This research involves integration of Optimization, Control and Estimation Theory with
Computational Fluid Dynamics into a unified framework. In our work we focus on adjoint
based methods for optimization problems and Riccati based methods for feedback control
and estimation problems. Such problems are often ill-posed, especially when formulated
in the context of multiscale fluid systems such as high Reynolds number turbulence.
Therefore, numerical solution of such problems usually requires some form of regularization.
My computational studies involve an array of model systems with a varying degree of computational
complexity ranging from the periodic 1D Kuramoto Sivashinsky equation to the 3D Navier Stokes
equation in wall-bounded domains. The primary applications of my research are in industrial
flow control (e.g., in the aerospace industry) and in numerical weather prediction.