Result: Using an adjoint approach to eliminate mesh sensitivities in computational design

An adjoint algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered large-scale design optimization for practical applications. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product whose cost scales with the number of design variables and the resolution of the parameterized surface grid. The methodology augments the current practice of using adjoints solely for the flowfield and leads to a dramatic computational savings. The accuracy of the implementation is established, and several sample design optimizations are shown.