Analytic Full Potential Adjoint Solution for Two-dimensional Subcritical Flows

[2506.16886] Properties of Adjoint Solutions of the Full-potential Equations for Two-Dimensional Subcritical Flow Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Fluid Dynamics arXiv:2506.16886 (physics) [Submitted on 20 Jun 2025 ( v1 ), last revised 1 Jul 2026 (this version, v4)] Title: Properties of Adjoint Solutions of the Full-potential Equations for Two-Dimensional Subcritical Flow Authors: Carlos Lozano , Jorge Ponsin View a PDF of the paper titled Properties of Adjoint Solutions of the Full-potential Equations for Two-Dimensional Subcritical Flow, by Carlos Lozano and Jorge Ponsin View PDF HTML (experimental) Abstract: The adjoint full-potential equations are studied for two-dimensional (2D) steady subcritical flows. In contrast with the incompressible case, explicit closed-form solutions are generally not available in the compressible setting, so the emphasis is placed here on the underlying structure. Using the Green's-function approach and the relation between the adjoint full-potential and compressible adjoint Euler equations, we identify the adjoint potential and stream function with linear combinations of the Euler adjoint variables associated with point mass and vorticity sources. For lift-based cost functions, the corresponding adjoint solutions contain two unknown functions that encode the effect of perturbations to the Kutta condition. We show that these functions obey the linearized full-potential equations, are linked by generalized Cauchy-Riemann equations, and reduce in the incompressible limit to the Poisson kernel of the Laplacian on the exterior of the circle and its harmonic conjugate. Their properties are examined analytically and through numerical adjoint solutions. Finally, a continuous formulation of the Kutta condition for the adjoint full-potential equations is discussed and interpreted in terms of singular boundary forcing, Green-function kernels, and an equivalent Lagrange-multiplier formulation. Comments: 31 pages, 6 figures. Revised version Subjects: Fluid Dynamics (physics.flu-dyn) ; Optimization and Control (math.OC) Cite as: arXiv:2506.16886 [physics.flu-dyn] (or arXiv:2506.16886v4 [physics.flu-dyn] for this version) https://doi.org/10.48550/arXiv.2506.16886 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carlos Lozano [ view email ] [v1] Fri, 20 Jun 2025 10:16:16 UTC (1,465 KB) [v2] Mon, 7 Jul 2025 11:48:46 UTC (1,472 KB) [v3] Thu, 9 Apr 2026 11:05:58 UTC (1,466 KB) [v4] Wed, 1 Jul 2026 06:05:04 UTC (1,146 KB) Full-text links: Access Paper: View a PDF of the paper titled Properties of Adjoint Solutions of the Full-potential Equations for Two-Dimensional Subcritical Flow, by Carlos Lozano and Jorge Ponsin View PDF HTML (experimental) TeX Source view license Current browse context: physics.flu-dyn < prev | next > new | recent | 2025-06 Change to browse by: math math.OC physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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