A monolithic Lagrangian approach for fluid-structure interaction problems

Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.Peer Reviewe