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

Abstract

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.

On the number of subproblem iterations per coupling step in partitioned fluid-structure interaction simulations

“…For details on the concept of interface quasi-Newton methods, different variants, and implementation aspects the authors recommend the works [15,[18][19][20][21][22].…”

“…They differ in when the interface data is updated, i.e., after only one of the solvers or after both, and in the technique employed to approximate the Jacobian, such as the least-squares or the multi-vector approach [14]. An extensive overview is given in [15].…”

Effect of stochastic deformation on the vibration characteristics of a tube bundle in axial flow

“…This algorithm modifies the displacement between the structure solver and flow solver, such that spurious modes that impede convergence are attenuated. The partitioned coupling using IQN-ILS is implemented in CoCoNuT 3 , a lightweight coupling code written in Python (Delaissé et al, 2023).…”