Effect of approximations of the discrete adjoint on gradient-based optimization

An exact discrete adjoint of an unstructured finite-volume solver for the Reynolds-averaged Navier-Stokes equations has been developed. The adjoint is exact in the sense of being based on the full linearization of all terms in the solver, including all turbulence model contributions. From this starting point various approximations to the adjoint are derived with the intention of simplifying the development and memory requirements of the method; considered are many approximations already seen in the literature. The effect of these approximations on the accuracy of the resulting design gradients, and the convergence and final solution of optimizations is studied, as it applies to a two-dimensional high-lift configuration.