A partitioned scheme for fluid-composite structure interaction problems

We present a benchmark problem and a loosely-coupled partitioned scheme for fluid-structure interaction with composite structures. The benchmark problem consists of an incompressible, viscous fluid interacting with a structure composed of two layers: a thin elastic layer with mass which is in contact with the fluid and modeled by the Koiter membrane/shell equations, and a thick elastic layer with mass modeled by the equations of linear elasticity. An efficient, modular, partitioned operator-splitting scheme is proposed to simulate solutions to the coupled, nonlinear FSI problem, without the need for sub-iterations at every time-step. An energy estimate associated with unconditional stability is derived for the fully nonlinear FSI problem defined on moving domains. Two instructive numerical benchmark problems are presented to test the performance of numerical FSI schemes involving composite structures. It is shown numerically that the proposed scheme is at least first-order accurate both in time and space. This work reveals a new physical property of FSI problems involving thin interfaces with mass: the inertia of the thin fluid-structure interface regularizes solutions to the full FSI problem.