PhD Title: Nonlinear, but under control: a hierarchical modelling approach to manipulating liquid films

PhD Supervisors: Radu Cimpeanu and Susana Gomes

My research:

The PhD project is focused on developing a new methodology for hierarchical modelling of complex physical systems in a control-theoretic setting, specifically thin-film fluid flow down inclined planes. The full description of these strongly nonlinear waves is too complex to be analytically tractable and so it is prohibitively computationally expensive to adequately develop controls for the full system. However, if we simplify the model down to either weakly nonlinear models or more advanced reduced-order models, it becomes possible to design optimal feedback controls to force the system towards certain states. By coupling the rapid numerical controls from lower order models to Navier-Stokes solvers we can show that such approximations are sufficient to stabilise the interface of falling liquid films.

Papers:

• Holroyd, Oscar A., Radu Cimpeanu, and Susana N. Gomes. "Linear quadratic regulation control for falling liquid films." SIAM Journal on Applied Mathematics 84.3 (2024): 940-960. pdfLink opens in a new window

Talks:

• British Applied Maths ColloquiumLink opens in a new window, Bristol, March 2023
• Basilisk/Gerris Users MeetingLink opens in a new window, Paris, July 2023
• British Applied Maths ColloquiumLink opens in a new window, Newcastle, April 2024
• New Trends in Optimal ControlLink opens in a new window, Venice, May 2024

Background:

My undergraduate degree was in Mathematics from the University of Warwick, specialising in applied maths and numerical methods. During the summer preceding my final year I completed a URSS summer research project affiliated with HetSys on new adaptive grid methods designed to decrease the CPU time required to solve thin-film fluid flow initial value problems with highly-local control terms. My final year research project was on the hybrid modelling of droplet ejecta after drop impact on a surface. It focussed on developing a hydrodynamic description of the expanding droplet cloud and methods to couple this to direct numerical simulations of the initial impact and particle trajectory models at greater distances.

• MMath Mathematics, University of Warwick

Contact: O.Holroyd@warwick.ac.uk