Distributed Parameter Control of Thermal Fluids

(ABSTRACT) We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional model and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation. Acknowledgments I would like to express my sincere appreciation to all the people who encouraged and supported me throughout my academic endeavor. I wish to thank those with whom I have discussed my work as well as those who were beside me with their friendship during these years. In particular, my deepest gratitude to my advisor, John A. Burns for his constant support, contagious enthusiasm and guidance. It was gratifying to work with him. He was not only my advisor but also a good friend, always there to listen. I would also like to thank Terry Herdman, Eugene Cliff, Jeff Borggaard and Tao Lin for serving in my committee and all the people at the Interdisciplinary Center for Applied Mathematics (ICAM) for their friendship and kindness. Finally, I would like to thank my family for their encouragement, in particular my father who would have be happy to share this moment with me. Thanks also to my friends, those from Argentina who follow each of my steps and those who I met at Virginia Tech. They gave me the indispensable support to accomplish this work.