Brownian drift in suspensions of arbitrary-shaped particles, compatible with fast hydrodynamic interaction methods.

Findings

The gDC scheme achieves similar accuracy to existing methods.

It enhances computational efficiency by requiring only one mobility solve per time-step.

The scheme is suitable for simulating complex systems like liquid crystals and complex fluids.

Abstract

The efficient computation of the overdamped, random motion of micron and nanometre scale particles in a viscous fluid requires novel methods to obtain the hydrodynamic interactions, random displacements and Brownian drift at minimal cost. Capturing Brownian drift is done most efficiently through a judiciously constructed time-integration scheme that automatically accounts for its contribution to particle motion. In this paper, we present a generalised drift-correcting (gDC) scheme that accounts for Brownian drift for suspensions of rigid particles with arbitrary shape. The scheme seamlessly integrates with fast methods for computing the hydrodynamic interactions and random increments and requires a single full mobility solve per time-step. As a result, the gDC provides increased computational efficiency when used in conjunction with grid-based methods that employ fluctuating hydrodynamics to obtain the random increments. Further, for these methods the additional computations that the scheme requires occur at the level of individual particles, and hence lend themselves naturally to parallel computation. We perform a series of simulations that demonstrate the gDC obtains similar levels of accuracy as compared with the existing state-of-the-art. In addition, these simulations illustrate the gDC's applicability to a wide array of relevant problems involving Brownian suspensions of non-spherical particles, such as the structure of liquid crystals and the rheology of complex fluids.