Adjoint boundary conditions for turbomachinery flows

This article discusses non-local boundary conditions for an adjoint flow solver. The discrete adjoint methodology is used to derive adjoint non-reflecting boundary conditions that are consistent with the non-reflecting boundary conditions of the underlying steady solver. It is shown that the adjoint boundary conditions correspond to discretisations of non-reflecting boundary conditions for the adjoint partial differential equations. We discuss to what extent the implementation of the adjoint non-local conditions can be circumvented by using approximative boundary conditions based on characteristics for the adjoint approach. It is shown, however, that there may occur significant discrepancies in the sensitivity predictions when such simplifying assumptions are used. To analyse these errors, calculations in the linear forward mode are carried out that indicate that the flow sensitivities may be affected heavily by using simpler boundary conditions in the linear mode. The methods presented here are extended in order to derive a discrete adjoint non-reflecting mixing plane