Implicit Runge-Kutta Time Integrators for Fluid-Structure Interactions

This paper presents the application of high-order time integrators in the context of monolithic approach simulation of Fluid-Structure Interaction by the Finite Element Method. The numercial method relies on an ALE formulation satisfying the Geometric Conservation Law designed in such a way that the high order accuracy of the Implicit Runge-Kutta time integrator observed on fixed meshes is preserved on deforming meshes. The same integrator is used for both the flow and structural components. We also use coincidents nodes on the fluid structure interface, so that the interface loads, velocities and displacements are evaluated at the same place and at the same times. The formulation is applied to the analysis of the flow induced vibration of a flexible strip mounted on the wake side of a square obstacle placed in a uniform flow. Results compare favorably with previous works. Near optimal time accuracy is observed for 3 and 5 order Implicite Runge-Kutta time integrators (IRK). That’s why, while higher order IRK require more memory than the classical schemes, they are also much faster for a same accuracy.

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