Regional dynamic modelling and control of flow problems with wavelets

In this thesis, wavelet transform is used to obtain dynamical models describing thebehavior of fluid flow in a local spatial region of interest. First, snapshots of the floware obtained from computational fluid dynamics (CFD) simulations of the governingequations. A wavelet family and decomposition level is selected by assessing thesuccess of reconstruction under the resulting inverse transform. The flow is thenexpanded 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 ofthe flow within the spatial region covered by the support of basis vectors. A dynamicalmodel is established for these coefficients by using subspace identification methods.The approach developed is applied to a sample flow configuration on a square domainwhere the input affects the system through the boundary conditions. It is observed thatthere is good agreement between CFD simulation results and the predictions of thedynamical model. A controller is designed based on the dynamical model and is seento be successful in regulating the velocity of a given point within the region of interest.