Persona: Ponsin Roca, Jorge
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Ponsin Roca
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Publicación Acceso Abierto Explaining the lack of mesh convergence of inviscid adjoint solutions near solid walls for subcritical flows(Multidisciplinary Digital Publishing Institute (MDPI), 2023-04-24) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed, and an explanation is provided by comparing a numerical incompressible adjoint solution with an analytic adjoint solution, showing that the anomaly observed in numerical computations is caused by a divergence of the analytic solution at the wall. The singularity causing this divergence is of the same type as the well-known singularity along the incoming stagnation streamline, and both originate at the adjoint singularity at the trailing edge. The argument is extended to cover the fully compressible case, in subcritical flow conditions, by presenting an analytic solution that follows the same structure as the incompressible one.Publicación Restringido Exact inviscid drag-adjoint solution for subcritical flows(Aerospace Research Central, 2021-09-25) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)Publicación Acceso Abierto On the Characteristic Structure of the Adjoint Euler Equations and the Analytic Adjoint Solution of Supersonic Inviscid Flows(Multidisciplinary Digital Publishing Institute (MDPI), 2025-05-30) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)The characteristic structure of the two-dimensional adjoint Euler equations is examined. The behavior is similar to that of the original Euler equations, but with the information traveling in the opposite direction. The compatibility conditions obeyed by the adjoint variables along characteristic lines are derived. It is also shown that adjoint variables can have discontinuities across characteristics, and the corresponding jump conditions are obtained. It is shown how this information can be used to obtain exact predictions for the adjoint variables, particularly for supersonic flows. The approach is illustrated by the analysis of supersonic flow past a double-wedge airfoil, for which an analytic adjoint solution is obtained in the near-wall region. The solution is zero downstream of the airfoil and piecewise constant around it except across the expansion fan, where the adjoint variables change smoothly while remaining constant along each Mach wave within the fan.Publicación Restringido Singularity and mesh divergence of inviscid adjoint solutions at solid walls(Elsevier, 2023-09-15) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)The mesh divergence problem occurring at subsonic and transonic speeds with the adjoint Euler equations is reviewed. By examining a recently derived analytic adjoint solution, it is shown that the explanation is that the adjoint solution is singular at the wall. The wall singularity is caused by the adjoint singularity at the trailing edge, but not in the way it was previously conjectured.Publicación Restringido Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach(Cambridge University Press, 2022-06-13) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)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.Publicación Acceso Abierto Shock equations and jump conditions for the 2D adjoint euler equations(Multidisciplinary Digital Publishing Institute (MDPI), 2023-03-10) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)This paper considers the formulation of the adjoint problem in two dimensions when there are shocks in the flow solution. For typical cost functions, the adjoint variables are continuous at shocks, wherein they have to obey an internal boundary condition, but their derivatives may be discontinuous. The derivation of the adjoint shock equations is reviewed and detailed predictions for the behavior of the gradients of the adjoint variables at shocks are obtained as jump conditions for the normal adjoint gradients in terms of the tangent gradients. Several numerical computations on a very fine mesh are used to illustrate the behavior of numerical adjoint solutions at shocks.Publicación Restringido Analytic adjoint solution for incompressible potential flows(AIP Publishing, 2025-06-10) Lozano, Carlos; Ponsin, J.; Ponsin Roca, Jorge; Instituto Nacional de Técnica Aeroespacial (INTA)We obtain the analytic adjoint solution for two-dimensional 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 naïve 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.
