Analytic adjoint solutions for the 2D incompressible Euler equations using the Green's function approach
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 twodimensional incompressible Euler equations around irrotational base flows. The dragbased 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 liftbased 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.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 July 2022
 DOI:
 10.1017/jfm.2022.415
 arXiv:
 arXiv:2201.08128
 Bibcode:
 2022JFM...943A..22L
 Keywords:

 Physics  Fluid Dynamics;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 doi:10.1017/jfm.2022.415