In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

中文翻译：

---

浸没式柔性固体的流-固耦合问题的公式：应用于流经不同横截面圆柱体的分流器


在有限元方法框架中，通过将欧拉固定网格流体方法与柔性固体的拉格朗日变形网格描述耦合来开发流固公式。耦合公式在时间上使用交错方案求解。对于流体溶解阶段，实体壁被视为时间可变的内部边界。速度和压力场是通过求解流体动力学方程的弱形式获得的，其中固体速度通过惩罚项施加在内部边界上。对于固溶阶段，位移场是通过求解离散固体动力学方程获得的，该方程考虑了通过对属于实体壁的节点上的压力和粘性应力进行积分来计算的牵引力。由于这个问题，首先将这种新技术应用于分析流经方圆柱体的流动下柔性分流器，被认为是文献中的基准。目前的解与使用 body-fit 技术计算的解一致，从而验证了该提案。其次，全面研究了流经不同截面和分流器长度的圆柱体时柔性分流器运动。总体而言，计算结果证实，由于分流器的存在，圆柱体上的流体动力学系数降低了。