Efficient Algorithms for Solution of the Adjoint Compressible Navier-Stokes Equations with Applications

The complete discrete adjoint equations for an unstructured finite volume compressible Navier-Stokes solver are discussed with respect to the memory and time efficient evaluation of their residuals, and their solution. It is seen that application of existing iteration methods for the non-linear equation - suitably adjointed - have a property of guaranteed convergence provided that the nonlinear iteration is well behaved. For situations where this is not the case, a stabilization method based on the Recursive Projection Method is developed. The resulting adjoint solver is applied to 3D optimization of a turbulent wing-fuselage configuration, as well as to goal-oriented adaptation using an error representation formula