A finite element model for fluid-structure interaction problems involving closed membranes, internal and external fluids

In this paper we propose a Finite Element model for analyzing closed membranes (“bags”) interacting with internal and external (surrounding) fluids. The approach is based on embedding a Lagrangian monolithic model describing the membrane containing an internal fluid into an Eulerian external fluid model. The combination of kinematic frameworks allows us to accurately track the location of the membrane and naturally represent flow variables discontinuities across it. In order to obtain stable coupling for membrane materials with low density, a slight fluid compressibility is assumed. The coupling between the membrane and the internal fluid is automatically accounted for by a monolithic set-up. The filled membrane and the external fluid are coupled in a Dirichlet-Neumann fashion. The model is validated in several numerical examples and its potential application to a civil engineering problem of coast protection via water-filled bag reefs is shown.