On the coupling between an ideal fluid and immersed particles

TL;DR

This paper uses Lagrange-Poincare reduction to analyze fluid-particle coupling, providing error estimates and inspiring new particle-based numerical methods that incorporate shape and deformation parameters for better momentum conservation.

Contribution

It reinterprets existing fluid-particle coupling models through velocity interpolation, introduces error analysis, and proposes new hybrid methods considering particle shape and deformation.

Findings

Error estimates for velocity interpolation methods

Development of particle and hybrid particle-spectral methods

Insights into shape and deformation effects on momentum conservation

Abstract

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.