Aerospace Engineering : Fully Funded EPSRC PhD in Data-driven methods to accelerate discontinuous Galerkin solver for Boltzmann-BGK equation for rarefied, hypersonic flow (RS752)

Funding provider: EPSRC

Subject areas: Computational Engineering; Gas Dynamics; High-performance Computing

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

Supervisors: Dr 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 data-driven 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 the Navier-Stokes equation are not eligible. Solving the BBGK equation is extremely challenging due to the high computational cost originating 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 data-driven approaches, including but not limited to machine learning and reduced order modelling, into the DG finite element solver to reduce computational costs while maintaining accuracy. The key objective of this work will be to provide step-change solver acceleration using data-driven 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 in 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.

Candidates must hold a UK Bachelor's degree with a minimum of Upper Second Class honours in Aerospace or a related subject. Or overseas Bachelor's degree deemed equivalent to UK Bachelor (by UK ECCTIS) and achieved a grade equivalent to UK Upper Second Class honours in Aerospace or a related subject.

Or a master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University) – see country-specific qualifications

IELTS 6.5 overall (with at least 6.0 in each individual component) or Swansea recognised equivalent. Details on the Swansea University English Language entry policy can be found here.

ATAS 

Please note that the programme requires some applicants to hold ATAS clearance, further details on ATAS scheme eligibility are available on the UK Government website.

ATAS clearance IS NOT required to be held as part of the scholarship application process, successful award winners (as appropriate) are provided with details as to how to apply for ATAS clearance in tandem with the scholarship course offer.

This scholarship covers the full cost of UK tuition fees and an annual stipend of £19,237.

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

Scholarship open to UK and international fee-eligible applicants.

EPSRC DTP studentships are available to home and international students. Up to 30% of our cohort can comprise international students, once the limit has been reached, we are unable to make offers to international students. We are still accepting applications from international applicants.

International students will not be charged the fee difference between the UK and international rates. Applicants should satisfy the UKRI eligibility requirements.

To apply, please complete your application online with the following information:

1. Course choice – please select:

Aerospace Engineering / PhD / Full-time / 3 Years / October

In the event you have already applied for the above programme previously, the application system may issue a warning notice and prevent application, in this case, please email pgrscholarships@swansea.ac.uk where staff will be happy to assist you in submitting your application.

2. Start year – please select 2025

3. Funding (page 8 on the application process) – ‘Are you funding your studies yourself?’ – please select No; ‘Name of Individual or organisation providing funds for study’ – please enter ‘RS752 - Hypersonic Flows’

*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.

Equality, Diversity and Inclusion (EDI) Monitoring Form (online form)

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

· CV
· Degree certificates and transcripts
· A cover letter
· One reference
· Evidence of meeting English Language requirements (if applicable)
· Copy of UK resident visa (if applicable)
· Confirmation of submission of EDI Form

*For ALL scholarship applications from February 2023 an EDI (Equality, Diversity and Inclusion) Monitoring Form is required.

Informal enquiries are welcome; please contact Dr. 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.