Fluid-solid interaction (FSI) poses a significant challenge in engineering applications. Due to the presence of off-diagonal coupling terms in the matrices, it is difficult to use explicit time integration method directly. Consequently, the whole system often needs to be solved using implicit method, albeit at the expense of considerably increased computational cost. In this paper, an innovative approach, namely an explicit-implicit hybrid scaled boundary finite element method (SBFEM), is proposed to mitigate this issue. In this method, the implicit time integration scheme is employed to tackle the coupling part between solid and fluid, while the remainder of the system is solved directly by explicit time integration. The solid and fluid domains are both discretized by an automatic quadtree mesh generation, ensuring efficient mesh size transitions and facilitating local mesh refinement near the interface. An overlapping zone is constructed near the interface for data exchange between the explicit and implicit schemes, which is derived directly from the quadtree data structure. The elements in the quadtree mesh are treated as general polygons formulated by the SBFEM. As a result, the proposed method capitalizes on the advantages of both implicit and explicit techniques, leading to enhanced computational efficiency. Combining the quadtree mesh with the explicit-implicit hybrid SBFEM allows for the simulation of wave propagation in FSI system with complex geometric shapes and boundary conditions. Benchmark tests are conducted to verify the accuracy of the proposed method, followed by a vibration analysis of an underwater cavity to demonstrate its engineering applicability.

中文翻译：

---

具有四叉树网格的显式-隐式混合 SBFEM 用于流固相互作用


流固相互作用（FSI）给工程应用带来了重大挑战。由于矩阵中存在非对角耦合项，很难直接使用显式时间积分方法。因此，整个系统通常需要使用隐式方法来求解，尽管这样做的代价是计算成本显着增加。本文提出了一种创新方法，即显式-隐式混合尺度边界有限元法（SBFEM）来缓解这一问题。该方法采用隐式时间积分方案来解决固体与流体之间的耦合部分，而系统的其余部分则直接通过显式时间积分来求解。固体和流体域均通过自动四叉树网格生成进行离散化，确保有效的网格尺寸转换并促进界面附近的局部网格细化。在显式和隐式方案之间的数据交换接口附近构造了一个重​​叠区域，该重叠区域直接源自四叉树数据结构。四叉树网格中的元素被视为由 SBFEM 制定的一般多边形。因此，所提出的方法利用了隐式和显式技术的优点，从而提高了计算效率。将四叉树网格与显隐混合 SBFEM 相结合，可以模拟具有复杂几何形状和边界条件的 FSI 系统中的波传播。进行基准测试来验证所提出方法的准确性，然后对水下腔体进行振动分析以证明其工程适用性。