The influence of the structural model on the stability of coupling iterations in partitioned fluid-structure interaction simulations

In partitioned simulations of fluid-structure interaction (FSI), the flow equations and the structural equations are solved with separate solvers. If the interaction between the flow and the flexible structure is strong, coupling iterations between both solvers have to be performed in each time step. In previous work, a Fourier stability analysis of Gauss-Seidel coupling iterations was presented for the unsteady, incompressible flow in a straight flexible tube. The error on the displacement of the fluid-structure interface during the coupling iterations was decomposed as a sum of Fourier modes. Subsequently, the amplification of each Fourier error mode was determined analytically as a function of a dimensionless time step tau and a dimensionless stiffness kappa. However, the structural model in this analysis was an independent-rings model without inertia. Recently, this Fourier stability analysis has been extended with a more complex structural model. The structural inertia and the interaction between the tube segments are now taken into account. It has been observed that the interaction between the tube segments reduces the amplification factor of the Fourier error modes compared to the independent-rings model. Moreover, the number of unstable modes is only influenced by tau for a range of tau if the structural inertia is substantial while it increases indefinitely as tau decreases if the structural inertia is negligible. These tendencies are confirmed by numerical experiments with the quasi-Newton IQN-ILS algorithm. As expected, numerical experiments with Gauss-Seidel iterations for the entire range of tau are impossible due to the presence of unstable modes. In conclusion, the stability analysis of coupling iterations in partitioned FSI simulations is strongly influenced by the structural model