The paper deals with the rebound of an elastic solid off a rigid wall of a container filled with an incompressible Newtonian fluid. Accordingly, a new fluid-structure interaction benchmark is introduced. We show that the benchmark captures a rebound without the solid touching the wall, hence omitting any artificial bouncing law. An adaptive numerical scheme that reconstructs the rebound for very small viscosities is introduced. As the viscosity decreases, the solution converges to the free rebound in a vacuum. The 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. This is done by newly developed geometrically driven adaptive strategies. A rebound is simulated in the absence of topological contacts. The benchmark is further tested by a here-introduced adaptive purely Eulerian level-set method, which produces the same dynamics but with a much higher computational cost. 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：本文研究了浸入不可压缩牛顿流体中的弹性固体在刚性容器壁上的回弹现象。为此，我们提出了一种新的流固耦合基准测试。研究表明，该基准测试能够捕捉固体未接触壁面的回弹过程，从而避免了任何人为弹跳定律的引入。我们开发了一种自适应数值方案，可在极小黏度条件下重建回弹过程。随着黏度降低，解收敛于真空中的自由回弹。该方案基于Glowinski时间步进格式与空间有限元上的局部任意拉格朗日-欧拉映射。由于无拓扑接触，需以足够精度求解极薄液层，这通过新开发的几何驱动自适应策略实现。我们在无拓扑接触的情况下模拟了回弹过程。该基准测试还通过本文提出的自适应纯欧拉水平集方法进行了验证，该方法虽能得到相同动力学结果，但计算成本显著更高。通过实验可更深入理解流体对弹性物体动力学行为的影响。我们讨论了几项观测结果，包括弹性能与动能的耗散量，以及流体压力与固体回弹之间的精确关联。