Finite Element Procedures for Fluid-structure Interaction
This thesis concerns finite element (FE) methods for solving fluid-structure interaction (FSI) problems. Two types of fluid-structure interaction are considered.
A finite element method for solving the interaction between a flowing incompressible fluid and a linear elastic structure is proposed. The flow is assumed to be laminar. The fluid is discretized using space-time finite elements in order to obtain an arbitrary Lagrangian-Eulerian formulation. The coupling, which uses velocities, is enforced weakly by the use of Nitsche's method. The weak coupling allows for non-matching meshes at the interaction boundaries. Since linear elasticity is assumed the deformations of the solid are not taken into account. However, the formulation allows the solid to undergo rigid body translations. In such cases, or if a free surface is present, the FE mesh is smoothed using a new algorithm based on Winslow's method. The proposed smoother can produce, or preserve, stretched elements. Numerical examples are given.
Two formulations for solving acoustic FSI problems in the frequency domain are proposed. The fluid is formulated in displacements using the Raviart-Thomas element. This choice gives eigensolutions free from spurious eigenmodes with non-zero eigenfrequencies. A formulation with a strong coupling is proposed. The formulation uses the stabilized Crouzeix-Raviart element for the solid. Finally, a formulation where the coupling is enforced weakly by the use of Nitsche's method is proposed. This allows for non-matching meshes. Numerical examples are given.