Strongly-coupled fluid-structure interaction of lightweight membranes and shells

Numerical fluid-structure interaction simulations of lightweight, flexible structures, such as membranes and shells, are notoriously tricky due to the large deformations and the significant added-mass effect. These effects generate a very strongly coupled problem that requires implicit coupling algorithms to solve them or, in extreme cases, prevent reaching a stable solution altogether.

We discuss the numerical challenges of coupling a lightweight, flexible structure to an incompressible flow with two typical problems, an inverted flag undergoing limit-cycle flapping and a fluttering membrane wing. We compare different coupling approaches to a quasi-Newton scheme that constructs a least-square approximation of this Jacobian from input/output pairs of the previously converged time steps. We show that the quasi-Newton scheme performs well under mild added-mass effects. Convergence is heavily penalized when the added-mass effects are strong, preventing reasonable solution time. We apply these methods to lightweight membrane flutter and demonstrate the influence of unsteady fluid-structure interaction on coupling efficiency. Finally, we investigate using pre-trained machine learning approximations to the coupling Jacobian to speed up strongly coupled fluid-structure interaction simulations.