Aerodynamic Design Using Unstructured Meshes

A methodology for performing optimization on 2D and 3D unstructured grids based on the Euler equations is presented. The same, low-memory-cost explicit relaxation algorithm is used to resolve the discrete equations which govern the ow, linearized direct and adjoint problems. The analysis schemes, for both 2D and 3D, are high resolution Local-Extremum-Diminishing (LED) schemes and use Roe decomposition for the dissipative uxes. The local time-stepping relaxation scheme is based on a multidimensional equivalent of a TVD CFL-like condition guaranteeing convergence of ow and sensitivity computations to machine accuracy. Mesh movement is performed in such a way that optimization of arbitrary geometries is allowed. Sensitivities based on direct and adjoint methods are validated and sample optimizations are performed: the inverse pressure design of a multielement airfoil in high-lift mode, an innnite-span straight transonic wing and a transonic wing/body conng-uration. It is shown that, due to its near-elimination of CPU cost dependence on the number of design variables, the adjoint method is preferred over the direct and nite difference methods for practical single-discipline aerodynamic optimization.