Investigation of fluid-structure interactions using a velocity-linked P2/P1 finite element method and the generalized- α method

A velocity-linked algorithm for solving unsteady fluid-structure interaction (FSI) problems in a fully coupled manner is developed using the arbitrary Lagrangian-Eulerian method. The P2/P1 finite element is used to spatially discretize the incompressible Navier-Stokes equations and structural equations, and the generalized- α method is adopted for temporal discretization. Common velocity variables are employed at the fluid-structure interface for the strong coupling of both equations. Because of the velocity-linked formulation, kinematic compatibility is automatically satisfied and forcing terms do not need to be calculated explicitly. Both the numerical stability and the convergence characteristics of an iterative solver for the coupled algorithm are investigated by solving the FSI problem of flexible tube flows. It is noteworthy that the generalized- α method with small damping is free from unstable velocity fields. However, the convergence characteristics of the coupled system deteriorate greatly for certain Poisson's ratios so that direct solvers are essential for these cases. Furthermore, the proposed method is shown to clearly display the advantage of considering FSI in the simulation of flexible tube flows, while enabling much larger time-steps than those adopted in some previous studies. This is possible through the strong coupling of the fluid and structural equations by employing common primitive variables.