A Higher Order Artificial Compression Reduced Order Model for Control of Thermally Convective Flows

A second-order in time discretization of the artificial compression proper-orthogonal decomposition reduced-order model (POD-ROM) for control of thermally convective flows is presented. It is a velocity-pressure reduced-order model that does not require satisfaction of div-stability (Ladyzhenskaya-Babuska-Brezzi) condition for mixed reduced-order subspaces. Second-Order in time artificial compression POD-ROM approximations of solutions of the optimality system are defined and error estimates are derived. Numerical experiments are performed to validate the accuracy and efficiency of the scheme in solving a boundary control problem involving mixed convection flow.