PDE-Constrained Optimisation for Thin Film Flow #

Sattam Alrashidy, Kris van der Zee, Anna Kalogirou, Dante Kalise

Poster session

Abstract #

The objective of this poster is to present the solution of time-dependent optimal control for nonlinear partial differential equations that arise in fluid dynamics, in particular, thin-film equations. Controlling thin film flow has been novel and desirable in many applications. For example, flat-flow film stability is preferred in coating processes, while interfacial deformation could be valuable in heat and mass transfer. Our main contribution is to develop the time-dependent optimality system for controlling thin-film flow by finding the appropriate topography for the relevant system that minimises the differences between thin-fluid film flow and the preferred state. We use the approach of Optimize then Discretize, that is optimality system will be derived as coupled systems of partial differential equations and then discretised and solved. An iterative algorithm is used for the optimality system as it contains a coupled system of time-dependent PDEs, including adjoint equations which are backward in time.