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Published January 10, 2001 | Published
Journal Article Open

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


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 duct of arbitrary shape. This analysis reveals a logarithmic singularity at the sonic throat and confirms the expected properties at the shock.

Additional Information

© Cambridge University Press 2001. Reprinted with permission. (Received 11 June 1998 and in revised form 8 August 2000) [Published online 12 January 2001] This research was supported by EPSRC under grant GR/K91149.

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