Geometrically optimized projection bases for parametric model reduction for large-scale fluid dynamics systems

• Applicant: Dr. Ralf Zimmermann
• Subject Area: Mathematics
• Term: from 2014 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 259082702

Fluid dynamics play a fundamental role in modeling a large variety of physical systems. Examples of practical interest include automotive and aeronautical aerodynamics, hydrodynamics and weather and climate modeling. The enormous costs associated with wind tunnel test campaigns using scaled models or real-scale prototypes render the deployment of Computational Fluid Dynamics an indispensable tool for treating industrial fluid flow problems. However, computing flow solutions over a continuous parameter range, say from start to landing of an aircraft or repeatedly within a design optimization loop, leads to numerical problems reaching easily computation times of several weeks. Hence, parametric reduced order modeling of high-dimensional systems becomes essential. Here, the term parametric means that the reduced order model can be adapted efficiently to parameter changes. The most prominent approaches to model order reduction all have in common that the original large-scale model is projected onto suitable subspaces spanned by low-dimensional bases. The projection bases essentially determine the approximation quality of the resulting reduced order models. In order to account for the underlying parametric dependency, it is suggested in the current literature to apply interpolation techniques on matrix manifolds for computing projection bases at arbitrary parameter conditions. The main objective of the proposed research project is to enhance the prediction capabilities of the projection bases by optimizing a suitable goal function on the matrix manifold in question, which actually measures the approximation quality. This multidisciplinary problem can be tackled only by combining tools from numerics and differential geometry, while additionally taking the engineering aspects of the problem into account. It is planned to demonstrate the applicability and benefit of the proposed method for real-life test cases.

• DFG Programme: Research Fellowships
• International Connection: USA
• Participating Institution: Massachusetts Institute of Technology ; Department of Aeronautics and Astronautics
• Host: Professorin Dr. Karen Willcox