Adjoint-Based Error Estimation and Mesh Refinement in an Adjoint-Based Airfoil Shape Optimization of a Transonic Benchmark Problem

In this article, we apply a new airfoil shape optimization algorithm based on adaptive higher order Discontinuous Galerkin methods with discretization error control to a 2D benchmark problem of the AIAA Design Optimization Discussion Group. Each flow solution in the optimization process is computed on a sequence of goal-oriented h-or hp-refined meshes until the estimation of the discretization error in a given target quantity (like the drag coefficient) is below a prescribed error tolerance. Furthermore, the optimization is driven by the Sequential Quadratic Programming (SQP) algorithm and the corresponding gradient of the objective function is evaluated via the adjoint approach. Finally, the effect of the discretization error on the quality of the optimized airfoil shapes is investigated.