The first figure illustrates the rapid spatial convergence of the forward state-backward adjoint sweep strategy. It is a plot of the velocity component in the direction normal to the wall evaluated at a point inside the flow near the wall vs. distance along the wall. The points marked A and S are the locations of the actuating orifice and the matching strip, respectively. (The point marked F is a point at which we artificially force the flow in order to accelerate the build-up of instabitlities.) The index i is the iteration counter, e.g., i = 4 means that 4 forward state-backward adjoint sweeps have been carried out. Note that convergence is achieved after about 4 iterations, i.e., after 4 forward state-backward adjoint sweeps.
The second figure illustrates the rapid temporal convergence of the forward state-backward adjoint sweep strategy. It is a plot of the the normal stress at the matching strip vs. time. Again, the index i is the iteration counter, e.g., i = 4 means that 4 forward state-backward adjoint sweeps have been carried out. Note that again we see that convergence is achieved after about 4 iterations, i.e., after 4 forward state-backward adjoint sweeps.
Comparison of the controlled and uncontrolled flows