The lack of understanding of most of the relevant physical mechanisms when applying flow control limits the prospects of successfully transitioning flow-control technologies into real flight vehicles. Successful control of boundary-layer separation for lifting surfaces promises major performance gains especially when large laminar runs are desired in order to minimize the skin-friction drag. We systematically explore the fundamental1 mechanisms of the interaction of separation and transition that are relevant for effective and efficient flow control applications. Toward this end, we are employing computational fluid dynamics (CFD) for investigating active flow control for a NACA 643-618 airfoil at a chord Reynolds number ReC=64,200 and various angles-of-attack. CFD results are compared to wind/water tunnel experiments carried out at the University of Arizona. For simulations of the entire wing section we are using a high-order-accurate finite volume code based on the compressible Navier-Stokes equations. For very highly resolved DNS which focus exclusively on the separated region on the suction side of the wing, we are employing a higher-order-accurate compact finite difference code based on the incompressible Navier-Stokes equations in vorticity-velocity formulation. These simulations are set up to fully resolve the flow field and enable us to reveal some of the intricate physical mechanisms associated with unsteady separation and transition, flow instabilities, and active flow control.