Abstract An extended immersed boundary methodology utilizing a semi-implicit direct forcing approach was formulated for the simulation of incompressible flows in the presence of periodically moving immersed bodies. The methodology utilizes a Schur complement approach to enforce no-slip kinematic constraints for immersed surfaces. The methodology is split into an “embarrassingly” parallel pre-computing stage and a time integration stage, both of which take advantage of the general parallel file system (GPFS) for efficient writing and reading of large amounts of data. The methodology can be embedded straight forwardly into the whole family of pressure–velocity segregated solvers of incompressible Navier–Stokes equations based on projection or fractional step approaches. The methodology accurately meets the no-slip kinematic constraints on the surfaces of immersed oscillating bodies. In this study, it was extensively verified by applying it for the simulation of a number of representative flows developing in the presence of an oscillating sphere. The capabilities of the methodology for the simulation of incompressible flow generated by a number of bodies whose motion is governed by general periodic kinematics were demonstrated by simulation of the flow developing in the presence of two out-of-phase oscillating spheres. The physical characteristics of the generated flows in terms of the time evolutions of the total drag coefficients were presented as a function of Reynolds values. The vortical structures inherent in the generated flows were visualized by presenting the isosurfaces of the λ 2 criterion.

中文翻译：

---

用于周期性移动浸入体的半隐式直接强迫浸入边界方法：Schur 补充方法

摘要 一种利用半隐式直接强迫方法的扩展浸入边界方法被公式化，用于模拟存在周期性移动浸入体的不可压缩流动。该方法利用 Schur 补充方法对浸没表面强制执行无滑移运动学约束。该方法分为“令人尴尬”的并行预计算阶段和时间集成阶段，这两个阶段都利用通用并行文件系统（GPFS）来高效写入和读取大量数据。该方法可以直接嵌入到基于投影或分数步法的不可压缩 Navier-Stokes 方程的压力-速度分离求解器的整个系列中。该方法准确地满足浸入式振荡体表面的无滑移运动学约束。在这项研究中，它通过将其应用于模拟在存在振荡球体的情况下发展的许多代表性流动而得到了广泛验证。通过模拟在存在两个异相振荡球体的情况下发展的流动，证明了该方法模拟由许多物体产生的不可压缩流动的能力，这些物体的运动受一般周期性运动学控制。根据总阻力系数的时间演变，生成的流动的物理特性被表示为雷诺值的函数。通过呈现 λ 2 准则的等值面，可以将生成的流中固有的涡旋结构可视化。