An arbitrary Lagrangian Eulerian finite‐element approach for fluid–structure interaction phenomena

The present contribution is concerned with the design of a family of consistent fluid–structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations. The characterization of the moving fluid–structure interface is realized by means of the arbitrary Lagrangian Eulerian technique. The spatial discretization is performed with the finite‐element method, whereby either a first‐order upwind scheme or the classical second‐order upwind Petrov–Galerkin technique are used to discretize the linearized fluid equations while the standard Bubnov–Galerkin method is applied to the structural equations. In order to streamline coupling, the structure is discretized in a velocity‐based fashion. The temporal discretization of both the fluid and the structural equations is embedded in the generalized‐α framework by making use of classical Newmark approximations in time. To quantify the sources of error of the proposed algorithms, systematic studies in terms of the one‐dimensional piston model problem are presented.