Two active flow control methods are investigated numerically to understand the mechanism by which they control aerodynamics in the presence of severe flow separation on an airfoil. In particular, synthetic jets are applied to separated flows generated by additional surface feature (the actuators) near the trailing edge to obtain Coanda-like effects, and an impulse jet is used to control a stalled flow over an airfoil. A moving-grid scheme is developed, verified and validated to support simulations of external flow over moving bodies. Turbulent flow is modeled using detached eddy simulation (DES) turbulence models in the CFD code CDP (34) developed by Lopez (54). Synthetic jet actuation enhances turbulent mixing in flow separation regions, reduces the size of the separation, deflects stream lines closer to the surface and changes pressure distributions on the surface, all of which lead to bi-directional changes in the aerodynamic lift and moment. The external flow responds to actuation within about one convective time, which is significantly faster than for conventional control surfaces. Simulation of pitching airfoils shows that high-frequency synthetic jet affects the flow independently of the baseline frequencies associated with vortex shedding and airfoil dynamics. These unique features of synthetic jets are studied on a dynamically maneuvering airfoil with a closed-loop control system, which represents the response of the airfoil in wind-tunnel experiments and examines the controller for a rapidly maneuvering free-flight airfoil. An impulse jet, which is applied upstream of a nominal flow separation point, generates vortices that convect downstream, interact with the separating shear layer, dismantle the layer and allow following vortices to propagate along the surface in the separation region. These following vortices delay the separation point reattaching the boundary layer, which returns slowly to its initial stall condition, as observed in wind-tunnel experiments. A simple model of the impulse jet actuator used herein is found to be sufficient to represent the global effects of the jet on the stalled flow because it correctly represents the momentum injected into the flow.