Quasi-Newton Methods for Partitioned Simulation of Fluid–Structure Interaction Reviewed in the Generalized Broyden Framework

Fluid–structure interaction simulations can be performed in a partitioned way, by coupling a flow solver with a structural solver. However, Gauss–Seidel iterations between these solvers without additional stabilization efforts will converge slowly or not at all under common conditions such as an incompressible fluid and a high added mass. Quasi-Newton methods can then stabilize and accelerate the coupling iterations, while still using the solvers as black boxes and only accessing data at the fluid–structure interface. In this review, the IQN-ILS, IQN-MVJ, IBQN-LS, MVQN, IQN-IMVLS and IQN-ILSM methods are reformulated in the generalized Broyden framework to illustrate their similarities and differences. Also related coupling techniques are reviewed and a performance comparison is provided where available.