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Title: Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach
Authors: Lozano, Carlos
Ponsin, J.
Issue Date: 13-Jun-2022
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2022.415
Published version:
Citation: Journal of Fluid Mechanics 943: A22(2022)
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.
Description: © The Author(s), 2022. Published by Cambridge University Press
E-ISSN: 1469-7645
ISSN: 0022-1120 
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