University of Exeter funding: Improving mesh generation

Improving mesh generation for high-order simulations. Self-funded PhD in Engineering Ref: 3073

About the Research Project


Dr David Moxey, Department of Engineering, College of Engineering, Mathematics and Physical Sciences,  University of Exeter

Streatham Campus, University of Exeter, Exeter, EX4 4QJ

Project Description:
The combination of cutting-edge simulation software and modern computing hardware has the potential to give scientists and engineers in both industry and academia the ability to investigate complex fluid dynamics problems at an unprecedented level of detail and fidelity. However, the core numerical methods and models that underpin present industry-standard commercial tools have remained relatively unchanged across the last two decades. As computational hardware becomes more advanced, it is becoming more and more difficult for these tools to effectively use the power offered by modern supercomputers.

One of the most recent developments in simulation technology towards tackling this issue is the trend towards using spectral element methods, which use a high-order polynomial expansion inside each element versus the linear functions used in current industry-standard tools. This gives several advantages over widely-used techniques such as linear finite element or finite volume methods. Most notably, these methods allow us to use computational hardware more effectively, giving far greater fidelity for an equivalent or reduced cost when compared against commercial tools.  Whilst high-order methods therefore have great potential in tackling some of the major bottlenecks in current engineering tools, one of the major challenges that stands in the way of these methods becoming more widely used, for industrial applications in particular, is the generation of high-order meshes. In a high-order setting, the edges and faces of elements have to be curved so that they align with complex geometrical features that are standard to modern aeronautical and automotive design (such as those that can be found, for example, on the front wing of a Formula 1 car). For the method to be efficient, the mesh must also be coarse so that when high-order polynomials are introduced, the simulation is not vastly over-resolved. The combination of these two requirements means that when curvature is introduced into an element, it frequently causes the element to self-intersect and become invalid. Developing techniques to avoid these issues is therefore at the forefront of spectral element method research. 

The aim of this project is to improve various aspects of the high-order mesh generation process by considering techniques that aim to correct invalid meshes through an energy minimisation approach. The successful candidate will then apply these techniques in the context of a number of important fluid dynamics test cases and application areas to demonstrate their effectiveness in addressing some of the key challenges facing this topic. These developments will be performed inside the open-source Nektar++ spectral element framework ( and its related mesh generation software NekMesh

For more information about the project and informal enquiries, please contact the primary supervisor Dr David Moxey

Information about current fees can be found here:
Information about possible funding sources can be found here:

Entry requirements

Applicants for this research project must have obtained a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology. Experience in Engineering is desirable.

If English is not your first language you will need to meet the English language requirements and provide proof of proficiency. Click here for more information and a list of acceptable alternative tests.

How to apply

To apply, please use the 'Apply Now' button above.

You will need to upload the following documents to the application form. Please note our preferred format is PDF, each file named with your surname and the name of the document, eg. “Smith – CV.pdf”, “Smith – Cover Letter.pdf”, “Smith – Transcript.pdf”:

Letter of application outlining your academic interests, prior research experience. You should also indicate your reasons for wishing to undertake the project.
Transcript(s) giving full details of subjects studied and grades/marks obtained. This should be an interim transcript if you are still studying.
Two references (see Reference information section below)
If you are not a national of a majority English-speaking country you will need to submit evidence of your current proficiency in English.  For further details of the University’s English language requirements please see

Reference information

If possible, please upload your references to the online application form. If your referees would prefer to send their reference directly to the University, please ask them to send these via email to

References should be in the form of a letter. Referees must email their references to us from their institutional email accounts. We cannot accept references from personal/private email accounts, unless it is a scanned document on institutional headed paper and signed by the referee.

All application documents must be submitted in English. Certified translated copies of academic qualifications must also be provided.

The closing date for applications is midnight (GMT) on 03 June 2019


Application deadline:3rd June 2019
Value:This project is self-funded
Duration of award:Not applicable
Contact: EMPS Postgraduate Research Office