流-固-接触相互作用的数值基准
A numerical benchmark for fluid--structure--contact interaction
- Mathematical Institute, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院数学研究所）
- University of Konstanz, Department of Mathematics & Statistics（康斯坦茨大学数学与统计系）
- Leibniz University Hannover, Institute of Applied Mathematics（汉诺威莱布尼茨大学应用数学研究所）
- Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院数学分析系）
- Department of Mathematics, Uppsala University（乌普萨拉大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该论文提出一个二维流-固-接触相互作用基准，包含可变形弹性圆盘在粘性流体中下落并反弹，通过八种数值方法验证，为求解器评估提供参考。
AI中文摘要：
我们提出了一个二维流-固-接触相互作用基准，该基准由一个在粘性不可压缩流体中受重力下落并在底部壁面附近反弹的可变形弹性圆盘组成。固体可变形性至关重要，因为刚性固体在此框架中不会反弹。此外，该设置被刻意保持简单以方便复现。由于众所周知的“无接触悖论”，该构型特别具有挑战性，该悖论可能导致无接触反弹，并迫使数值方法解析近接触区域中极薄的流体层，从而使动力学对空间和时间离散化高度敏感。除了无滑移边界和界面条件外，还考虑了在圆盘边界或底部壁面上对表面粗糙度进行简化多孔建模；这规避了无接触悖论并实现了真实接触。理论上为所有三种情况推导了能量平衡定律。由五个研究团队开发的八种数值方法，涵盖不同的模型公式、数值方法和代码（包括贴体和非贴体离散化），在多个空间和时间细化水平上应用于该基准。收集并比较了不同复杂度的感兴趣量，结果显示在下落阶段高度一致，而在近接触和反弹区域敏感性增加。该设置和结果为系统评估流-固-接触相互作用求解器提供了合适的参考。所有方法及细化水平的感兴趣量时间历程均作为补充材料提供。
英文摘要：
We propose a two-dimensional benchmark for fluid-structure-contact interaction consisting of a deformable elastic disk falling under gravity within a viscous incompressible fluid and rebounding in the vicinity of the bottom wall. Solid deformability is essential, as rigid solids do not rebound in this framework. Besides this, the setting is deliberately kept simple to facilitate reproduction. The configuration is particularly challenging due to the well-known no-contact paradox, which can lead to a contactless rebound and forces numerical methods to resolve a vanishingly thin fluid layer in the near-contact region, making the dynamics highly sensitive to the spatial and temporal discretizations. In addition to no-slip boundary and interface conditions, a reduced porous modeling of surface roughness, either on the disk boundary or on the bottom wall, is also considered; this circumvents the no-contact paradox and enables genuine contact. An energy balance law is derived theoretically for all three cases. Eight numerical methodologies, developed by five research groups and spanning different model formulations, numerical methods, and codes (including both fitted and unfitted discretizations), are applied to the benchmark at several levels of spatial and temporal refinement. Quantities of interest of varying complexity are collected and compared, showing close agreement during the falling phase and increased sensitivity in the near-contact and rebound regimes. The setting and the results provide a suitable reference for the systematic assessment of fluid-structure-contact interaction solvers. The time histories of all quantities of interest for every approach and refinement level are provided as supplementary material.
