使用润滑自适应镜像系统的斯托克斯球体精确近接触相互作用
Accurate close interactions of Stokes spheres using lubrication-adapted image systems
AI总结：
本文提出将基本解法与镜像法相结合，通过接触自适应镜像源线解析润滑效应，实现对近接触刚性球体斯托克斯流的高精度、低成本数值模拟，并通过快速多极方法实现近线性扩展。
摘要：
近接触刚性粒子在相对运动下会诱发近奇异的润滑力，这使得对斯托克斯流进行精确数值处理具有挑战性。为了以计算成本低廉的方法控制精度，我们提出了一种将基本解法（MFS）与镜像法相结合的新技术。对于刚性球体，我们提出使用内部球面上的Stokeslet代理源来表示流场，并辅以针对每个近接触点自适应调整的镜像源线来解析润滑效应。源强度通过在接触自适应边界配点节点上进行最小二乘求解来确定。我们进行了大量数值测试，并与来自高分辨率边界积分公式的参考解进行了验证。对于每个粒子每个接触点少于60个额外镜像源的情况，我们展示了表面速度的三位相对数字的受控均匀精度，以及粒子力和力矩的精度可达五位数字，适用于所有小至半径千分之一的间距。在固定粒子周围流动的特殊情况下，仅使用代理球即可获得受控精度。一种单体预处理策略允许使用快速多极方法进行加速，从而在粒子数量上接近线性扩展。通过在工作站上求解多达2000个球体的问题（每个粒子仅使用700个代理源）证明了这一点。
英文摘要：
Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap method, we present a new technique that combines the method of fundamental solutions (MFS) with the method of images. For rigid spheres, we propose to represent the flow using Stokeslet proxy sources on interior spheres, augmented by lines of image sources adapted to each near-contact to resolve lubrication. Source strengths are found by a least-squares solve at contact-adapted boundary collocation nodes. We include extensive numerical tests, and validate against reference solutions from a well-resolved boundary integral formulation. With less than 60 additional image sources per particle per contact, we show controlled uniform accuracy to three relative digits in surface velocities, and up to five digits in particle forces and torques, for all separations down to a thousandth of the radius. In the special case of flows around fixed particles, the proxy sphere alone gives controlled accuracy. A one-body preconditioning strategy allows acceleration with the fast multipole method, hence close to linear scaling in the number of particles. This is demonstrated by solving problems of up to 2000 spheres on a workstation using only 700 proxy sources per particle.
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