Stable and contact-free time stepping for dense rigid particle suspensions

TL;DR

This paper introduces an implicit time stepping method for dense rigid particle suspensions in viscous fluids, enabling larger time steps and smaller minimum separation distances while avoiding unphysical overlaps.

Contribution

The paper extends the method of Lu et al. by treating all particle interactions implicitly, improving stability and efficiency in simulating dense suspensions.

Findings

Able to simulate dense suspensions with large time steps

Maintains small minimum separation distances without overlaps

Successfully tested on various flow scenarios

Abstract

We consider suspensions of rigid bodies in a two-dimensional viscous fluid. Even with high-fidelity numerical methods, unphysical contact between particles occurs because of spatial and temporal discretization errors. We apply the method of Lu et al. [Journal of Computational Physics, 347:160-182, 2017] where overlap is avoided by imposing a minimum separation distance. In its original form, the method discretizes interactions between different particles explicitly. Therefore, to avoid stiffness, a large minimum separation distance is used. In this paper, we extend the method of Lu et al. by treating all interactions implicitly. This new time stepping method is able to simulate dense suspensions with large time step sizes and a small minimum separation distance. The method is tested on various unbounded and bounded flows, and rheological properties of the resulting suspensions are computed.