Cilia are hair-like structures that move in unison with the purpose of propelling fluid. They are found, for example, in the human bronchiole respiratory system and molluscs. Here, we validate a novel model of fluid flow due to the movement of cilia in a fixed computational domain. We consider two domains, a porous medium and a free-fluid domain and numerically solve the Stokes–Brinkman system of equations where the cilia geometry and velocity are input and the velocity of fluid due to the movement of cilia is determined. The cilia velocities and geometry are approximated using human lung cilia experimental data available in the literature. We use a mixed finite element method of Taylor-Hood type to calculate the fluid velocities in a three-dimensional domain. The results are validated in a simple case by comparison with an exact solution with good agreement. This problem can be used as a benchmark for the movement of fluid phases due to the self-propelled movement of a solid phase in a porous medium.

中文翻译：

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纤毛运动对流体速度的影响：II 固定域上的数值解

纤毛是毛发状结构，它们与推进流体的目的一致移动。例如，它们存在于人类细支气管呼吸系统和软体动物中。在这里，由于纤毛在固定计算域中的运动，我们验证了一种新的流体流动模型。我们考虑两个域，多孔介质和自由流体域，并数值求解 Stokes-Brinkman 方程组，其中输入纤毛几何形状和速度，并确定纤毛运动引起的流体速度。纤毛速度和几何形状使用文献中可用的人肺纤毛实验数据进行近似。我们使用 Taylor-Hood 类型的混合有限元方法来计算三维域中的流体速度。通过与具有良好一致性的精确解进行比较，结果在一个简单的案例中得到了验证。由于固相在多孔介质中的自推进运动，该问题可以用作流体相运动的基准。