Application of Simultaneous Perturbation Stochastic Approximation Method for Aerodynamic Shape Design Optimization

Aerodynamic shape design optimization problems, such as inverse and constrained airfoil design and axisymmetric nozzle design, are investigated by applying the simultaneous perturbation stochastic approximation (SPSA) method to objective functions that are estimated during each design iteration using a finite volume computational fluid dynamics technique for solving the compressible Navier–Stokes equations. The SPSA method has been demonstrated in the literature as having significant advantages over stochastic global optimization methods such as the simulated annealing (SA) method. In this work the SPSA is compared with SA method for a class of twodimensional and axisymmetric aerodynamic design optimization problems. The numerical studies show that the SPSA method is robust in reaching optimal aerodynamic shapes, is easy to implement, and is highly efficient. The SPSA method can also decrease the computational costs significantly compared with the SA method.