WITHDRAWN: Adjoint-Based Shape Optimization Framework for High-Lift Design Using Three-Dimensional Mixed-Element Unstructured Grids

An adjoint-based aerodynamic optimization framework is proposed for three-dimensional high-lift design. This framework contains multiple components that provide an accurate and efficient evaluation of adjoint linear systems, solutions, and surface gradients. The flow Jacobian is constructed using a novel process for a finite-volume computational aerodynamics flow solver based on unstructured heterogeneous meshes of up to four different element shapes. Due to the heterogeneous grid structure, applying automatic differentiation directly to the flow residual would incur a high computational cost, as each row of the residual can potentially have a unique configuration. Automatic differentiation by operator overloading is applied to primitive calculations, such as flux and boundary condition calculations, to build the Jacobian. Since these primitive calculations possess only a few variations, only a few sets of instructions to differentiate each term need to be stored. These calculations are then combined using the chain rule to form the Jacobian matrix. This approach enables us to take advantage of the code maintainability provided by automatic differentiation at a manageable computational cost. The constructed ill-conditioned adjoint linear system is solved by a preconditioned iterative method. An incremental linear elasticity mesh mover and mesh adjoint approach is employed to enhance the robustness and efficiency of mesh movement and surface gradient evaluation. In this work, the convergence of the preconditioned iterative method, applied to solve the adjoint linear system of a three-dimensional high-lift common research model (CRM-HL), is investigated. The surface gradient computed by the mesh adjoint is verified. The rigid-body design framework is applied to improve the aerodynamic performance of a CRM-HL airfoil.