Control of cavity flow based on a macroscopic observation

A common approach to fluid flow modelling is based on a fine spatial discretization of the Navier-Stokes equations, which results in a large number of flow variables (i.e., microstates). For the purpose of flow control, the flow variables may be considered to be aggregated on a macroscopic level that goes beyond the fine modelling grid for a practical application. This paper addresses the problem of stabilizing fluid motions using a macroscopic variable that describes a flow pattern on a macroscopic level of observation. The results are illustrated using a lid driven cavity case in order to verify applicability of the macroscopic quantitative observation for a feedback control design.