This report presents a study of the interaction of AFC (specifically, synthetic jets) with the laminar boundary layer of a NACA 0012 airfoil. First of all, in order to understand the phenomenology of Navier-Stokes equations, a spectro-consistent Computational Fluid Dynamics (CFD) code has been developed from scratch. By using a spectro-consistent discretization, the fundamental symmetry properties of the underlying differential operators are preserved. This code also helps to understand how the energy is transported from big to small scales. After solving a paradigmatic problem (TGV) using the aforementioned code, a mature CFD code (Alya) is used to simulate the flow around the NACA 0012 airfoil. Alya software also uses a spectro-consistent code but in Finite Element Method (FEM). Once the reference cases are solved for different angles of attack, a boundary condition representing an idealized synthetic jet is implemented. A systematic parametrization of the synthetic jet has been performed in order to assess the level of flow control in the boundary layer. Results demonstrate that, by selecting a correct combination of actuator frequency and momentum coefficient, the lift coefficient increases while the drag coefficient decreases producing a better lift-to-drag ratio. This aerodynamic improvement implies that a better circulation control is achieved, less noise is produced and less fuel consumption is required. It is also worth noting that, for high angles of attack, it is necessary to perform 3D flow simulations in order to capture the entire physics of the problem.