An explicit-implicit hybrid SBFEM with quadtree mesh for fluid-solid interaction

Fluid -solid interaction (FSI) poses a significant challenge in engineering applications. Due to the presence of offdiagonal 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.