Aerodynamic shape design using higher order derivatives

摘要

Parametric solution methods are very efficient for optimal design problems. A parametrization method using higher order derivatives is applied to the Euler and Navier Stokes equations. The derivatives are obtained by a new class of automatic differentiator which permits to deal with large numerical codes, and in particular codes using iterative methods. As test case the parametrization of the inviscid flow inside a 2D Laval nozzle was studied. The results showed that the method can be applied to the Euler equations, and parametric solutions using derivatives of order 4 are sufficient to describe subsonic flows. For supersonic flows, the method permits to capture the shock wave, and to follow its displacement when varying the geometrical or thermodynamical parameters.