Treatment of the small time instability in the finite element analysis of fluid structure interaction problems

In this paper, the fluid–structure interaction problem in mechanical systems in which a high frequency vibrating solid structure interacts with the surrounding fluid flow is considered. Such a situation normally appears in many microelectromechanical systems like a wide variety of microfluidic devices. A different implementation of the residual-based variational multiscale flow method is employed within the arbitrary Lagrangian–Eulerian formulation. The combination of the variational multiscale method with appropriate stabilization parameters is used to handle the so-called small time step instability in the finite element analysis of the fluid part in the coupled fluid–structure interaction problem. The capability of the employed approach has been demonstrated through finite element study of a benchmark example and FEM simulation of two different mechanical micropumping devices. High frequency vibrations of the solid membrane are used to derive the fluid flow in these micropumps. Results of FEM simulations are shown to be in good agreement with available experimental data. Copyright © 2012 John Wiley & Sons, Ltd.