论文标题
弹性物体的非接触式反弹
Contactless rebound of elastic bodies in a viscous incompressible fluid
论文作者
论文摘要
在本文中，我们研究了粘性不可压缩的流体环境中粒子反弹的现象。我们专注于无滑动边界条件的重要情况，现在经典的情况下，在某些假设下，碰撞在有限的时间内不可能发生。我们的愿望是理解这种迷人但违反直觉的流体结构相互作用的愿望，我们引入了一个简化的模型，我们在分析和数值上研究了模型。在这个简化的框架中，我们提供的条件可以证明即使没有拓扑接触，也可以证明反弹是可能的。我们的结果导致猜想，固体形状的质量变化对于获得物理有意义的反弹是必要的。我们还通过将对还原模型进行的数值模拟与针对相应良好成熟的PDE系统获得的有限元解决方案进行比较来支持猜想。
In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, for which it is by now classical that, under certain assumptions, collisions cannot occur in finite time. Motivated by the desire to understand this fascinating yet counterintuitive fluid-structure interaction, we introduce a reduced model which we study both analytically and numerically. In this simplified framework, we provide conditions which allow to prove that rebound is possible even in the absence of a topological contact. Our results lead to conjecture that a qualitative change in the shape of the solid is necessary for obtaining a physically meaningful rebound. We support the conjecture by also comparing numerical simulations performed for the reduced model with the finite element solutions obtained for the corresponding well-established PDE system.
