Improving the efficiency of aerodynamic shape optimization on unstructured meshes

In this paper the exact discrete adjoint of a finite volume formulation on unstructured meshes for the Euler equations in two dimensions is derived and implemented to support aerodynamic shape optimization. The accuracy of the discrete exact adjoint is demonstrated and compared with that of the approximate adjoint. A solution process for the adjoint equations, which is similar to that used for the flow equations, is modified to account for multiple functionals. An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to a Sequential Quadratic Programming optimization algorithm, is tested on constrained and unconstrained airfoil design cases. Preliminary results are also presented for a Sequential Linear Programming algorithm, which appears to be able to deal properly with constrained design in spite of its simplicity