Two-Dimensional Aerodynamic Optimization Using the Discrete Adjoint Method with or without Parameterization

An optimization method based on the use of the derivatives of functional outputs with respect to (w.r.t.) solid body mesh nodes is presented. These derivatives are obtained by a discrete adjoint method that first computes the derivatives of functional outputs w.r.t. all volume mesh nodes. They are smoothed before being used in a numerical optimization algorithm. The procedure is demonstrated for a 2D flow governed by the compressible Reynolds-Averaged Navier-Stokes equations (RANS) completed by the Spalart-Allmaras turbulence model. Discrete derivatives are computed with or without making the frozen eddy-viscosity assumption. The design algorithm is compared with a more classical one using design variables related to B-splines on the four test cases introduced by Kim et al. 1

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