Simultaneous Pseudo-Timestepping for Aerodynamic Shape Optimization Problems with State Constraints

Abstract

This paper presents a numerical method for constrained aerodynamic shape optimization problems. It is based on simultaneous pseudo-timestepping 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 a previously existing pseudo-timestepping method for the states only, and that a preconditioner can be used for convergence acceleration which stems from the reduced SQP methods. Design examples for drag reduction with constant lift and drag reduction with constant pitching moment for an RAE2822 airfoil are included. The overall cost of computation is 4--8 times that of the forward simulation runs depending on the grid size and the number of design parameters.