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Numerical computation of interface problems


   Faculty of Engineering and Physical Sciences

   Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

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 [1], 

Developing and/or analysing novel approaches for transporting the computational mesh. This could be based on the discrete DeTurck trick [2], 

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 (). 


Funding Notes

This project is eligible for several funding opportunities. Please visit our website for further details.

References

References 
[1] C M Elliott, T Ranner, A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains, IMA Journal of Numerical Analysis, Volume 41, Issue 3, July 2021, Pages 1696–1845, https://doi.org/10.1093/imanum/draa062 
[2] C M Elliott, H Fritz, On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick, SMAI journal of computational mathematics, Volume 2, 2016, Pages 141-176, https://doi.org/10.5802/smai-jcm.12 

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