A multi-grid coupled finite element-Eulerian–Lagrangian method for fluid–structure interaction problems

In this paper, a multi-grid coupled finite element-Eulerian–Lagrangian method is proposed for addressing fluid–structure interaction between large deformations in fluids and structures. This method utilizes multiple Eulerian grids to encompass the entire computational domain, employs Lagrangian particles to discretize the fluid domain, and adopts finite elements to discretize the solid domain. The multi-grid domain system calculates the structures and fluids independently, thereby avoiding the cross-interference of multiple velocity fields within a single grid domain, and facilitates the fluid–structure interaction between finite elements and particles. To address issues of nonphysical penetration and false contact between finite elements and particles, we introduce a fluid–structure interaction method based on contact mechanics in the volume domain. This method accurately applies the real contact forces at actual contact nodes, which are identified through specified contact conditions and detection mechanisms. Subsequently, the convergence, accuracy, and stability of this method are verified using representative numerical tests. Finally, we conduct experiments and simulations of shock wave impacts on elastic panels. The correlation between the numerical and experimental results demonstrates the accuracy of our method, and we provide an analysis of the variation patterns observed in both the flow field and the panel.