Physics-informed deep learning (PIDL) is a novel method to solve various types of problems in computational physics. By embedding the governing equations and boundary conditions into the training of the neural network, physics-informed neural networks (PINNs) can be utilized to solve forward problems, inverse problems, or to reconstruct sparse data sets. This feature can be useful to reduce the efforts of numerical simulations or to retrieve missing information from incomplete experimental data. Hence, PINNs are relevant for experimental as well as computational fluid dynamics. This thesis focuses on researching the application of PIDL to Reynolds-averaged flow fields and is a contribution to evaluating the capabilities, challenges, and limitations which are associated when applying the technique to flows at elevated Reynolds numbers. For this aim, several studies were conducted to explore the application of PINNs to surrogate modeling, forward problems, and sparse data reconstruction.

In the first step, a PINN was trained to serve as a surrogate model of the parameterized Reynolds-averaged wake behind a square cylinder. In a second step, the suitability of different turbulence modeling techniques to reconstruct the flow field of a backward-facing step was analyzed. Based on the findings of the two preliminary studies, in a third step, a surrogate model of the Reynolds-averaged flow around an airfoil under variable angles of attack was developed. Then, shifting the focus towards forward problems, a mixed-variable approach and the effect of different network architectures on PIDL of the flow around cylinders without training data was investigated. The findings on a superior deep learning method were then transferred to firstly predict the flow around an airfoil at a fixed angle of attack and to secondly evaluate the capabilities and limitations of the techniques to serve as surrogate models of two airfoils under variable angles of attack. In a last step, the mixed-variable network technique was applied to reconstruct the sparse grid size independent estimation of the solution of a large eddy simulation (LES) for the flow around an airfoil equipped with vortex generators.

The thesis gains an insight into the capabilities of PIDL when applied to Reynolds-averaged flows at elevated Reynolds numbers and contributes to harnessing its capabilities in fluid dynamics. The work emphasizes the suitability of the technique for surrogate modeling and sparse data reconstruction in experimental and computational fluid dynamics and indicates how the method could be applied in practice. The work also sheds light on the current performance of PIDL when used to solve forward problems. While this field of application could potentially replace traditional numerical simulations and while featuring promising capabilities, it is shown that, at the moment, more research and development is necessary. The challenges associated with elevated Reynolds numbers are outlined and potential future methodological improvements and research questions are discussed. Overall, the work provides a perspective on the current performance and potential applications of PIDL to Reynolds-averaged flow scenarios.