In this thesis, an approach to the computation of shape sensitivity in transient ow problems using analytic derivatives is introduced. In the first chapter, governing fluid equations are illustrated and the use of the Navier Stokes equations is motivated. Different time integration schemes are explained, including their advantages and draw-backs. Subsequently, the Bossak (WBZ) time integration scheme is illustrated and the use for this work is justified. For spatial discretization, the finite element discretization is chosen and explained. In order to overcome stability issues, the variational multi-scale element is applied, together with the algebraic sub-grid scale stabilization technique. In the second chapter, the shape sensitivity approach is illustrated. Different types of shape sensitivity computations are depicted together with their area of application. Following up, the discrete adjoint based shape sensitivity is derived. First, the adjoint shape sensitivity computation for steady state problems is pointed out. Second, the approach is extended for the computation of transient shape sensitivity. For illustrative purpose, the BDF1 time scheme is used. Afterwards, the transient shape sensitivity and the corresponding adjoint equations are derived for the Bossak time scheme promising more accurate result computation. All necessary analytic derivatives are stated. In the third chapter, the implementation of the proposed scheme is explained including the program ow. Hence, the used software and programming language is motivated and justified. The last chapter evaluates results obtained by the use of the implemented software and tested against a finite difference shape sensitivity solution. The results showed high accuracy for a cylinder in a transient ow. Additionally, numerical tests are elaborated in order to check the limitations of the proposed scheme. It was found, that the result computation is limited to a small amount of disjoint computation intervals. Correct results are only obtained by a single computation interval or by a proper check-pointing scheme. However, the application to moderate Reynolds numbers is justifiable.     «

In this thesis, an approach to the computation of shape sensitivity in transient ow problems using analytic derivatives is introduced. In the first chapter, governing fluid equations are illustrated and the use of the Navier Stokes equations is motivated. Different time integration schemes are explained, including their advantages and draw-backs. Subsequently, the Bossak (WBZ) time integration scheme is illustrated and the use for this work is justified. For spatial discretization, the finite el...     »