On Finite Element Analysis of Fluid Flows Fully Coupled with Structural Interactions

The solution of fluid flows, modeled using the Navier-Stokes or Euler equations, fully coupled with structures/solids is considered. Simultaneous and partitioned solution procedures, used in the solution of the coupled equations, are briefly discussed, and advantages and disadvantages of their use are mentioned. In addition, a simplified stability analysis of the interface equations is presented, and unconditional stability for certain choices of time integration schemes is shown. Furthermore, the long-term dynamic stability of fluid-structure interaction systems is assessed by the use of Lyapunov characteristic exponents, which allow differentiating between a chaotic and a regular system behavior. Some state-of-the-art numerical solutions are also presented to indicate the type of problems that can now be solved using currently available techniques. keyword: Fluid-structure interaction, arbitrary Lagrangian-Eulerian formulation, finite element methods, coupled procedures, Lyapunov characteristic exponent, dynamic stability.