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The Green's function approach of Giles and Pierce is used to build the liftand drag based analytic adjoint solutions for the two-dimensionalincompressible Euler equations around irrotational base flows. The drag-basedadjoint solution turns out to have a very simple closed form in terms of theflow variables and is smooth throughout the flow domain, while the lift-basedsolution is singular at rear stagnation points and sharp trailing edges owingto the Kutta condition. This singularity is propagated to the whole dividingstreamline (which includes the incoming stagnation streamline and the wall)upstream of the rear singularity (trailing edge or rear stagnation point) bythe sensitivity of the Kutta condition to changes in the stagnation pressure.

Analytic Adjoint Solutions for the 2D Incompressible Euler Equations Using the Green's Function Approach