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

Published online by Cambridge University Press:  12 January 2001

MICHAEL B. GILES  and
NILES A. PIERCE
MICHAEL B. GILES
Affiliation:
Oxford University Computing Laboratory, Oxford, OX1 3QD, UK
NILES A. PIERCE
Affiliation:
Oxford University Computing Laboratory, Oxford, OX1 3QD, UK Present address: Applied Mathematics, California Institute of Technology, Pasadena, CA, 91125, USA.
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 426 , 10 January 2001 , pp. 327 - 345
Copyright
© 2001 Cambridge University Press

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