A discrete adjoint method for e�ciently computing gradients for aerodynamic shape op-
timizations is presented. The chain itself involves an unstructured mesh Reynolds-Averaged
Navier-Stokes solver, and is suitable for the optimization of complex geometries in three
dimensions. In addition to the discrete
ow adjoint the method introduces a second ad-
joint equation for the mesh deformation. Using the adjoint chain it is possible to evaluate
the gradients of a cost function for the cost of one adjoint
ow solution and one adjoint
volume mesh deformation, without performing any (forward) mesh deformation. By choos-
ing a suitable mesh deformation operator, like linear elasticity, the chain may be readily
constructed by hand. Furthermore, this adjoint chain can be subsequently used with pa-
rameterized surface grids. The accuracy and the computational savings of the resulting
procedure is examined for the gradient-based shape optimization of a wing in inviscid
ow
