One-Shot Pseudo-Time Method for Aerodynamic Shape Optimization Using the Navier-Stokes Equations

This paper presents a numerical method for aerodynamic shape optimization problems in compressible viscous flow. It is based on simultaneous pseudo-time stepping in which stationary states are obtained by solving the pseudo-stationary system of equations representing the state, costate and design equations. The main advantages of this method are that it blends in nicely with previously existing pseudo-time-stepping methods for the state and the costate equations, that it requires no additional globalization in the design space, and that a preconditioner can be used for convergence acceleration which stems from the reduced SQP methods. For design examples of 2D problems, the overall cost of computation can be reduced to less than 2 times the forward simulation runs. Copyright 2011 John Wiley & Sons, Ltd.