Real-time computational algorithm for optimal control of an MHD flow system

The flow of weakly electrically conducting fluids can be controlled by electromagnetic forces originating from electrodes and permanent magnets. We consider the possibility of separation control for an electrically conducting bluff body flow with reduced-order modeling. The reduced-order model is derived using the proper orthogonal decomposition (POD) and Galerkin projection. The POD allows one to extract the dominant modes in the observed physical phenomena and to de. ne the smallest possible solution space. This can be exploited in a Galerkin framework to reduce the nonlinear infinite dimensional model to a small finite dimensional model. We investigate the design of a reduced-order nonlinear optimal controller for flow separation in a channel. We present numerical experiments with an applied spanwise magnetic field distribution and a boundary electric potential actuation on a part of the boundary. Our methods are found to be efficient and fast, and our methods demonstrate a significant reduction in computational time.