## Special Colloquium

### Wednesday, February 13th, 2019

**Time:** 3:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Weiwei Hu (Oklahoma State University)

**Title:** Theoretical and Computational Issues in Control and Optimization of Fluid Flows.

**Abstract: ** In this talk, we mainly focus on control and optimization of a thermal fluid modeled by the Boussinesq equations. This work was motivated by the design and operation of low energy consumption buildings. We investigate the problem of feedback stabilization of a fluid flow in natural convection, which is important in the theory of hydrodynamical stability. In particular, we are interested in stabilizing a possible unstable steady state solution to the Boussinesq equations in a two dimensional open and bounded domain. The challenge of stabilization of the Boussinesq equations lies in the stabilization of the Navier-Stokes equations and its coupling with the convection-diffusion equation for temperature. We show that a finite number of controls acting on a portion of the boundary through Neumann/Robin type of boundary conditions is sufficient to locally stabilize the full nonlinear equations, where the problems of sensor placement and observer designs will also be addressed. Numerical results are provided to illustrate the idea and suggest areas for future research.

In the end, we briefly introduce our current work on optimal control designs for the Boussinesq equations with zero diffusivity and its application to control of optimal transport and mixing via flow advection. The challenges in numerical implementation will be discussed.

**Weiwei Hu** is an Assistant Professor of Mathematics at Oklahoma State University. She obtained her Ph.D. in Mathematics from Virginia Tech, Blacksburg. Her research interests include mathematical control theory of partial differential equations, optimal control of transport and mixing via fluid flows, and mathematical fluid dynamics.