流场中轴对称弹性表面数值模拟的ALE方法
An ALE method for simulations of axisymmetric elastic surfaces in flow
摘要：
流体流动中的膜、壳和胶囊的动力学已成为计算物理和计算生物学的一个活跃的研究领域。这些弹性材料的小厚度使得它们能够有效地近似为超曲面，该超曲面表现出对面内拉伸和面外弯曲的弹性响应，可能伴随有表面张力力。在这项工作中，我们提出了一种新的ALE方法来模拟这样的弹性表面浸没在Navier-Stokes流体。该方法结合了高精度和计算效率，因为网格与弹性表面相匹配，因此可以用相对较少的网格点进行求解。这项工作的重点是轴对称的形状和流动条件，这是目前在广泛的生物物理问题。我们制定轴对称弹性表面力，并提出了一个离散化与表面有限差分耦合到不断发展的有限元。我们进一步发展了一个隐式耦合策略，以减少时间步长的限制。我们在几个数值测试的情况下，准确的结果可以实现在计算时间上的顺序分钟的单核CPU。我们展示了两个国家的最先进的应用程序，据我们所知，不能用任何其他数值方法模拟到目前为止：我们提出了第一个模拟观察到的形状振荡的新型微游泳壳和单轴压缩的生物细胞的皮质在AFM实验。
英文摘要：
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. The focus of this work is on axisymmetric shapes and flow conditions which are present in a wide range of biophysical problems. We formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. 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 demonstrate two state-of-the-art applications which to our knowledge cannot be simulated with any other numerical method so far: We present first simulations of the observed shape oscillations of novel microswimming shells and the uniaxial compression of the cortex of a biological cell during an AFM experiment.
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