基于积分算子的弹性流体动力学的有效实现
Efficient Implementation of Elastohydrodynamics via Integral Operators
摘要：
几何非线性柔性细丝的动力学在许多生物过程中起着重要作用，从鞭毛驱动的细胞运输到复杂流体的聚合结构。由于与不可扩展性约束相关的数值刚度以及高阶偏微分方程的非平凡边界条件，这些问题在历史上一直是计算昂贵的。最近发现，通过切线角中的积分方程来制定细丝形状演变的问题，可以大大减轻这种数值刚度。本手稿的贡献是使非本地的多个细丝的相互作用的模拟在计算上有效的方式使用正则化stokeslet在这个框架内的方法。所提出的方法是基准对非本地珠和链接模型，最近的代码利用当地的阻力速度法。系统的多个细丝（1）在一个背景流体流，（2）在一个恒定的体力，（3）进行积极的自我运动有效地建模。屈曲不稳定性进行了分析，通过检查不断变化的细丝曲率，以及粗粒化的身体框架的切线角使用切比雪夫近似的各种选择的相关的无量纲参数。从这些实验中，洞察力的纤维相互作用可以促进屈曲，并进一步揭示了复杂的流体动力学从这些相互作用的纤维阵列。通过检查积极的时刻驱动的细丝，我们调查蠕虫和精子一样的游泳者的速度为不同的管理参数。MATLAB（R）实现作为一个开源库提供，可以灵活扩展交替离散化和不同的周围流。
英文摘要：
The dynamics of geometrically non-linear flexible filaments play an important role in a host of biological processes, from flagella-driven cell transport to the polymeric structure of complex fluids. Such problems have historically been computationally expensive due to numerical stiffness associated with the inextensibility constraint, as well as the often non-trivial boundary conditions on the governing high-order PDEs. Formulating the problem for the evolving shape of a filament via an integral equation in the tangent angle has recently been found to greatly alleviate this numerical stiffness. The contribution of the present manuscript is to enable the simulation of non-local interactions of multiple filaments in a computationally efficient manner using the method of regularized stokeslets within this framework. The proposed method is benchmarked against a non-local bead and link model, and recent code utilizing a local drag velocity law. Systems of multiple filaments (1) in a background fluid flow, (2) under a constant body force, and (3) undergoing active self-motility are modeled efficiently. Buckling instabilities are analyzed by examining the evolving filament curvature, as well as by coarse-graining the body frame tangent angles using a Chebyshev approximation for various choices of the relevant non-dimensional parameters. From these experiments, insight is gained into how filament-filament interactions can promote buckling, and further reveal the complex fluid dynamics resulting from arrays of these interacting fibers. By examining active moment-driven filaments, we investigate the speed of worm- and sperm-like swimmers for different governing parameters. The MATLAB(R) implementation is made available as an open-source library, enabling flexible extension for alternate discretizations and different surrounding flows.
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