Fluid–shell structure interactions with finite thickness using immersed method

Abstract

This study presents a computational framework for simulating shell structures interacting with fluids using the immersed approach. The approach captures the complex movement and motion of a thin structure represented with shell elements that have a finite thickness. Utilizing the concept of the immersed approach, the fluid domain is described using a fixed set of Eulerian grids and the shell structure uses finite element shell Lagrangian descriptions, thus allowing non-intrusive coupling of independent fluid and shell finite element solvers. Different from the traditional immersed boundary method where the boundary cannot replicate the thickness of the thin boundary or shell structures, our approach projects the shell structure along the directions normal to the shell surface based on a given thickness to create a volumetric structure. Such projection allows robust, accurate and realistic interfacial loading and immersed geometry when interacting with the surrounding fluid. The dynamic solution of the mid-surface obtained from the shell solver is extended and extrapolated into the thickness direction, which is then used to calculate the forces acting on the Eulerian grid nodes to manage the effects of the overlapping solid. The volume representation also helps in calculating consistent nodal forces and moments acting on the shell surface. In particular, the moments yielded across the thickness capture the additional bending that would otherwise be missed for an infinitely thin boundary. Allowing the volumetric representation of the thin shell thickness, deformation modes such as bending and shearing can be more accurately calculated. Intricate transformations between local shell element coordinate and global coordinate were also considered to enable the coupling process. The presented fluid–shell coupling algorithm is carefully verified and validated using three numerical test cases. The accuracy and the robustness of the results also demonstrate the versatility of the developed coupling technique for thin shells and structures with finite thickness.