This paper focuses on the stability of the coupling iterations in the partitioned approach to fluid-structure interaction. Previous research has shown that the number of coupling iterations increases when the time step decreases or when the structure becomes more flexible which is explained here by Fourier error analysis of the unsteady, incompressible flow in an elastic tube. Substituting a linearized model of the structural solver into the flow solver makes the coupling more stable but is impracticable if the flow solver is a black box. Therefore the coupling iterations are stabilized by coupling with reduced-order models and Aitken underrelaxation.

Partitioned simulations of fluid-structure interaction can be solved for the interface's position with Newton-Raphson iterations but obtaining the exact Jacobian is impossible if the solvers are "black boxes". It is demonstrated that only an approximate Jacobian is needed, as long as it describes the reaction to certain components of the error on the interface's position. Based on this insight, a quasiNewton coupling algorithm with an approximation for the inverse of the Jacobian (IQN-ILS) has been developed and compared with a monolithic solver in previous work. Here, IQN-ILS is compared with other partitioned schemes such as IBQN-LS, Aitken relaxation and Interface-GMRES(R).

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Partitioned fluid-structure interaction simulations of the arterial system are difficult due to the incompressibility of the fluid and the shape of the domain. The interface artificial compressibility method (IAC) mitigates the incompressibility constraint by adding a source term to the continuity equation in the fluid domain adjacent to the fluid-structure interface. This source term imitates the effect of the structure's displacement as a result of the fluid pressure and disappears when the coupling iterations have converged. The IAC method requires a small modification of the flow solver but not of the black box structural solver and it outperforms a partitioned quasi-Newton coupling of two black box solvers in a simulation of a carotid bifurcation.

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