Analytic adjoint solutions for the quasi-one-dimensional Euler equations
نویسندگان
چکیده
The analytic properties of adjoint solutions are examined for the quasi-onedimensional 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.
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Article history: Received 6 March 2008 Received in revised form 8 September 2008 Accepted 24 September 2008 Available online 10 October 2008
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