Control-based methods for model validation in fluid dynamics #

Joao Fontana, Alice B Thompson

11:50 Tuesday in 4Q04.

Part of the Complex systems and control session.

Abstract #

Most models of physical systems are validated by comparing stable steady states with experimental results. Unstable steady states are typically not used for validation, since they are difficult to observe experimentally. The methods of feedback control and control-based continuation (CBC) can be utilized to find and stabilize unstable steady states of experimental non-linear physical systems. In feedback control, actuation is exerted onto the system, based on a measure of the difference between the system state and a prescribed target state. In CBC, which relies on feedback control, the steady solutions are calculated as function of the prescribed target state. In this study, we investigate how control-based methods can be utilized to reveal unstable steady states of the propagation of bubbles within a Hele-Shaw channel. This system is an appealing prototype for CBC: (i) it presents multiplicity of solutions with complex non-linear behaviour, and (ii) it is a continuous system, while most systems on which CBC is utilized have few degrees of freedom. Additionally, our depth-averaged model of the system is validated experimentally. We use finite element (FE) numerical simulations to design and test a suitable feedback actuation that could be used in an experimental realization of this system. Such realization would permit the direct experimental observation of unstable steady states, and the validation of the unstable solutions of our depth-averaged model.