论文标题
一种基于整体的光谱方法，用于在Stokes流中不可扩展的细长纤维
An integral-based spectral method for inextensible slender fibers in Stokes flow
论文作者
论文摘要
每个动物细胞都充满了细胞骨架，这是一种由不可延迟的纤维制成的动态凝胶，例如微管，肌动蛋白纤维和中间丝，都悬浮在粘性液中。该凝胶的数值模拟是具有挑战性的，因为纤维纵横比的大小可能高达$ 10^4 $。我们描述了一种新方法，用于快速计算定期剪切的Stokes流中不可扩展细长细丝的动力学。细丝的动力学由非本地细长的身体理论支配，我们根据rotne-prager-yamakawa流体动力张量进行了部分重构。为了强制执行不可扩展性，我们将不可扩展的光纤运动的空间进行参数化，并严格将动力学限制在不可扩展配置的歧管上。为此，我们在细丝上引入了一组拉格朗日乘数，以使其在细丝上的拉伸力密度，并在$ l^2 $弱感中施加了无虚拟工作的约束。我们通过局部和非局部细长的身体理论操作员的光谱离散化来增强这种方法，该操作员在未知数的数量中是线性的，并且基于解决线张力方程的方法具有改善的空间精度。对于动力学，我们开发了一个二阶的半度颞集成剂，该集成剂最多需要对非局部流体动力学的评估，并且每个时间步长的几个块对角线线性求解。在通过数值示例证明了方法的提高准确性和鲁棒性之后，我们将公式应用于背景振荡性剪切流中的永久交联肌动蛋白网格。我们观察到一个特征频率，在该频率中，网络从准静态的，主要是弹性行为转变为动态，主要是粘性行为。我们发现，即使对于半脱水纤维悬浮液，非局部流体力学将粘性模量增加多达25％。
Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible fibers, such as microtubules, actin fibers, and intermediate filaments, all suspended in a viscous fluid. Numerical simulation of this gel is challenging because the fiber aspect ratios can be as large as $10^4$. We describe a new method for rapidly computing the dynamics of inextensible slender filaments in periodically-sheared Stokes flow. The dynamics of the filaments are governed by a nonlocal slender body theory which we partially reformulate in terms of the Rotne-Prager-Yamakawa hydrodynamic tensor. To enforce inextensibility, we parameterize the space of inextensible fiber motions and strictly confine the dynamics to the manifold of inextensible configurations. To do this, we introduce a set of Lagrange multipliers for the tensile force densities on the filaments and impose the constraint of no virtual work in an $L^2$ weak sense. We augment this approach with a spectral discretization of the local and nonlocal slender body theory operators which is linear in the number of unknowns and gives improved spatial accuracy over approaches based on solving a line tension equation. For dynamics, we develop a second-order semi-implicit temporal integrator which requires at most a few evaluations of nonlocal hydrodynamics and a few block diagonal linear solves per time step. After demonstrating the improved accuracy and robustness of our approach through numerical examples, we apply our formulation to a permanently cross-linked actin mesh in a background oscillatory shear flow. We observe a characteristic frequency at which the network transitions from quasi-static, primarily elastic behavior to dynamic, primarily viscous behavior. We find that nonlocal hydrodynamics increases the viscous modulus by as much as 25%, even for semi-dilute fiber suspensions.
