ISBN 9783843944182

978-3-8439-4418-2, Reihe Mathematik

Johanna Katharina Biehl
Adaptive Multilevel Optimization of Fluid–Structure Interaction Problems

171 Seiten, Dissertation Technische Universität Darmstadt (2020), Softcover, B5

Zusammenfassung / Abstract

Fluid–structure interaction is a phenomenon which appears in many fields of engineering, for example in civil engineering, aerodynamics, or medical engineering. The prediction of the behavior of such a system is difficult and the possibilities of experiments are limited, since they are complex and very expensive. Therefore, it is of interest to find a way how the interaction can be modeled and simulated computationally. Particularly when it comes to the control of the interaction, to, for example, minimize the forces acting on constructional elements, a computer-aided prevision of a system is helpful.

In this thesis, we consider the optimal control of the interaction of an incompressible Newtonian fluid with a hyperelastic structure in a two dimensional setting. The system is modeled monolithically with the help of an Arbitrary Lagrangian Eulerian formulation. The corresponding weak system is then discretized with finite elements in space and a Crank-Nicolson scheme in time.

To reduce the computational cost of the optimization, an adaptive multilevel SQP algorithm is used. Therefore, first a reduced order model based on proper orthogonal decomposition is introduced to reduce the dimension of the system significantly. Furthermore, residual based error estimators for the finite element discretization are derived to estimate the space-time error and adapt the mesh iteratively during the optimization.

Finally, numerical results of the discretization, the reduced order model, and the optimization of a benchmark problem are shown.