In this paper, we utilize wavelet transform to obtain dynamical models describing the behaviour 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 that 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 the 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.

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.

In this paper a novel approach to the modeling and control of flow problems is considered. The main extension over existing methods is the ability to handle a local region of interest, and the capability to deal with the fluid viscosity being non-constant and unmeasurable. For the modeling part, first a number of snapshots of the fluid flow process at different viscosity values are obtained by computational fluid dynamics simulations of the Navier–Stokes equations governing the flow. Wavelet transform, thresholding and reconstruction are applied to these snapshots and it is seen that the flow process can be represented with acceptable accuracy using only the approximation coefficients of the wavelet transform. The support of the basis functions are selected to tightly cover the desired region of interest so that the flow dynamics outside the desired region do not affect the model significantly. Subspace system identification methods are used to fit a low-dimensional dynamical system model to the approximation coefficients, which yields a set of linear time invariant models, one for each breakpoint viscosity. A single uncertain model is built to capture all of the models in this set, and a robust controller is designed for this uncertain model using D-K iteration. The technique is illustrated on a sample flow configuration on a square domain where the input affects the system through the boundary conditions.