论文标题
基于细长身体理论的积分模型，并应用于弯曲的刚性纤维
An integral model based on slender body theory, with applications to curved rigid fibers
论文作者
论文摘要
我们提出了一个新颖的积分模型，描述了粘性流动中弯曲的细长纤维的运动，并开发了一种数值方法来模拟刚性纤维的动力学。该模型源自非局部细长体理论（SBT），该理论使用沿纤维中心线集成的Stokes方程的单数解在纤维附近近似流动。与基于（单数）SBT的其他模型相反，我们的模型产生了平滑的积分内核，该内核自然结合了（可能变化的）光纤半径。正如PDE理论所预期的那样，在非物理理想化的几何形状中，积分运算符在非物理理想化的几何形状中是负面的。这在物理相关的几何形状中得到了数值验证。我们提出了一种收敛的数值方法，用于求解积分方程并讨论其收敛性和稳定性。模型和方法的准确性是针对已知模型的椭圆形模型进行了验证的。最后，开发了用于计算具有复杂几何形状的刚性纤维动力学的快速算法。
We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a non-physical idealized geometry, as expected from PDE theory. This is numerically verified in physically relevant geometries. We propose a convergent numerical method for solving the integral equation and discuss its convergence and stability. The accuracy of the model and method is verified against known models for ellipsoids. Finally, a fast algorithm for computing dynamics of rigid fibers with complex geometries is developed.
