Multipoint and Multi-Objective Aerodynamic Shape Optimization

TLDR

The study focuses on aerodynamic shape optimization, exemplified by lift‑enhancement and multi‑point lift‑constrained drag minimization problems. It introduces a Newton–Krylov algorithm for optimizing single‑ and multi‑element airfoil configurations. The method solves the compressible Navier–Stokes equations with a one‑equation turbulence model, uses a preconditioned GMRES adjoint solver, enforces constraints via a penalty formulation, and applies a quasi‑Newton step, while also generating a Pareto front validated against a genetic algorithm. The algorithm delivers an efficient and robust solution, successfully computing a validated Pareto front for complex aerodynamic multi‑objective problems.

Abstract

A Newton‐Krylov algorithm is presented for the aerodynamic optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier‐Stokes equations in conjunction with a one-equation turbulence model. The preconditioned generalized minimum residual method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. Design examples include lift-enhancement and multi-point lift-constrained drag minimization problems. Furthermore, the new algorithm is used to compute a Pareto front for a multi-objective problem, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an ecient and robust approach for addressing the issues of complex aerodynamic