Optimal Control Design for Fluid Mixing: from Open-Loop to Closed-Loop

Next Thursday, May 19, 2022 we have a talk by Weiwei Hu, visitor scientist from the University of Georgia:

Event: Optimal Control Design for Fluid Mixing: from Open-Loop to Closed-Loop
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Speaker: Prof. Dr. Weiwei Hu
Affiliation: University of Georgia (USA)

Abstract. The question of what velocity fields effectively enhance or prevent transport and mixing, or steer a scalar field to a desired distribution, is of great interest and fundamental importance to the fluid mechanics community. In this work, 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 which 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 an optimal control and the first-order necessary conditions for optimality will be addressed. Moreover, feedback laws will be constructed based on the idea of instantaneous control as well as a direct approximation of the optimality system. Finally, numerical experiments will be presented to demonstrate our ideas and control designs.


FAU Department of Mathematik
Conference Room

The event is finished.


May 19 2022


10:30 - 11:30