Airfoil design on unstructured grids for turbulent flows

An aerodynamic design algorithm for turbulent hows using unstructured grids is described. The current approach uses adjoint (costate) variables to obtain derivatives of the cost function, The solution of the adjoint equations is obtained by using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite difference gradients, and a few sample computations are shown. Recommendations on directions of further research into the Navier-Stokes design process are made.