An ALE framework for the fluid-structure interaction of freely moving soft and rigid bodies in complex environments
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Fluid flows containing deformable soft bodies that interact with obstacles are common in biological processes, such as cell transport in arteries or the locomotion of living organisms. However, modeling and simulating these processes remain challenging due to the complexity of fluid-structure interactions and contact conditions. Our goal is to track the trajectory and deformation of soft bodies using the finite element method within the Arbitrary Lagrangian-Eulerian framework of the open-source finite element library Feel++. This method has been employed in the work of Van Landeghem et al. to simulate the motion and collision of rigid passive and active bodies under different flow conditions in Newtonian fluids, and has shown promising results. The aim is to extend this method to soft bodies, thus capturing, on the one hand, the body deformations caused by fluid-structure interactions and, on the other hand, the contact between soft bodies and their environment. In this presentation, we will describe a model that decomposes the body motion into elastic and rigid components and employs a semi-implicit scheme that iterates on the fluid-structure interaction problem. Additionally, we use a Nitsche method to simulate the contact with rigid obstacles. It reformulates the Signorini contact inequalities as a single equality condition that is weakly enforced in the variational formulation. First, we will detail our approach and consider a dynamic numerical experiment to validate our decomposition model with contact in the absence of fluid. Then, we will describe the integration of this model into the fluid-structure interaction system and present applications of the latter, both with and without contact.