Regional dynamical modeling and control of flow problems under unmeasurable and non-constant viscosity

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.