Analytic adjoint solutions for the quasi-one-dimensional Euler equations

@article{Giles2001AnalyticAS,
  title={Analytic adjoint solutions for the quasi-one-dimensional Euler equations},
  author={Michael B. Giles and Niles A. Pierce},
  journal={Journal of Fluid Mechanics},
  year={2001},
  volume={426},
  pages={327 - 345}
}
The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is required at the shock. A Green's function approach is used to derive the analytic adjoint solutions corresponding to supersonic, subsonic, isentropic and shocked transonic flows in a converging–diverging… 
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