The Smoothed Sensitivity Equations Method for Fluid Design Problems

We consider shape optimization problems involving compressible fluid flows, which are characterized by nonsmooth and/or noisy objective functions. Such functions are difficult to optimize using derivative-based techniques. To overcome such a difficulty, we suggest an approach for estimating the sensitivity derivatives, based on a suitable smoothing of the sensitivity equations, The smoothing affects only the sensitivity derivatives and not the accuracy of the analysis. The basic mechanism by which the smoothing process achieves this result is illustrated with the help of an inverse design problem involving an inviscid quasi-one-dimensional how having a closed-form solution. The convergence properties and the computational efficiency of the approach are demonstrated on two inverse design problems involving two-dimensional inviscid, compressible flows,