We propose a novel integral model describing the motion of both flexible and rigid slender fibers in viscous flow and develop a numerical method for simulating dynamics of curved 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 nonphysical idealized geometry, as expected from the partial differential equation theory. This is numerically verified in physically relevant geometries. We discuss the convergence and stability of a numerical method for solving the integral equation. The accuracy of the model and method is verified against known models for ellipsoids. Finally, we develop an algorithm for computing dynamics of rigid fibers with complex geometries in the case where the fiber density is much greater than that of the fluid, for example, in turbulent gas-fiber suspensions.

中文翻译：

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基于细长体理论的积分模型，应用于弯曲刚性纤维

我们提出了一个新颖的积分模型，描述了柔性和刚性细长纤维在粘性流中的运动，并开发了一种数值方法来模拟弯曲刚性纤维的动力学。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积分的Stokes方程的奇异解来近似纤维附近的流动。与其他基于（单一）SBT的模型相比，我们的模型产生了一个平滑的积分内核，该内核自然地并入了（可能变化的）光纤半径。正如偏微分方程理论所预期的那样，在非物理理想几何中，积分算子可证明是负定的。这在物理上相关的几何形状中得到了数值验证。我们讨论了求解积分方程的数值方法的收敛性和稳定性。相对于已知的椭球模型，验证了模型和方法的准确性。最后，在纤维密度远大于流体密度的情况下，例如在湍流的气态纤维悬浮液中，我们开发了一种用于计算具有复杂几何形状的刚性纤维动力学的算法。