Fluid-structure interaction of incompressible flows and thin-walled structures

A numerical approach to simulate the coupled problem of slender structures and incompressible Newtonian flows is described. The formulation is based on a partitioned scheme while finite elements are employed on the single fields. The structural field is discretized in space by finite elements based on a seven-parameter shell formulation capable of dealing with the complex dynamics of very slender structures. An efficient solver for the structural system of equations exploiting an algebraic multigrid approach has been developed. A stabilized fluid element following an ALE formulation of the incompressible Navier-Stokes equations is used to model the flow on a time dependent domain. The geometric conservation law is built in into the formulation to obtain a stable scheme which is second order accurate in time. The accuracy and reliability of the approach with respect to critical parameters such as very small time steps, distorted meshes or steep gradients in particular within the flow field has been analyzed. The approach is able to also deal with free fluid surfaces. The inherent instability of weakly coupled approaches is analyzed which reveals the devastating influence of the so-called 'artificial added mass' effect. The convergence of the strongly coupled approach depends on an appropriately chosen relaxation parameter. Ways to automatically adjust the proper amount of relaxation are given. Special emphasis is also put on the efficient implementation particularly of the fluid problem. Vectorization is employed to significantly speed up the time spent for calculating element matrices on vector machines.