A discrete gradient-based approach for aerodynamic shape optimisation in turbulent viscous flow

A shape design algorithm for viscous compressible turbulent flows is described. This approach is based on the coupling of an incomplete gradient formulation, which avoids adjoint state computation, with a multi-level method. Using the coarsest level of control parameters, a completed gradient formulation is also proposed to improve the accuracy of the approximate gradient computation. The performance of the present approach is demonstrated by several numerical experiments for aeronautical applications (inverse and direct problems for transonic airfoils) as well as naval ones (optimisation of upwind flying sail for sailing yacht).