We consider a fluid in a cavity, the unit square, modeled by the two dimensional incompressible steady state Navier Stokes equations. Let the bottom wall (y=0) of the cavity be moved with a constant (horizontal) velocity. We want to determine a top velocity of the fluid so that the fluid is separated at the line y=0.4.

The mathematical formulation of the problem leads to a constrained optimization problem. The constraints are the Navier Stokes equations.
The optimization problem has been solved using the TRICE_U algorithms.
An interesting aspect of the problem is the importance of the infinite dimensional problem formulation and its interaction with the finite dimensional problem and the optimizer.

In the following, the problem formulation is sketched in the and the results of some computations More details can be found in the paper M. Heinkenschloss: Sequential Quadratic Programming Methods for the Control of Fluids Governed by the Steady State Navier Stokes Equations.