PhD Studentship: Advanced Wall Modelling for Magnetohydrodynamics Simulations Using Physics-Informed Machine Learning

Overview

Magnetohydrodynamics (MHD) is critical in engineering applications such as fusion power plant design and metallurgical processes. However, the computational demands of full-scale 3D MHD simulations are significant, particularly due to the need for extra fine meshing in boundary layers, such as those on Hartmann and side walls, where the behaviour of electric currents must be precisely captured.

The proposed new research aims to develop efficient wall models for MHD simulations using advanced deep learning techniques, specifically Physics-Informed Neural Networks (PINNs) and Physics-Informed Neural Operators (PINOs). By leveraging these methods, the research seeks to reduce the computational load associated with these meshing requirements, enabling faster and more accessible parametric analysis and design optimisation.

The aim of this research is to leverage PINNs and PINOs to build accurate wall models for MHD simulations and extend this work to further develop surrogate models which would provide an additional layer of efficiency by approximating the behaviour of complex systems with significantly reduced computational costs. 

The primary objective of this research is to develop a set of wall models for MHD simulations using PINNs/PINOs that can reduce computational costs and enable fast parametric analysis. The specific goals include:

• Developing mathematical models for PINNs and PINOs tailored to MHD wall modelling, particularly for capturing the behaviour of electric currents in boundary layers adjacent to conductive walls.
• Creating wall models that are applicable to both laminar and turbulent MHD flows.
• Conducting a parametric analysis of key variables, (eg., conductivity ratio, characteristic length, wall thickness, surface heat flux, velocity).
• Investigate various configurations, eg.( (non-)isothermal circular and rectangular pipes subjected to (non-)uniform magnetic fields.
• Investigating the impact of these parameters on critical outputs (eg. pressure gradients, Nusselt number and surface temperature).
• Creating surrogate models that can approximate complex MHD system behaviours with reduced computational demands.
• Develop a flexible, expandable and efficient framework that can be used for design purposes.

This research is expected to provide advanced wall models and surrogate models that significantly reduce the computational load imposed by strict meshing requirements in MHD simulations. By leveraging the strengths of PINNs and PINOs, the developed models will enable rapid parametric analysis and design optimisation, making MHD simulations more practical and accessible. The framework could also be adapted for other fluid dynamics problems where computational efficiency is essential.

Supervisor: Primary supervisor: Dr Hao Xia

Entry requirements

Applicants should have or expect to achieve a 2:1 undergraduate degree in a relevant subject. Particular interest in fluid mechanics, computational engineering and electro-magnetic physics would be an advantage.

Fees and funding

The studentship, which is partially funded by EPSRC, is for 3.5 years and provides a tax-free stipend of £19,237 per annum plus tuition fees at the UK rate. Excellent International candidates are eligible for a full international fee waiver however due to UKRI funding rules, no more than 30% of the studentships funded by this grant can be awarded to International candidates.

How to apply

All applications should be made online via the 'Apply' button above. Under programme name, select *School of AACME/AAE Department of Automotive and Aeronautical Engineering*. Please quote the advertised reference number: *AAE-HX-2501* in your application.

To avoid delays in processing your application, please ensure that you submit the minimum supporting documents.

The following selection criteria will be used by academic schools to help them make a decision on your application.

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