Annals of Mathematical Sciences and Applications

Volume 9 (2024)

Number 1

Mathematical and computational framework for moving and colliding rigid bodies in a Newtonian fluid

Pages: 59 – 89

DOI: https://dx.doi.org/10.4310/AMSA.2024.v9.n1.a2

Authors

Céline Van Landeghem (Cemosis, IRMA UMR 7501M, CNRS, Université de Strasbourg, France)

Luca Berti (Cemosis, IRMA UMR 7501M, CNRS, Université de Strasbourg, France)

Vincent Chabannes (Cemosis, IRMA UMR 7501M, CNRS, Université de Strasbourg, France)

Agathe Chouippe (ICube Laboratory, UMR 7357, Université de Strasbourg, France)

Laetitia Giraldi (CALISTO team, INRIA, Université Côte d’Azur, Nice, France)

Yannick Hoarau (ICube Laboratory, UMR 7357, Université de Strasbourg, France)

Christophe Prud’homme (Cemosis, IRMA UMR 7501M, CNRS, Université de Strasbourg, France)

Abstract

We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To model the interactions between bodies, we consider a repulsive collision-avoidance model, defined by R. Glowinski in $\href{https://doi.org/10.1016/S1570-8659(03)09003-3}{[8]}$. The main emphasis in this work is the generalization of this collision model to multiple rigid bodies of arbitrary shape. Our model first uses a narrow-band fast marching method to detect the set of colliding bodies. Then, collision forces and torques are computed for these bodies via a general expression, which does not depend on their shape. Numerical experiments examining the performance of the narrow-band fast marching method and the parallel execution of the collision algorithm are discussed. We validate our model with literature results and show various applications of colliding bodies in two and three dimensions. In these applications, the bodies move due to forces such as gravity, a fluid flow, or their own actuation. Finally, we present a tool to create arbitrarily shaped bodies in discretized fluid domains, enabling conforming body-fluid interface and allowing to perform simulations of fluid-body interactions with collision treatment in these realistic environments. All simulations are conducted with the Feel++ open source library.

Keywords

fluid-structure interaction, rigid body motion, collision simulation, Feel++

2010 Mathematics Subject Classification

65M60, 70E99, 74F10, 76M10

Full Text (PDF format)

The authors acknowledge the financial support of the French Agence Nationale de la Recherche (grant ANR-21-CE45-0013 project NEMO), ITI Irmia++, and Cemosis.

Received 16 May 2023

Accepted 21 October 2023

Published 5 April 2024