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The present thesis considers the compressible Navier-Stokes equations to simulate the flow of air about basic and complex test cases. As numerical solution method the unstructured finite-volume solver DLR-TAU is used. The aim of the work is to provide a hybrid RANS/LES simulation strategy for the reliable numerical prediction of the stall behavior of high-lift airfoils under the influence of turbulent inflow. The Algebraic Delayed DES (ADDES) is extended, improved, and validated for several fundamental flow cases and application challenges. In the ADDES the distinction between RANS and LES zones is controlled by algebraic sensors, which detect the flow state by evaluating boundary-layer velocity profiles. To allow for complex application cases, the evaluation of the boundary-layer properties is implemented in a fully parallelized algorithm, which can handle complex geometries. Furthermore, the ADDES is coupled with wall-modeled LES capabilities to provide a model for attached boundary layers with turbulent onflow. In order to mitigate the so-called grey-area problem at the RANS-to-LES interface, a vorticity-based LES filter width was adopted and reformulated for the unstructured dual-grid approach of TAU, in order to stimulate the generation of resolved turbulent structures. Moreover, a grid-resolution sensor for Large-Eddy Simulations is proposed, which enables assessing the grid from a single LES solution. This sensor can be used to control an automatic local grid adaptation in order to provide an appropriate spatial resolution for the respective flow problem. In the target application of the present thesis, the interaction of a generic airfoil-generated vortex with a two-element high-lift airfoil is simulated.