Keywords: fluid-structure interaction, partitioned solution, reduced-order models, Aitken under-relaxation, Interface-GMRES(R), flexible tube, Fourier error analysis.

In a partitioned fluid-structure interaction simulation, the flow and the displacement of the structure are calculated with separate codes. Although the interaction between the flow and the structure influences the entire flow and the displacement of the complete structure, information is only exchanged between the problems on the fluid-structure interface. If the interaction between the flow and the structure is strong, the coupled solution of a time step which satisfies the equilibrium conditions on the fluid-structure interface can be obtained with coupling iterations between both solvers. In each coupling iteration, the flow solver calculates the fluid load on the interface, given its position and the structural solver determines the interface's position for a given fluid load.

From the position of the interface and the fluid load on the interface in the coupling iterations, sensitivities of the output of the solvers with respect to a change of their input can be calculated. This paper compares Aitken underrelaxation [1], interface-GMRES(R) [2] and coupling with reduced-order models [3] which all stabilize and accelerate the coupling iterations by using these sensitivities. Aitken underrelaxation and interface-GMRES(R) intervene in the coupling iterations after the solution of both the flow problem and the structural problem, while coupling with reduced-order models intervenes after the solution of each of the problems.

The performance of these algorithms in a partitioned simulation of the unsteady flow in a flexible tube is measured by the number of coupling iterations in a time step which is given as a function of the time step size and structural stiffness for all coupling techniques. Coupling with reduced-order models and interface-GMRES(R) perform similarly and require less coupling iterations than Aitken under-relaxation and interface-GMRES(R). The change in performance due to a variation of the time step and structural stiffness is explained by means of a Fourier error analysis of the fixed-point iterations between the flow and the structure.

1

U. Küttler, W.A. Wall, "Fixed-point fluid-structure interaction solvers with dynamic relaxation", Computational Mechanics, 2008. doi:10.1007/s00466-008-0255-5

2

C. Michler, E.H. van Brummelen and R. de Borst, "An interface Newton-Krylov solver for fluid-structure interaction", International Journal for Numerical Methods in Fluids, 47, 1189-1195, 2005. doi:10.1002/fld.850

3

J. Vierendeels, L. Lanoye, J. Degroote and P. Verdonck, "Implicit coupling of partitioned fluid-structure interaction problems with reduced order models", Computers and Structures, 85, 970-976, 2007. doi:10.1016/j.compstruc.2006.11.006

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