On fluid–shell coupling using an arbitrary Lagrangian–Eulerian fluid solver coupled to a positional Lagrangian shell solver

In this work, we develop a partitioned algorithm for three-dimensional geometric non-linear fluid–structure interaction analysis using the finite element method. The fluid solver is explicit and its time integration based on characteristics, which automatically introduces stabilising terms on stream direction. The Navier–Stokes equations are written using the arbitrary Lagrangian–Eulerian (ALE) description, in order to accept moving boundaries and coupling with Lagrangian shell elements. The structure is modelled using a novel finite element method formulation for geometric non-linear shell dynamics. Such shell formulation, so-called positional formulation, is based on the minimum potential energy theorem, written regarding nodal positions and generalised unconstrained vectors, not displacements and rotations. These characteristics avoid the use of large rotation approximations. The coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell positions and velocities. The efficiency and robustness of the proposed approach is demonstrated by examples.