The paper deals with the rebound of an elastic solid off a rigid wall of a container filled with an incompressible Newtonian fluid. Our study focuses on a collision-free bounce, meaning a rebound without topological contact between the elastic solid and the wall. This has the advantage of omitting any artificial bouncing law. In order to capture the contact-free rebound for very small viscosities an adaptive numerical scheme is introduced. The here-introduced scheme is based on a Glowinski time scheme and a localized arbitrary Lagrangian-Eulerian map on finite elements in space. The absence of topological contact requires that very thin liquid channels are solved with sufficient accuracy. It is achieved via newly developed geometrically driven adaptive strategies. Using the numerical scheme, we present here a collection of numerical experiments. A rebound is simulated in the absence of topological contacts. Its physical relevance is demonstrated as, with decreasing viscosities, a free rebound in a vacuum is approached. Further, we compare the dynamics with a second numerical scheme; a here-introduced adaptive purely Eulerian level-set method. The scheme produced the same dynamics for large viscosities. However, as it requires a much higher computational cost, small viscosities can not be reached by this method. The experiments allow for a better understanding of the effect of fluids on the dynamics of elastic objects. Several observations are discussed, such as the amount of elastic and/or kinetic energy loss or the precise connection between the fluid pressure and the rebound of the solid.

翻译：本文研究浸没于不可压缩牛顿流体中的弹性固体撞击容器刚性壁面的回弹现象。我们聚焦于无碰撞回弹，即弹性固体与壁面之间无拓扑接触的反弹过程，其优势在于无需引入任何人工弹跳定律。为捕捉极小黏度下的无接触回弹，本文提出了一套自适应数值方案。该方案基于Glowinski时间离散格式和有限元空间上的局域化任意拉格朗日-欧拉映射。由于拓扑接触的缺失，需要以足够精度求解极薄液膜通道，这通过新开发的几何驱动自适应策略得以实现。借助该数值方案，我们展示了一系列数值实验：在无拓扑接触条件下成功模拟回弹过程，其物理合理性通过随黏度降低趋近真空自由回弹现象得到验证。此外，我们将动力学行为与第二套数值方案（本文引入的自适应纯欧拉水平集方法）进行对比。该方案在大黏度条件下产生相同动力学特征，但由于计算成本高昂，无法应用于小黏度场景。这些实验有助于深入理解流体对弹性体动力学行为的影响，并讨论了弹性/动能损耗量、流体压力与固体回弹间的精确关联等重要观测现象。