EPSRC Project Proposals 2025/26 - Numerical Computation of Interface Problems

Number of Positions: 1

Funding: School of Computer Science Scholarship, providing the award of full academic fees, together with a tax-free maintenance grant at the standard UKRI rate of £20,780 per year for 3.5 years. 

Lead Supervisor’s full name & email address

Dr Thomas Ranner: T.Ranner@leeds.ac.uk

Project summary

Interface problems arise in many different areas of engineering, physical and life sciences. A typical example is the interface between two immiscible fluids separated by an interface governed by surface tension. A more complicated example would involve an active swimming (micro-) organism moving through different fluids. In this project, we are interested in developing moving mesh finite element methods for their dynamical simulation. We aim to produce efficient, accurate and robust computational tools.

The specific aspect of the project to be worked on will depend on the strengths of the candidate. Good projects in this area could include:

• Mathematical or numerical analysis of the underlying partial differential equation system and our finite element approach. This could be based on our abstract framework
• Developing and/or analysing novel approaches for transporting the computational mesh. This could be based on the discrete DeTurck trick
• Developing and implementing methods and models for a specific application area such as active swimmers (in a variety of environments), tumour growth, surfactants, or any other relevant problem.

Informal enquires are welcome from all potential candidates. For more details, please contact Dr Thomas Ranner (T.Ranner@leeds.ac.uk). Machine learning applications to improve project cost, risk, and schedule performance

Please state your entry requirements plus any necessary or desired background

A first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline.

Candidates should have a strong undergraduate degree in a relevant area (including but not restricted to mathematics, physics or computer science). A suitable candidate for this project should have some knowledge of aspects of the design, analysis and/or implementation of finite element methods for partial differential equations. Prior experience in research (e.g. a Masters degree or work in industry) is a plus. 

Subject Area

Applied mathematics, computer science & IT, mathematics

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