Improving accuracy and robustness of a discrete direct differentiation method and discrete adjoint method for aerodynamic shape optimisation

This paper describes the recent activities developed at ONERA in the field of aerodynamic shape optimization using gradient based methods. Both discrete direct differentiation method and discrete adjoint method have been considered for the computation of the derivatives of a function with respect to the design parameters. The numerical methods for flow computations (solving RANS equations) and for gradient computations are briefly described.The linearization of Wilcox (k-w) model for improving accuracy of standart gradient computation method- with "frozen" turbulent viscosity - is presented. Also described are two techniques for robustness enhancement of iterative resolution of discrete adjoint equation