We present a hybrid Eulerian–Lagrangian method for the direct simulation of three-dimensional, heterogeneous, active, and self-propelling structures made of soft fibers and operating in incompressible viscous flows. 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, swimming 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, two-way coupling with three-dimensional flows, and self-propulsion all render the problem numerically challenging. To address this, we couple Cosserat rod theory, where fibers’ dynamics is accurately captured in one-dimensional fashion, with the velocity–vorticity formulation of the Navier–Stokes equations, through a virtual 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 untethered swimming.

中文翻译：

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流体中的自推进、柔软和细长结构：Cosserat 棒浸入不可压缩的 Navier-Stokes 方程的速度-涡度公式中


我们提出了一种混合欧拉-拉格朗日方法，用于直接模拟由软纤维制成并在不可压缩的粘性流中运行的三维、异质、活性和自走式结构。基于纤维的物质组织在自然界和工程学中无处不在，从纤毛、头发、肌肉或骨骼制成的生物结构到聚合物、复合材料或软机器人。在自然界中，许多这样的结构都适应于纵流动以进行喂食、游泳或能量收集，而这些机制通常不完全清楚。虽然仿真可以支持这些系统的分析（以及随后的转化工程），但极端纤维的纵横比、较大的弹性变形、与三维流的双向耦合以及自推进都使该问题在数值上具有挑战性。为了解决这个问题，我们通过虚拟边界技术将 Cosserat 杆理论（其中纤维的动力学以一维方式准确捕获）与 Navier-Stokes 方程的速度-涡度公式耦合在一起。所得的水弹性求解器的有利特性在一系列基准测试中得到了证明，并在一系列多物理场场景中进一步展示，包括磁驱动、粘性流、生物力学、多体交互和无绳游泳。