Hierarchical solution concepts for flow control problems

• Antragsteller: Professor Dr. Michael Hinze; Professor Dr. Stefan Turek
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2006 bis 2015
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 25188282

Flow control problems form the core in many practical applications. Their numerical solution for (3D) time dependent flows still represents one of the main challenges in the area of modern scientific computing. The goal of the project is the development of a generally applicable hierarchical (multigrid) solution framework for flow control problems which allows their numerical solution requiring a computational effort of only a small multiple of that of the flow simulation itself, i.e. for the performance measureeffort of optimization < constant, effort of simulationshould hold with a constant of moderate size. Furthermore, within the solution framework control and state constraints should be easily integrable. To achieve our goal we combine¿ High performance scientific computing techniques in flow simulation,¿ Discrete concepts in space and time which are tailored to the structure of the first-order necessary optimality conditions of the underlying optimization problem (Karush-Kuhn-Tucker system, short KKT system), and¿ Sophisticated optimization algorithms combined with multigrid concepts which allow to exploit the structure of the underlying optimization problem.Within this first application period we concentrate on methodic and algorithmic aspects which are validated at optimization problems for 2D time dependent flows with prototypical character. Upon successful completion of the project we have available the still missing links between the three items mentioned above, i.e. fast and robust numerical solution routines for the flow equations and their corresponding adjoints are linked to discretization concepts for flow control which mimic the coupling through the KKT system of state, adjoint state, and controls, and to hierarchical optimization algorithms which also allow to cope with control and state constraints. In a second application period we then are in the position to tackle more general and more complex flow control problems in realistic applications.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1253: Optimierung mit partiellen Differentialgleichungen