Goal oriented mesh adaptation using total derivative of aerodynamic functions with respect to mesh coordinates – With applications to Euler flows

In aeronautical CFD, engineers require accurate predictions of the forces and moments but they are less concerned with the accuracy of the detailed flow-field. Hence, the so-called “goal oriented” mesh adaptation strategies have been introduced to get satisfactory values of functional outputs at an acceptable cost, using local node displacement and insertion of new points rather than mesh refinement guided by uniform accuracy. Most often, such methods involve the adjoint vector of the function of interest. Our purpose is precisely to present new goal oriented mesh adaptation strategies in the framework of finite-volume schemes and a discrete adjoint method. It is based on the total derivative of the goal with respect to (w.r.t.) mesh nodes. More precisely, a projection of the goal derivative, removing all components corresponding to geometrical changes in the solid walls or the support of the output, is used to adapt the meshes either by inserting new nodes or by displacing current mesh nodes. The methods are assessed in the case of 2D and 3D Euler flow computations.