Contact-aware simulations of particulate Stokesian suspensions

TL;DR

This paper introduces a contact-aware simulation method for dense particulate suspensions in Stokesian fluids, improving stability and efficiency by explicitly preventing particle contact.

Contribution

The authors develop a novel boundary integral approach that incorporates explicit contact constraints, enabling larger time steps and fewer discretization points in dense suspension simulations.

Findings

Maintains high accuracy at lower computational cost.

Enables larger stable time steps in dense suspensions.

Reduces the number of discretization points needed.

Abstract

We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the problem as the foundation of our approach. This type of formulations, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions between particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as well as a large number of discretization points are required to avoid non-physical contact and intersections between particles, leading to infinite forces and numerical instability. Our method maintains the accuracy of previous methods at a significantly lower cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly. Introducing contact constraints results in a significant increase in stable time-step size for explicit time-stepping, and a reduction in the number of points adequate for stability.