Towards efficient aerodynamic shape optimization based on the Navier-Stokes equations

An accurate and efficient algorithm for Navier—Stokes aerodynamic shape optimization problems is presented. The gradient of the objective function is obtained via the discrete adjoint and flow-sensitivity methods. The adjoint and flow-sensitivity equations are solved using a preconditioned GMRES solver. A complete linearization of the discretized Navier—Stokes and turbulence model equations results in an accurate and efficient evaluation of the gradient. Furthermore, this linearization is also used to accelerate the convergence rate of the flow solver, which is based on an inexact-Newton strategy. The gradient is generally obtained in less than one third of the time required to fully converge a flow solution. Factors affecting gradient accuracy are examined. The performance of the new algorithm is demonstrated for several design problems, such as inverse design, lift-constrained drag minimization, lift enhancement and maximization of lift-to-drag ratio.

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