Abstract

Many properties of fluid systems, such as stability, receptivity to external or internal forcing, or sensitivity to uncertainties or imperfections, can be formulated as an optimization problem with partial-differential equations (PDEs) as side-constraints. Only in the limit of overly restrictive assumptions do these optimisation problems reduce to standard and familiar tools for the analysis of fluid systems. We will introduce a framework for the analysis of large-scale fluid systems by PDE -constrained optimization techniques. This framework will make use of adjoint information which is extracted efficiently from direct numerical simulations of the fluid problem via a modified automatic differentiation approach. The adjoint methodology will be demonstrated on various test cases where its flexibility and versatility will be stressed. Current research directions, generalizations and challenges will be outlined as well.