Computational Engineering: Fully Funded EPSRC Studentship-AI accelerated discontinuous Galerkin solver for Boltzmann-BGK equation for rarefied, hypersonic flows (RS817)

Funding provider: EPSRC 

Subject area: Computational Engineering; Gas dynamics; High-performance Computing 

Project start date: 1 October 2025 (Enrolment open from mid-September) 

Supervisors: Xi Zou and Professor Ben Evans 

Aligned programme of study: PhD in Aerospace Engineering 

Mode of study: Full-time 

Project description: 

This PhD project will focus on developing AI-based methods to accelerate the Swansea University in-house discontinuous Galerkin (DG) finite element solver for the Boltzmann-BGK (BBGK) equation (developed  by B.J. Evans, O. Hassan and K. Morgan). This solver directly solves the Boltzmann-BGK model equation for the velocity distribution function, which is a fundamental quantity in rarefied gas dynamics and statistical physics. The BBGK equation is the governing equation for hypersonic, rarefied flow problems in aerospace and microfluidics, where the continuum and equilibrium assumptions of Navier-Stokes equation are not eligible. Solving the BBGK equation is extremely challenging due to the high computational cost originated from its high-dimensionality. As a deterministic method, the potential of a DG method for solving the hyperbolic BBGK equation has not yet been fully exploited by the rarefied gas dynamics community which continues to rely heavily on the costly direct simulation Monte Carlo (DSMC) method. To date there are few practical 3D solvers that address a direct solution of the Boltzmann-BGK equation. 

The project aims to integrate AI accelerated approaches, including but not limited to machine learning and deep neural networks, into the DG finite element solver to reduce computational costs while maintaining the accuracy. The key objective of this work will be to provide step-change solver acceleration using the developed techniques to enhance the efficiency of Swansea’s in-house DG-BBGK solver. The student will further develop this world leading solver, performing numerical studies of DG finite element methods and kinetic theories of rarefied gas dynamics, taking advantage of supercomputing resources at facilities based in Swansea, in the United Kingdom, and overseas. The student will also have the opportunity to participate activities in the wider PGR research community within the Zienkiewicz Institute (ZI) for Data, AI and Modelling including HPC training sessions, the ZI research seminar series as well as financial support for attending international conferences.  This project is expected to lead to collaborative research opportunities with our industry partners across the UK aerospace sector. 

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations 

Applicants for PhD must normally hold an undergraduate degree at 2.1 level (or Non-UK equivalent as defined by Swansea University) in Engineering or similar relevant science discipline. See - Country Specific Entry Requirements - Swansea University

English Language 

IELTS 6.5 Overall (5.5+ each comp.) or Swansea University recognised equivalent. Full details of our English Language policy, including certificate time validity, can be found here. 

For further information, please see the Swansea University English Language Entry Policy. 
If you have any questions regarding your academic or fee eligibility based on the above, please email pgrscholarships@swansea.ac.uk with the web-link to the scholarship(s) you are interested in. 

This scholarship covers the full cost of tuition fees and an annual stipend at UKRI rate (currently £20,780 for 2025/26). 

Additional research expenses of up to £1,000 per year will also be available. 

To apply, please complete your application here in Learner Gateway 

In order to be considered for this scholarship award the following steps are also required. 

1. In section ‘Programme Related Information’ please input the relevant RS Code for the scholarship award i.e. RS817 – Hypersonic Flows 
2. In section ‘Research’ you will see ‘Proposed project title/studentship title’* (Mandatory) 
   • In ‘Proposed project title/studentship title’ please input either:  
     • the relevant scholarship advert link, or 
     • the RS Code, or  
     • the scholarship title.   
   • Please leave Proposed Supervisor field blank 
   • Please leave Research Project (if applicable) blank 
   • In ‘Do you have a proposal to upload?*’(Mandatory) Please select Yes 
   • Then upload copy of advert (you can save the advert by clicking print, and then print to pdf) 
3. In section ‘Funding information’ please choose the option ‘Scholarship Funding’ only. Please ensure no other options are selected.  

*It is the responsibility of the applicant to list the above information accurately when applying, please note that applications received without the above information listed will not be considered for the scholarship award. 

One application is required per individual Swansea University led research scholarship award; applications cannot be considered listing multiple Swansea University led research scholarship awards. 

NOTE: Applicants for PhD/EngD/ProfD/EdD - to support our commitment to providing an environment free of discrimination and celebrating diversity at Swansea University you are required to complete an Equality, Diversity and Inclusion (EDI) Monitoring Form in addition to your programme application form.    

Please note that completion of the EDI Monitoring Form is mandatory; your application may not progress if this information is not submitted. 

As part of your online application, you MUST upload the following documents (please do not send these via email): 

• CV 

• Degree certificates and transcripts (if you are currently studying for a degree, screenshots of your grades to date are sufficient) 

• A cover letter including a ‘Supplementary Personal Statement’ to explain why the position particularly matches your skills and experience and how you choose to develop the project. 

• One reference (academic or previous employer) on headed paper or using the Swansea University reference form. Please note that we are not able to accept references received citing private email accounts, e.g. Hotmail. Referees should cite their employment email address for verification of reference. 

• Evidence of meeting English Language requirement (if applicable). 

• Copy of UK resident visa (if applicable) 

• Confirmation of EDI form submission 

Informal enquiries are welcome; please contact Xi Zou xi.zou@swansea.ac.uk 

*External Partner Application Data Sharing – Please note that as part of the scholarship application selection process, application data sharing may occur with external partners outside of the University, when joint/co-funding of a scholarship project is applicable.