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

The characteristic structure of the two-dimensional adjoint Euler equations is examined. The characteristic behaviour is similar to that of the original Euler equations, but with the characteristic information travelling 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.