Multilevel parameterizations and fast multigrid methods for aerodynamic shape optimization

• Antragsteller: Professor Dr. Nicolas R. Gauger; Professor Dr. Volker Schulz
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2006 bis 2010
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 25186865

Numerical flow simulation is an integral part of the construction process of commercial aircrafts. Due to the advance of computing power and improvements in the efficiency of simulation algorithms, it is nowadays conceivable to design parts of aircrafts or even whole aircrafts on the computer only. Therefore, numerical shape optimization will play a strategic role for future aircraft design and for the respective industry. Current limitations of numerical optimization methods in this field are mainly due to the high complexity of numerical flow models, resulting in long computation times in the order of weeks and months if a standard optimization algorithm is coupled with a flow solver. Additionally, the computation time typically even depends on the shape parameterization. That leads to questions of highly efficient optimization algorithms. Moreover, the optimal representation of shapes on the computer is principally open, resulting in questions of parameterizations and local design refinements. Both questions are of fundamental concern for aerodynamic shape design and, of course, are interacting.In this application, we propose to investigate multilevel shape parameterizations and fast optimization algorithms by exploiting the arising multilevel structures in the shape and in the flow problem. The algorithmic paradigm favored is that of an overall multigrid optimization method for all variables involved, which is in contrast to traditional optimization approaches. This methodological paradigm will potentially lead to optimization methods, which require a numerical effort equivalent to only a few simulation runs - regardless of the resolution of the discretizations. The goal of the project is to explore the exploitation of this potential in the best way. Because elastic effects play an important role in wing design, also aspects of multi-disciplinary design optimization will be addressed.

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