Aerodynamic design optimization on unstructured meshes using the Navier-Stokes equations

A discrete adjoint method is developed and demonstrated for aerodynamic des ign optimization an unstructured grids. The governing equations are the thr ee-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one -equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompr essible solvers are differentiated and the accuracy of the sensitivity deri vatives is verified by comparing with gradients obtained using finite diffe rences. several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivat ives is examined. Demonstration optimizations for both compressible and inc ompressible flows are given.