How is adjoint-based optimization used in aerodynamic design?

Adjoint methods efficiently compute gradients of objective functions with respect to many design variables in a single additional solve. Applications include: Shape optimization for drag minimization at fixed lift; Multi-point optimization for different flight conditions; Inverse design matching target pressure distributions; Mesh adaptation based on output sensitivities. The continuous adjoint solves a modified PDE, while discrete adjoint differentiates the discretized equations. Adjoint methods enable optimization with hundreds of design variables (surface mesh node coordinates or FFD control points), achieving 10-20% drag reductions in hours instead of months. Tools include SU2, ADflow, and commercial codes.