# Computational geometric methods for preferential clustering of particle suspensions

## TL;DR

This paper introduces a geometric numerical method for simulating suspensions of particles with improved accuracy and efficiency, preserving key physical properties and better capturing particle distribution dynamics.

## Contribution

The paper presents a novel divergence-free radial basis function interpolation combined with a splitting integrator for particle suspension simulation, enhancing accuracy and computational cost-effectiveness.

## Key findings

- More accurate particle distributions compared to conventional methods
- Preserves the sum of the Lyapunov spectrum and mimics centrifuge effects
- Effective for large suspensions of 10^4 particles in flow fields

## Abstract

A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field with a splitting method integrator that preserves the sum of the Lyapunov spectrum while mimicking the centrifuge effect of the exact solution. We discuss how breaking the divergence-free condition in the interpolation step can erroneously affect how the volume of the particulate phase evolves under numerical methods. The methods are tested on suspensions of $10^4$ particles evolving in discrete cellular flow field. The results are that the proposed geometric methods generate more accurate and cost-effective particle distributions compared to conventional methods.