Inverse aerodynamic shape design using the Navier-Stokes equations

The inverse problem being addressed is the construction of an aerodynamic airfoil shape which gives a prescribed target pressure distribution. The inverse problem is posed as a minimization problem of an objective functional. The minimum of the functional represents the realization of the target pressure distribution by the airfoil. The design variables consists of geometric parameters defining the airfoil shape, the angle of attack defining the orientation of the airfoil with respect to the free-stream, and an appropriately defined set of target pressure parameters which are introduced to assure well-posedness of the inverse problem. The minimization problem is solved by a gradient-based optimization algorithm. The variational method is employed for an efficient computation of the objective functional gradient with respect to the design variables. Numerical results are presented to demonstrate how the solution procedure works.