Pseudotime method for shape design of Euler flows

Abstract

We exploit a novel idea for the optimization of flows governed by the Euler equations. The algorithm consists of marching on the design hypersurface while improving the distance to the state and costate hypersurfaces. We consider the problem of matching the pressure distribution to a desired one, subject to the Euler equations, for both subsonic and supersonic flows. We limited our investigation to two-dimensional test cases. The rate of convergence to the minimum for the cases considered is three to four times slower than that of the analysis problem. Results are given for Ringleb flow and a shockless compression case.