The flow about high-lift configurations is characterized by complex physics which include the interaction of boundary layers and wakes as well as laminar-turbulent transition. The design of most aircraft relies on lightweight construction which decreases the stiffness of the wing. The elastic properties of the wing also influence the performance of high-lift configurations. Most importantly, an elastic flap can deform and thus change the size of the gap between the wing and the flap. This gap has an significant effect on the performance of a high-lift configuration. Numerical tools offer the potential to allow an accurate prediction of the flow about elastic high-lift configurations in an early phase of the design process. The tool QUADFLOW includes grid adaptation, which assures that the phenomena which exist in high-lift flows can be spatially resolved. On the modelling side, flow separation and laminar-turbulent transition are particularly important to properly simulate. Therefore, three additional two-equation turbulence models have been implemented in the flow solver within QUADFLOW to improve the prediction of the onset of flow separation. A transition criterion has been implemented to predict the onset of laminar-turbulent transition. The implemented turbulence and transition models have been validated against test cases found in the literature and good agreement between numerical and experimental results has been achieved. With increasingly complex models and mesh sizes, the reduction of computational runtime remains an important topic. Therefore, the potential of a new Jacobian-free Newton-Krylov method to decrease the computational time has been assessed and found to give significant accelerations. To enable direct aeroelastic simulations, QUADFLOW has been embedded into the elastic solver SOFIA. The coupling of the solvers has been validated against two test cases simulating an elastic wing and a good agreement between numerical and experimental data has been achieved. For the flow about a high-lift configuration, the prediction of lift and drag coefficients has been improved by taking transitional effects into account. In particular, the angle of attack where stall occurs has been predicted more accurately. The investigation of an elastic high-lift configuration revealed that the generated lift and drag coefficients are reduced due to the rotation of the flap to lower angles of attack.