Fluid flows contain deep structural information on the surrounding geometry as well as on physical and chemical parameters: if one modifies the geometry or the data, one may expect a different flow behavior. Our goal is to extract these parameters from measured data, especially for flows with chemical reactions. This leads to inverse problems which can be encountered with methods of optimization, optimal control coupled with the Lattice Boltzmann Method for fluid simulations. I am interested in the development of such methods as well as in their mathematical analysis and application.
Theses (Offered Topics)
|Existence of weak solutions for the BGK-Boltzmann equation (Existenz schwacher Lösungen für die BGK-Boltzmann-Gleichung)||Masterthesis|
|Solutions for transport equations (Lösungen von Transportgleichungen)||Bachelorthesis|
|Simulation of reactive flows with the Lattice Boltzmann Method (Simulation reaktiver Strömungen mit Lattice-Boltzmann-Verfahren)||Bachelor-/ Masterthesis|
|Comparison of different optimization methods for optimal flow control (Vergleich verschiedener Optimierungsverfahren zur optimalen Kontrolle von Strömungen)||Bachelor-/ Masterthesis|
These thesis topics are to be understood as examples of what a thesis could be about. If none of the topics seems to fit to your special interests, please feel free to ask for a different one. Anyway, all topics may be fitted individually to knowledge and experience of the student. The choice of the thesis language (German/ English) is as well up to the student.
|Jeßberger, J.; Marquardt, J.E.; Heim, L.; Mangold, J.; Bukreev, F.; Krause, M.J. Optimization of a Micromixer with Automatic Differentiation. Fluids 2022, 7, 144. open access: https://doi.org/10.3390/fluids7050144|
|Jeßberger, J.; Marquardt, J.E.; Heim, L.; Krause, M.J. Numerical Optimization of a Micromixer. Poster, ProcessNet 2022|
|Klemens, F; Jeßberger, J.; Thäter, G.; Krause, M.J. Characterization of fluid flows and identification of fluid flow domains by a coupled CFD-MRI method. Talk, GAMM 2021|