Mesh quality assessment based on aerodynamic functional output total derivatives

Our purpose is to develop a new goal oriented method based on the total derivative of the goal with respect to (w.r.t.) volume mesh nodes. The asymptotic behavior of this derivative as the characteristic cell size tends to zero is first studied. This behavior is assessed using numerical simulations on a hierarchy of meshes. Goal oriented criteria of mesh quality are then proposed based on the same derivative and the local characteristic cell length. Their relevance is assessed using several families of parametrized meshes. The criterion succeeds in sorting the better meshes for goal evaluation from the worse. Finally a local mesh adaptation strategy is proposed and validated. All demonstrations are done for 2D structured meshes with finite-volume schemes and cell-centered approach in the case of Eulerian flow computations.