CFD shape optimization using an incomplete-gradient adjoint formulation

A design methodology based on the adjoint approach for flow problems govern ed 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. I n addition, the methodology can be applied to any type of mesh. The partial derivatives of the Row equations with respect to the design parameters are computed by finite differences. In this way, this computation is independe nt of the numerical scheme employed to obtain the Row solution. Once the de sign parameters have been updated, the new solid surface is obtained with a pseudo-shell approach in such a way that local singularities, which can de grade or inhibit the convergence to the optimal solution, are avoided. Some 2D and 3D numerical examples are shown to demonstrate the proposed methodo logy. Copyright (C) 2001 John Wiley & Sons, Ltd.