Improvements to a Newton-Krylov Adjoint Algorithm for Aerodynamic Optimization

Abstract

We present and examine a number of improvements to a gradient-based algorithm for aerodynamic optimization. A Newton-Krylov algorithm is used to solve the compressible Navier-Stokes equations, the gradient is computed using the discrete-adjoint method with a preconditioned Krylov solver, and the optimum is found through a quasi-Newton algorithm with a rank-two update formula. Constraints are imposed by penalizing the objective function. Improvements are made in three areas: 1) thickness constraints are generalized to permit the location of maximum thickness to be determined by the optimizer or alternatively to constrain the cross-sectional area; 2) new scalings of design variables and initial estimates of the inverse Hessian matrix in the quasi-Newton method are investigated; 3) the algebraic grid perturbation algorithm is replaced by an algorithm based on a spring analogy. In each case, the effect of the improvements on the performance of the algorithm is presented.