The solution of the discrete adjoint equations for an unstructured finite volume compressible Navier-Stokes solver is discussed. In previous work fixedpoint iterations taken from the non-linear method - suitably adjointed - were applied to the adjoint problem. Here it is seen that there are often situations in which these iterations can not be expected to converge. To address this the Recursive Projection Method is developed as a stabilizer, and then used to perform an eigenmode analysis of attached and separated flow on a single geometry, allowing identification of flow regions that were unstable under the basic iteration. Finally an adjoint based optimization with 96 design variables is performed on a wing-body configuration. The initial flow has large regions of separation, which are significantly diminished in the optimized configuration.
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