中文摘要：

鱼类集群运动行为蕴含着复杂的水动力学机制.针对一种简化的鱼类集群运动模型,利用浸没边界方法对黏性流体中做自主推进运动的两个前后排列柔性细丝进行数值模拟,对其稳定运动时的排列形态以及相应的涡相互作用模态开展研究.为保证进行长时间的自主推进运动,本文将流体和固体运动方程写在非惯性系下,通过基于投影思想的隐式动量力实现流固耦合,避免了自主推进运动对计算域尺寸要求过大的问题,可以有效节省计算量.通过改变前后细丝的初始水平间距和垂向偏移距离,发现了3种稳定排列形态：远距离前后排列、近距离前后排列和并行排列.对于远距离前后排列形态,后排细丝受垂向偏移距离的影响较小,始终会穿过前排细丝脱落的涡;对于近距离前后排列形态,前排细丝表面的剪切层在脱落成涡之前和后排细丝表面的剪切层合并,脱落成较强的涡,推进速度较快,前后细丝的运动和受力会有一定的相位差;当垂向偏移距离增大,后排细丝受前排细丝的影响减小,最终稳定于并行排列同步运动,上下细丝两侧的同号剪切层合并脱落成较强的涡,但由于迎风面积增大而推进速度变慢.

英文摘要：

Fish schooling behavior contains very interesting but complicated hydrodynamics. A simplified and classic fish schooling model was simulated and analyzed in the present study, by using two self-propelled flexible filaments in a tandem arrangment. The two filaments plung harmonically in the vertical direction and are free to move in the horizontal direction in an incompressible viscous fluid flow. The simulations were carried out by using an efficient immersed boundary projection method, where the additional momentum forcing is calculated in an implicit way and an approximate factorization procedure is applied to solve the incompressible Navier-Stokes equations. The coupling between the fluid flow and the flexible structures is realized through the additional momentum forcing. In the immersed boundary projection method, both the pressure and the momentum forcing are considered as the Langrangian multipliers to satisfy the continuity constraint and the no-slip condition at the immersed boundary, respectively. To ensure a long period simulation, a non-inertial frame, which is fixed to the leading edge of the upstream filament, was adopted in the Navier-stokes equations and the structure motion equation, by introducing a translational acceleration in the motion equations. In this way, it significantly reduced the computational cost by avoiding a large compuational domain. Two-dimensional simulations were performed in the present study. The Reynolds number based on the plunging motion was fixed at 200, while the different initial horizontal and vertical distances between the two filaments were considered in simulations. The stable states of the two tandem filaments and the mechanism of the vortex interactions were mainly concerned. The numerical results reveal that three stable states are formed with different horizontal distances and vertical distances between the two filaments, i.e., long-distance tandem state, short-distance tandem state and parallel state. For the long-distance tandem state, the upstream filament