Artificial Compression POD Reduced Order Model for Control of MHD Flows

In this paper, we propose an artificial compression proper orthogonal decomposition reduced order model (POD-ROM) for the control of magnetohydrodynamic (MHD) flows. The control is effected by electromagnetic forces originating from electrodes and permanent magnets. The proposed POD-ROM is a velocity-pressure ROM that can be used to efficiently compute the reduced order pressure needed, for instance, in the control of drag and lift forces in sea water. We also propose and analyze a decoupled time-stepping scheme that uncouples the computation of velocity and electric potential from the pressure variable. The feasibility of the proposed approaches are shown by numerically solving a control problem involving flow separation in a backward-facing step channel.