On Mixed Finite Element Formulations for Fluid-structure Interactions

In this thesis, mixed primitive variable based finite element formulations are developed to solve linear and nonlinear fluid-structure interaction problems involving incompressible (or almost incompressible) fluid models. The mixed elements are used according to the inf-sup condition. It is pointed out that along the fluid-structure interfaces, different coupling conditions can be used according to different mathematical models or meshing conditions, but the requirements of both mass and momentum conservation must be satisfied on the discretized configuration. In this work, we correct one historical misunderstanding about the causes of the so-called spurious non-zero frequency rotational modes widely reported in the frequency analysis of acoustoelastic/slosh fluid-structure interaction problems. We also discuss mode superposition methods in both primitive variable and potential-based formulations. In nonlinear fluid-structure interaction analyses involving convection dominated flows, large free surface waves, material nonlinearities, large structural deformations and large fluid-structure interface motions, we apply arbitrary Lagrangian-Eulerian (ALE) descriptions to maintain mesh regularity within the analysis domain. In order to eliminate the spatial oscillations in flow regions with high Reynolds number (or Peclet number), as well as to use high order mixed elements satisfying the inf-sup condition in low Reynolds number (or Peclet number) flow regions, we propose a new upwinding scheme and develop a mixed treatment, i.e. the use of a control volume finite element upwinding formulation for the convective terms and the standard Galerkin formulation for the other terms. The proposed formulations are implemented experimentally, and various numerical examples are given to demonstrate and confirm the ideas in this thesis. Thesis Supervisor: Klaus-Jiirgen Bathe Title: Professor of Mechanical Engineering