Analytic adjoint solution for incompressible potential flows
Abstract
We obtain the analytic adjoint solution for two-dimensional (2D) incompressible potential flow for a cost function measuring aerodynamic force using the connection of the adjoint approach to Green's functions and also by establishing and exploiting its relation to the adjoint incompressible Euler equations. By comparison with the analytic solution, it is shown that the naive approach based on solving Laplace's equation for the adjoint variables can be ill-defined. The analysis of the boundary behavior of the analytic solution is used to discuss the proper formulation of the adjoint problem as well as the mechanism for incorporating the Kutta condition in the adjoint formulation
Cite
@article{arxiv.2503.15121,
title = {Analytic adjoint solution for incompressible potential flows},
author = {Carlos Lozano and Jorge Ponsin},
journal= {arXiv preprint arXiv:2503.15121},
year = {2025}
}
Comments
20 pages. This article has been accepted by Physics of Fluids. The version of record can be found at https://doi.org/10.1063/5.0271828