CFD shape optimization using an incomplete-gradient adjoint formulation

A design methodology based on the adjoint approach for ow problems governed by the incompressible Euler equations is presented. The main feature of the algorithm is that it avoids solving the adjoint equations, which saves an important amount of CPU time. Furthermore, the methodology is general in the sense it does not depend on the geometry representation. All the grid points on the surface to be optimized can be chosen as design parameters. In addition, the methodology can be applied to any type of mesh. The partial derivatives of the ow equations with respect to the design parameters are computed by nite di erences. In this way, this computation is independent of the numerical scheme employed to obtain the ow solution. Once the design parameters have been updated, the new solid surface is obtained with a pseudo-shell approach in such a way that local singularities, which can degrade or inhibit the convergence to the optimal solution, are avoided. Some 2D and 3D numerical examples are shown to demonstrate the proposed methodology