Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems

Aerodynamic shape optimization based on high-fidelity models is a computational intensive endeavor. The majority of the computational time is spent in the flow solver, and in the gradient calculation. In this paper, we present two approaches for reducing the overall computational cost of the optimiza-tion. The techniques are tested using the Common Research Model wing benchmark defined by the Aerodynamic Design Optimization Discussion Group (ADODG). The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the re-quired derivatives. The drag coefficient is minimized subject to lift, pitching moment, and geometric constraints. The first approach uses Richardson’s extrapolation to approximate the flow solutions and gradients. The second approach performs multilevel optimization with a series of grid sizes. We found the multilevel approach to be the most effective, achieving a 84.5 % reduction in computational cost. I