Control of Steady Incompressible 2D Channel Flow

We consider steady incompressible flows in a 2D channel with flow quantities measured along some fixed, transverse sampling line. From a set of allowable flows it is desired to produce a flow that matches a given set of measurements as closely as possible. Allowable flows are completely specified by a set of control parameters which determine the shape of the inflow at the boundary and the shape of an internal bump which partially obstructs the flow. Difficulties concerning the transformation of this problem into a standard optimization problem are discussed, including the correct choice of functional and algorithm, and the existence of local minima.