CFD shape optimization using an incomplete-gradient adjoint formulation.

*(English)*Zbl 1051.76012Summary: We present a design methodology based on the adjoint approach for flow problems governed by incompressible Euler equations. 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 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 flow equations with respect to the design parameters are computed by finite differences. In this way, this computation is independent of the numerical scheme employed to obtain the flow 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 singulanties which can degrade or inhibit the convergence to the optimal solution are avoided. Some two- and three-dimensional numerical examples demonstrate the proposed methodology.