Multi-level quasi-Newton coupling algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. Coupling iterations between the flow calculation and the structural calculation can be used to enforce the equilibrium conditions on the fluid–structure interface. Low wave number Fourier modes of the difference between the correct interface displacement and the interface displacement during Gauss–Seidel coupling iterations are typically unstable for strongly coupled problems with a Dirichlet–Neumann decomposition. Using interface quasi-Newton iterations with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS), these unstable modes are automatically detected and stabilized. As the unstable modes have a low wave number and can hence be resolved on coarser grids, the new multi-level IQN-ILS (ML-IQN-ILS) technique first constructs the approximation for the inverse of the Jacobian on coarser grid levels and then uses it and improves it further on the original, finest grid level. This multi-level approach reduces the number of coupling iterations on the finest grid level and can also be applied to the interface block quasi-Newton (IBQN-LS) technique. One-dimensional and three-dimensional numerical results demonstrate that this new class of multi-level quasi-Newton coupling techniques can reduce the duration of a partitioned fluid–structure interaction simulation.