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

Published online by Cambridge University Press:  13 June 2022

Carlos Lozano Open the ORCID record for Carlos Lozano [Opens in a new window]  and
Jorge Ponsin
Carlos Lozano
Affiliation:
Computational Aerodynamics, National Institute of Aerospace Technology (INTA), Carretera de Ajalvir, Km 4, 28850 Torrejon de Ardoz, Spain
Jorge Ponsin*
Affiliation:
Computational Aerodynamics, National Institute of Aerospace Technology (INTA), Carretera de Ajalvir, Km 4, 28850 Torrejon de Ardoz, Spain
*
† Email address for correspondence: lozanorc@inta.es
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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 edges owing to the Kutta condition. This singularity is propagated to the whole dividing streamline (which includes the incoming stagnation streamline and the wall) upstream of the rear singularity (trailing edge or rear stagnation point) by the sensitivity of the Kutta condition to changes in the stagnation pressure.

JFM classification

Aerodynamics: Aerodynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 943 , 25 July 2022 , A22
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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