Mathematical and Computational Modelling of Wave-Driven Propulsion

Key information

Lead supervisor: Dr Graham Benham
Application deadline: Ongoing
Project start date: 01 October 2026
Project duration: 4 years (full-time)
Studentship funding provided: Home tuition fees (currently £6,400/year) and maintenance stipend (currently £23,805/year) for 4 years

PhD project description

A fully funded PhD studentship is available as part of the ERC Starting Grant SurFSUP (Surfing on Free Surfaces by Undulating Propulsion), led by Dr Graham Benham in the Department of Mechanical Engineering at UCL. The SurFSUP project aims to underpin the hydrodynamics of Wave-Driven Propulsion (WDP), by combining theoretical, computational, and experimental approaches

Background

Wave-Driven Propulsion is a novel mechanism for locomotion on free surfaces, with potential applications in sustainable marine transport and environmental robotics.  Despite its potential, the WDP mechanism is not fully understood; in particular, the dominant controls on propulsion force and efficiency remain unclear.

To understand the WDP mechanism, high-fidelity numerical simulations are required, which — together with ongoing experimental work — will reveal the underlying fluid mechanics. A key approach for resolving these flows is Direct Numerical Simulation (DNS) of the Navier-Stokes equations, capturing a variety of phenomena, including turbulence and wave-vortex interactions. Since DNS is computationally demanding, additional insight can be gained through simplified modelling via asymptotic analysis. Together, these approaches form a powerful framework for understanding WDP.

Aims

This PhD project will focus on the theoretical and numerical modelling of WDP, with particular emphasis on DNS of the Navier–Stokes equations for free-surface flows. You will develop and apply computational models to investigate different aspects of WDP, such as wave-body interactions and vorticity, and will derive simplified models informed by these simulations. Numerical optimisation techniques (such as adjoint methods) will also be used to improve the efficiency of WDP by modifying the body shape and forcing controls.

The project aims to improve the understanding of WDP, identify efficient propulsion strategies, and connect theoretical predictions with experimental observations. While the primary focus is theoretical and computational, there will be opportunities to engage with experimental validation using data from a custom-built hydrodynamics tank.

The work will involve:

• Direct Numerical Simulation (DNS) of the Navier–Stokes equations
• Development of new and existing numerical methods for free surface flows
• Asymptotic analysis and simplified modelling
• Numerical optimisation techniques, such as adjoint methods
• Experimental validation, including comparison with data from a custom-built hydrodynamics tank.

Person specification

This PhD project would suit a highly motivated student with a strong background in applied mathematics, physics, or engineering, and a particular interest in fluid mechanics and computational modelling. The project is primarily theoretical and numerical, with an emphasis on the Direct Numerical Simulation (DNS) of the Navier–Stokes equations for free-surface flows, although there is scope to engage with experimental work too. 

• Applicants are preferred to have, or be about to receive, a first-class undergraduate and master’s degree (or equivalent) in applied mathematics, physics, engineering, or a closely related discipline, with a clear interest in fluid dynamics and computational modelling.
• A strong understanding of fluid mechanics and/or applied mathematics (e.g. partial differential equations, numerical methods) is essential.
• Experience with mathematical modelling and/or numerical simulation of physical systems is highly desirable.
• Programming experience (e.g. Python, MATLAB, C++, or similar) is highly desirable.
• Excellent organisational and time management skills, together with the ability to work independently, are essential.
• A willingness to engage in interdisciplinary research combining theory, computation, and experiment is important.
• Fluency and clarity in spoken English as well as good written English in accordance with UCL English requirements (TOEFL>92 or IELTS>6.5).
   

Eligibility

Please note that the available funding supports tuition fees at the Home/UK rate. Students who are eligible to pay fees at the UK rate are welcome to apply. Please refer to our website for further information about Home tuition fee eligibility.

International students who are eligible to pay tuition fees at the Overseas rate will also be considered, however the tuition fees covered by the studentship will be limited to the Home/UK level. International students will be required to find additional funding for the remaining Overseas tuition fees.

Applicants whose first language is not English are required to meet UCL’s English language entry requirements.

Please refer to this webpage for full eligibility criteria: Mechanical Engineering MPhil/PhD

How to apply

Eligible applicants should first contact Dr Graham Benham (g.benham@ucl.ac.uk). Please enclose the following documents:

• A personal statement (500 words maximum) outlining (i) your suitability for the project with reference to the criteria in the person specification, (ii) what you hope to achieve from the PhD and (iii) your research experience to-date.
• A CV, including full details of all University course grades to date, and, if relevant, details on scholarships, prizes and scientific papers published or in preparation.
• Academic transcripts for undergraduate (Bachelor) and graduate (Master) studies.
• Names, and email addresses of two academic or professional referees (at least one academic).

After discussing the project with Dr Benham, eligible applicants should also submit a formal PhD application via the UCL website.

The supervisory team will arrange interviews for short-listed candidates.