The dynamics of membranes, shells and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel ALE method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points, and the axisymmetric setting reduces the system effectively to a two-dimensional problem. We show in several numerical test cases that accurate results can be achieved at computational times on the order of minutes on a single core CPU. We further illustrate that the method can be easily extended to account for very different physics in both domains surrounding the surface. As an example, we present first simulations of the observed shape oscillations of novel microswimming shells and the uniaxial compression of biological cells filled with cytoplasm during an AFM experiment.

中文翻译：

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用于模拟流动中轴对称弹性表面的 ALE 方法

流体流动中的膜、壳和胶囊的动力学已成为计算物理学和计算生物学的一个活跃研究领域。这些弹性材料的小厚度使其能够有效地近似为超曲面，该超曲面对面内拉伸和面外弯曲表现出弹性响应，可能伴随着表面张力。在这项工作中，我们提出了一种新的 ALE 方法来模拟浸入纳维-斯托克斯流体中的这种弹性表面。该方法结合了高精度和计算效率，因为网格与弹性表面匹配，因此可以用相对较少的网格点来解决，轴对称设置有效地将系统简化为二维问题。我们在几个数值测试案例中展示了在单核 CPU 上以几分钟的计算时间可以获得准确的结果。我们进一步说明，该方法可以很容易地扩展到解决表面周围两个域中非常不同的物理现象。例如，我们首次模拟了在 AFM 实验期间观察到的新型微型游泳壳的形状振荡和充满细胞质的生物细胞的单轴压缩。