A single-layer based numerical method for the slender body boundary value problem
A single-layer based numerical method for the slender body boundary value problem
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DOI：
10.1016/j.jcp.2021.110865
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
William H. Mitchell;H. Bell;Yoichiro Mori;Laurel Ohm;Daniel Spirn
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文献类型：
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作者：
William H. Mitchell;H. Bell;Yoichiro Mori;Laurel Ohm;Daniel Spirn
含有细纤维的稀或稠悬浮液的流体流在生物和工业过程中广泛存在。为了描述细浸入光纤的运动，或描述作用在其上的力，使用一维光纤中心线和力密度而不是二维表面和表面牵引会更方便。细长体理论提供了仅使用一维数据来建模和模拟浸没纤维运动的方法。然而，当纤维表面接近与自身或其他纤维相交时，标准配方可能会失效。在本文中，我们介绍了一种用于最近导出的三维细长体边值问题的数值方法，该问题可以完全用中心线上力的一维分布来表示。该方法基于新完成的流体速度单层势公式，该公式消除了与未修改的单层势相关的零空间。我们对模型进行离散化并给出数值结果，证明该方法在存在近交叉点的情况下具有良好的条件和改进的性能。为了避免涉及自由端的建模和数值选择，我们考虑闭合纤维。
Fluid flows containing dilute or dense suspensions of thin fibers are widespread in biological and industrial processes. To describe the motion of a thin immersed fiber, or to describe the forces acting on it, it is convenient to work with one-dimensional fiber centerlines and force densities rather than two-dimensional surfaces and surface tractions. Slender body theories offer ways to model and simulate the motion of immersed fibers using only one-dimensional data. However, standard formulations can break down when the fiber surface comes close to intersecting itself or other fibers. In this paper we introduce a numerical method for a recently derived three-dimensionalslender bodyboundary value problemthat can be stated entirely in terms of a one-dimensional distribution of forces on the centerline. The method is based on a newcompleted single-layer potentialformulation of fluid velocity which removes the nullspace associated with the unmodified single layer potential. We discretize the model and present numerical results demonstrating the good conditioning and improved performance of the method in the presence of near-intersections. To avoid the modeling and numerical choices involved with free ends, we consider closed fibers.