CKSRI Seminar Series: “Optimal Control Design for Fluid Mixing: from Open-Loop to Closed-Loop”

Thank you to everyone who joined us today at CKSRI Seminar!

It’s been our great pleasure to have Prof. Weiwei Hu sharing her research in control and estimation of partial differential equations and computational methods for control designs.

Abstract: The question of what velocity fields effectively enhance or prevent transport and mixing, or steer a scalar field to the desired distribution, is of great interest and fundamental importance to the fluid mechanics community. In this talk, we mainly discuss the problem of optimal mixing of an inhomogeneous distribution of a scalar field via active control of the flow velocity, governed by the Stokes or the Navier-Stokes equations. Specifically, we consider that the velocity field is steered by a control input that acts tangentially on the boundary of the domain through the Navier slip boundary conditions. This is motivated by mixing within a cavity or vessel by rotating or moving walls. Our main objective is to design a Navier slip boundary control for achieving optimal mixing. Non-dissipative scalars governed by the transport equation will be our main focus. In the absence of molecular diffusion, mixing is purely determined by the flow advection. This essentially leads to a nonlinear control and optimization problem.  A rigorous proof of the existence of optimal open-loop control and the first-order necessary conditions for optimality will be addressed. Moreover, a feedback law (sub-optimal) will be also constructed  based on the idea  of instantaneous control.  Finally, numerical experiments will be presented to demonstrate our ideas and control designs.

Short Bio: Weiwei Hu obtained her Ph.D. degree in Applied Mathematics at Virginia Tech in 2012. Then she held an NTT Assistant Professorship at University of Southern California from 2012 to 2015, and a Postdoctoral Fellowship at the Institute for Mathematics and its Applications (IMA) at University of Minnesota from 2015 to 2016. Thereafter, she held a tenure-track Assistant Professorship at Oklahoma State Univeristy from 2016-2019.  She is currently an Associate Professor in the Department of Mathematics at the University of Georgia. Her current research interests mainly include control and estimation of partial differential equations and computational methods for control designs.