Aerodynamic Optimization Algorithm with Integrated Geometry Parameterization and Mesh Movement

Abstract

An efficient gradient-based algorithm for aerodynamic shape optimization is presented. The algorithm consists of several components, including a novel integrated geometry parameterization and mesh movement, a parallel Newton―Krylov flow solver, and an adjoint-based gradient evaluation. To integrate geometry parameterization and mesh movement, generalized B-spline volumes are used to parameterize both the surface and volume mesh. The volume mesh of B-spline control points mimics a coarse mesh; a linear elasticity mesh-movement algorithm is applied directly to this coarse mesh and the fine mesh is regenerated algebraically. Using this approach, mesh-movement time is reduced by two to three orders of magnitude relative to a node-based movement. The mesh-adjoint system also becomes smaller and is thus amenable to complex-step derivative approximations. When solving the flow-adjoint equations using restarted Krylov-subspace methods, a nested-subspace strategy is shown to be more robust than truncating the entire subspace. Optimization is accomplished using a sequential-quadratic-programming algorithm. The effectiveness of the complete algorithm is demonstrated using a lift-constrained induced-drag minimization that involves large changes in geometry.