Obtaining regional dynamical models for flow control using wavelet transform

In this paper, we utilize wavelet transform to obtain dynamical models describing the behavior of fluid flow in a local spatial region of interest. First, snapshots of the flow are obtained from experiments or from computational fluid dynamics (CFD) simulations of the governing equations. A wavelet family and decomposition level is selected by assessing the reconstruction success under the resulting inverse transform. The flow is then expanded onto a set of basis vectors which are constructed from the wavelet function. The wavelet coefficients associated with the basis vectors capture the time variation of the flow within the spatial region covered by the support of basis vectors. A dynamical model is established for these coefficients by using subspace identification methods. The approach developed is applied to a sample flow configuration on a square domain where the input affects the system through the boundary conditions. It is observed that there is good agreement between CFD simulation results and the predictions of the dynamical model. A controller is designed based on the dynamical model and is seen to be successful in regulating the velocity of a given point within the region of interest.