The boundary-layer behavior over an airplane's wings is of great importance in take-off and landing of the airplane. If its angle of attack is increased past a critical value, the flow separates from the lifting surface, resulting in a drastic loss of lift and a major increase in drag. In response to this phenomenon, many mechanisms have been studied to control the boundary-layer. First neglected because of implementation difficulties of its application, moving wall boundary-layer control methods have mainly relied on experimental research. The moving wall concept is principally applied as a rotating cylinder protruding into the airfoil. The purpose of this thesis is to provide a computational base to these experiments and to use mathematical tools of computational fluid dynamics and optimization to predict the optimum rotating speed of the cylinder, placed at the leading edge of the airfoil. For the sake of simplicity, we replace the airfoil by a flat plate with a wedge trailing edge. To model the incompressible viscous two-dimensional Navier-Stokes equations, the finite element method is applied on an unstructured two-dimensional mesh. An adaptive remeshing strategy utilized in conjunction with an error estimator controls the solution's accuracy. The aerodynamic forces acting on the total surface are computed from the finite element approximation. The ratio of the lift and the power required to move the flat plateairfoil and to rotate the cylinder forms the objective function to be optimized. A graph of the objective function versus the angle of attack is first constructed for several rotational speeds to provide a rough visual estimate of the optimum value for every angle of attack. Ultimately, an automatic optimization process provides the final solution. This results in the ideal rotational speed to be applied as the angle of attack varies. / Master of Science