Variable-fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation

An aerodynamic shape optimization methodology based on a discrete adjoint solver for Navier-Stokes flows is described. The flow solver at the heart of this optimization process is a Reynolds-averaged Navier-Stokes code for multiblock structured grids. It uses Osher's approximate Riemann solver and the algebraic turbulence model of Baldwin-Lomax. A corresponding discrete Navier-Stokes adjoint solver is derived analytically. It has to calculate accurately the Jacobian, including the effect of the turbulence modeling. The shape deformations are parameterized by the use of a Bezier-Bernstein formulation. The optimization is gradient-based and employs the variable-fidelity optimization method of Alexandrov et al. that combines low- (Euler equations on a coarse grid) and high-fidelity (Navier-Stokes equations on a fine grid) models for better efficiency. The accuracy of the adjoint solver is verified through comparison with finite difference. An airfoil drag minimization problem and the three-dimensional Navier-Stokes optimization of the ONERA M6 wing are presented.