Work

On the Characteristic Structure of the Adjoint Euler Equations and the Analytic Adjoint Solution of Supersonic Inviscid Flows

Year: 2025

Type: article

Abstract: 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.

Source: Aerospace

DOI: 10.3390/aerospace12060494

Authors: Carlos Lozano, Jorge Ponsin

Institution: Instituto Nacional de Técnica Aeroespacial

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Instituto Nacional de Técnica Aeroespacial