Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach

@article{Lozano2022AnalyticAS,
  title={Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach},
  author={Carlos Lozano and Jorge Pons{\'i}n},
  journal={Journal of Fluid Mechanics},
  year={2022},
  volume={943}
}
Abstract The Green's function approach of Giles and Pierce (J. Fluid Mech., vol. 426, 2001, pp. 327–345) is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution turns out to have a very simple closed form in terms of the flow variables and is smooth throughout the flow domain, while the lift-based solution is singular at rear stagnation points and sharp trailing… 
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Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls
TLDR
The mesh divergence problem occurring at subsonic and transonic speeds with the adjoint Euler equations is reviewed and it is shown that the explanation is that the adjointed solution is singular at the wall.

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