Research objectives and content
The research objective is the development of efficient numerical methods for the computation of optimal and suboptimal controls for fluid flows and the theoretical justification of the methods. On the way towards this aim the most sophisticated methods from numerical fluid mechanics and numerical optimisation must be combined.
The augmented Lagrange-SQP method as solver for the optimal control problem Involving the instationary Navier-Stokes equations as state constraints will be combined with state-of-the-art methods for the numerical solution of laminar flow problems, such as operator-splitting methods. This approach joins a second order numerical optimisation scheme with highly accurate time integration. Therefore it will provide a significant advance compared with only linear convergent gradient-type methods that are usually applied to the numerical solution of control problems in fluid flow. A similar idea will be used for the numerical treatment of suboptimal control strategies such as reduced order modelling and instantaneous optimisation. Application of augmented Lagrange-SQP methods to the solution of the control problems arising i this approaches will significantly speed up their numerical solution.
Training content (objective, benefit and expected impact)
The objective here is to gain expertise in the rapidly developing area of efficient numerical optimisation methods for large-sca problems and to bring in experience in modelling and the numerical solution of optimal and suboptimal control problems for laminar flows. The benefit clearly is in settling joint work with the members of the U-Graz group, especially with the participants of the 'Spezialforschungsbereich Optimierung und Kontrolle' in a very well developed research atmosphere. A further benefit is also in extending the joint work with professor Kunisch. The modern technical equipment and computing environment at U-Graz i well suited for tackling numerically the large systems of non-linear equations arising in control problems for fluid flow. The results obtained and methods developed at U-Graz will be incorporated into the research activities at the 'Technische Universitdt Berlin', and also into the education and teaching activities in form of diploma theses, seminars and lectures. Moreover, the research at U-Graz will be an important contribution to the 'habilitation' of the author.
Links with industry / industrial relevance (22)