Topology optimization in fluid flow problems

Abstract: In this thesis, the topic of topology optimization in fluids is studied. With emphasis on modeling aspects, the general framework for formulating such problems is presented through a derivation of a sample problem. A survey of the literature, summarizing the developments in the area, forms the first part of the thesis.The second part consists of two new contributions to this field. In the first paper, the problem of finding the optimal topology of fluid channels in a permeable material is examined. Theoretical results include proof of existence of solutions, as well as conditions for obtaining completely discrete designs. Numerical examples are provided to demonstrate the method.Using methodologies from topology opt imization, in paper two, a design method is proposed for creating optimal bottom profiles for shallow water flow systems. Although this is not a topology optimization problem, since a continuous solution is sought, several results carry over due to a close relation to the problem described in the first paper.