The sketch gives the relative placements of the actuator (an orifice in the wall through which fluid can be injected into the flow or sucked out of the flow) and the position of the "sensing strip," i.e., the portion of the wall along which we try to match the stress to that of Blasius flow. The actuator is placed upstream of the sensing strip.
At the actuator, fluid may be injected or sucked; we only have control of the total mass flow rate and the average direction of the fluid being introduced or removed from the flow field through the orifice. The objective functional is the time integral over a specified time interval of the L2 norm of the difference between the stresses of the flow and of Blasius flow along the matching strip. The functional is penalized by the sum of the squares of the L2 norms of the control and of its time derivative.
The results provided here are for normal injection so that we only have a single time-dependent control parameter, i.e., the total rate at which fluid is injected or sucked through the orifice at any given time. We also only match the normal stress component along the matching strip.
Convergence of the forward state-backward adjoint sweep strategy
Comparison of the controlled and uncontrolled flows