Drag Minimization Based on the Navier–Stokes Equations Using a Newton–Krylov Approach

Abstract

A methodology is presented for performing numerical aerodynamic shape optimization based on the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations. An initial multiblock structured mesh is first fit with B-spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on B-spline surfaces. The RANS equations and the one-equation Spalart–Allmaras turbulence model are solved in a fully coupled manner using an efficient parallel Newton–Krylov algorithm with approximate-Schur preconditioning. Gradient evaluations are performed using the discrete-adjoint approach with analytical differentiation of the discrete flow and mesh movement equations. The overall methodology remains robust even in the presence of large shape changes. Several examples of lift-constrained drag minimization are provided, including a study of the common research model wing geometry, a wing–body–tail geometry with a prescribed spanwise load distribution, and a blended-wing–body configuration. An example is provided that demonstrates that a wing optimized based on the Euler equations exhibits substantially inferior performance when subsequently analyzed based on the RANS equations relative to a wing optimized based on the RANS equations.