We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi: 10.17632/mf27c92nc3.1]. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change of the fluid domain and the contact between the wall and particle. In the numerical simulations we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare results obtained with the well established Arbitrary Lagrangian Eulerian (ALE) approach and a moving domain CutFEM method together with a simple and common approach for contact avoidance. For the full fluid-structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency we use the geometrical symmetry of the experimental set up to reformulate the FSI system into two spatial dimensions. Finally, we show full three dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries and the results are made freely available to aide reproducibility.

中文翻译：

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接触粘性流体中的落球：数值模拟与实验数据的比较

我们根据物理实验的数据评估了许多不同的流体-结构（接触）相互作用问题的有限元方法。为此，我们从 Hagemeier [Mendeley Data, doi: 10.17632/mf27c92nc3.1] 的实验中获取数据。这包括单个颗粒穿过高粘性流体并从底部流体罐壁反弹的轨迹。由此产生的流动处于蠕动和湍流之间的过渡状态。由于流体域的巨大变化以及壁与粒子之间的接触，这种类型的配置对于数值方法尤其具有挑战性。在数值模拟中，我们考虑下落粒子的刚体和线弹性模型。在第一种情况下，我们比较了使用完善的任意拉格朗日欧拉 (ALE) 方法和移动域 CutFEM 方法以及简单通用的避免接触方法获得的结果。对于具有接触的完整流固耦合 (FSI) 问题，我们使用完全欧拉方法与使用 Nitsche 方法的统一 FSI 接触处理相结合。为了提高计算效率，我们使用实验装置的几何对称性将 FSI 系统重新构造为两个空间维度。最后，我们展示了完整的三维 ALE 计算，以研究粒子初始状态中小扰动的影响，以研究与实验中观察到的完美垂直下降的偏差。