Extension of the one-shot method for optimal control with unsteady PDEs

Abstract

The one-shot approach has proven to be very efficient in optimization and control with steady partial differential equations (PDEs) which are solved by fixed-point iterations. The purpose of this paper is to extend the one-shot method to unsteady problems and to make it as efficient as in steady cases. We derive a framework for optimization and control with unsteady PDEs, whose structure is the same as in the steady one-shot method. First results in the direction of one-shot optimization with unsteady Reynolds-averaged Navier-Stokes equations (URANS) are presented. With the Van der Pol oscillator as a generic model problem, we investigate an adaptive time scaling approach, which demonstrates the classical one-shot efficiency on unsteady problems.