Soft, slender and active structures in fluids: embedding Cosserat rods in vortex methods

Abstract

We present a hybrid Eulerian-Lagrangian method for the direct simulation of three-dimensional, heterogeneous structures made of soft fibers and immersed in incompressible viscous fluids. Fiber-based organization of matter is pervasive in nature and engineering, from biological architectures made of cilia, hair, muscles or bones to polymers, composite materials or soft robots. In nature, many such structures are adapted to manipulate flows for feeding, locomotion or energy harvesting, through mechanisms that are often not fully understood. While simulations can support the analysis (and subsequent translational engineering) of these systems, extreme fibers' aspect-ratios, large elastic deformations and two-way coupling with three-dimensional flows, all render the problem numerically challenging. To address this, we couple Cosserat rod theory, which exploits fibers' slenderness to capture their dynamics in one-dimensional, accurate fashion, with vortex methods via a penalty immersed boundary technique. The favorable properties of the resultant hydroelastic solver are demonstrated against a battery of benchmarks, and further showcased in a range of multi-physics scenarios, involving magnetic actuation, viscous streaming, biomechanics, multi-body interaction, and self-propulsion.