Adjoint-based airfoil optimization with discretization error control

In this article, we develop a new airfoil shape optimization algorithm based on higher-order adaptive DG methods with control of the discretization error. Each flow solution in the optimization loop is computed on a sequence of goal-oriented h-refined or hp-refined meshes until the error estimation of the discretization error in a flow-related target quantity (including the drag and lift coefficients) is below a prescribed tolerance. Discrete adjoint solutions are computed and employed for the multi-target error estimation and adaptive mesh refinement. Furthermore, discrete adjoint solutions are employed for evaluating the gradients of the objective function used in the CGs optimization algorithm. Furthermore, an extension of the adjoint-based gradient evaluation to the case of target lift flow computations is employed. The proposed algorithm is demonstrated on an inviscid transonic flow around the RAE2822, where the shape is optimized to minimize the drag at a given constant lift and airfoil thickness. The effect of the accuracy of the underlying flow solutions on the quality of the optimized airfoil shapes is investigated. Copyright (c) 2014 John Wiley & Sons, Ltd.