Multigrid One-shot Method for Aerodynamic Shape Optimization

Abstract

The paper deals with a numerical method for aerodynamic shape optimization using simultaneous pseudo-timestepping. We have recently developed a method for the optimization problem in which stationary states are obtained by solving the pseudo-stationary system of equations representing state, costate, and design equations. The method requires no additional globalization techniques in the design space and a reduced sequential quadratic programming (RSQP) methods-based preconditioner can be used for convergence acceleration. The overall cost of computation is reduced up to 70the number of optimization iterations is comparatively large since we update the design parameters in each time-step of state and costate runs. In this paper we use a multigrid strategy to reduce the total number of optimization iterations keeping the idea of the one-shot method. Design examples of drag reduction, together with geometrical constraints, for an RAE2822 airfoil and an SCT wing are included. The total effort required for the convergence of the optimization problem is less than 2 times (4 times) that of the forward simulation runs in two dimensions (in three dimensions).