Two-way Coupling of Fluid--Structure Interaction for Elastic Magneto-Swimmers:A Finite Element ALE Approach

TL;DR

The paper develops a comprehensive finite element framework based on the Arbitrary Lagrangian–Eulerian (ALE) formulation to simulate deformable elastic magneto-swimmers in confined viscous flows, resolving full fluid dynamics while tracking swimmer deformation and global motion on conforming meshes. The approach couples incompressible Navier–Stokes fluid dynamics with hyper-elastic tail deformation (Saint-Venant–Kirchhoff) and rigid-body head motion through two-way fluid–structure interaction, using a two-subproblem decomposition (fluid–rigid and fluid–elastic) within a two-stage discretization and a fixed-point solver. Numerical results in 2D and 3D validate accuracy and robustness against experimental data, demonstrate the relationship between stroke area and net displacement, and reveal a resonant-like dependence of propulsion on actuation frequency, with tail flexibility enhancing performance. The framework enables high-fidelity digital twins for magneto-swimmers, supports adaptive remeshing and parallel computing (via Feel++ and PETSc), and lays the groundwork for multi-swimmer configurations, advanced control strategies, and exascale simulations in targeted biomedical applications.

Abstract

Artificial micro-swimmers actuated by external magnetic fields hold significant promise for targeted biomedical applications, including drug delivery and micro-robot-assisted therapy. However, their dynamics remain challenging to control due to the complex nonlinear coupling between magnetic actuation, elastic deformations, and fluid interactions in confined biological environments. Numerical modeling is therefore essential to better understand, predict, and optimize their behavior for practical applications. In this work, we present a comprehensive finite element framework based on the Arbitrary Lagrangian--Eulerian formulation to simulate deformable elastic micro-swimmers in confined fluid domains. The method employs a full-order model that resolves the complete fluid dynamics while simultaneously tracking swimmer deformation and global displacement on conforming meshes. Numerical experiments are performed with the open-source finite element library Feel++, demonstrating excellent agreement with experimental data from the literature. The validation benchmarks in both two and three dimensions confirm the accuracy, robustness, and computational efficiency of the proposed framework, representing a foundational step toward developing digital twins of magneto-swimmers for biomedical applications.

Figures (7)

• Figure 1: Configuration of the magneto-swimmer at time $t$ inside a fluid domain $\mathcal{F}^t$. The magnetic moment $M^t$ tends to align with the external magnetic field $B^t$, and $\theta^t$ represents the swimmer’s head orientation.
• Figure 2: The illustration of the two angles used for the phase configuration space.
• Figure 3: At the top, the deformations of the swimmer with respect to the stroke cycle plotted at the bottom in the configuration space.
• Figure 4: Displacement of the magneto-swimmer over one period as a function of the frequency of the magnetic field.
• Figure 5: Discretized geometry of the three-dimensional magneto-swimmer.