Model Order Reduction techniques for nonlinear elasticity and thermofluids

About the Project

High-fidelity computer simulations for complex engineering systems are computationally demanding. The challenges compound for problems in nonlinear regime and multiphysics loading conditions. To tackle large-scale complex systems in an efficient manner, model reduction techniques are usually pursued. The widely used mode superposition and component mode synthesis techniques are limited to linear models, and techniques based on proper-orthogonal decomposition struggle to perform in highly nonlinear regimes.

The project aims to develop and apply advanced reduced-order modelling techniques (ROMs) to enable efficient and accurate ROMs for challenging nonlinear problems in elasticity and thermofluids. It uses the finite element method (FEM)-based solvers for high-fidelity simulations and employs projection-based methods, dynamic mode decomposition, nonlinear normal modes, spectral submanifolds and Deep Learning, etc., for developing ROMs for a range of applications, including the development of Digital Twin frameworks.

The major research activities of the project are:

• Develop ROMs for nonlinear solid mechanics problems and thermofluids, e.g., hyperelasticity, Navier-Stokes and Heat Transfer.
• Extend the ROMs for dynamic problems.
• Test and validate the ROMs framework.
• Explore applications of ROMs in advanced materials, energy harvesting, sensing, bioengineering, etc.
• Disseminate research outputs in journals and at conferences.

Perspective applicants are encouraged to contact the supervisor, Dr Chennakesava Kadapa at c.kadapa@napier.ac.uk, before submitting their applications.

Academic qualifications

First degree (minimum 2:1 classification) in Mechanical/Civil/Aerospace/Ocean Engineering or Mathematics or Physics. The candidates must have a master’s degree in relevant fields.

English language requirement

IELTS score must be at least 6.5 (with not less than 6.0 in each of the four components). Other, equivalent qualifications will be accepted. Full details of the University’s policy are available online.

Essential attributes:

• A good fundamental knowledge of solid mechanics, fluid mechanics, heat transfer, engineering maths, numerical methods (FDM/FEM/FVM) and programming skills in MATLAB or Python or C or C++
• Experience of fundamental solid mechanics, fluid mechanics, heat transfer
• Strong knowledge of engineering mathematics and numerical methods for PDEs and ODEs.
• Competent in MATLAB or Python or C or C++ or Fortran or Julia.
• Knowledge of numerical methods (FEM/FVM/FDM), computer modelling and simulations.
• Good written and oral communication skills.
• Strong motivation for research, with evidence of independent research skills relevant to the project.
• Good time management

Desirable attributes:

• Experience in using simulation software such as ANSYS, Abaqus, COMSOL, OpenFOAM, StarCCM+, etc.
• Experience in using Unix/Linux OS.
• Self-motivated.
• Ability to learn and adopt quickly

APPLICATION CHECKLIST

• Completed application form
• CV
• 2 academic references, using the Postgraduate Educational Reference Form (download)
• Research project outline of 2 pages (list of references excluded). The outline may provide details about
1. Background and motivation of the project. The motivation, explaining the importance of the project, should be supported also by relevant literature. You can also discuss the applications you expect for the project results.
2. Research questions or objectives.
3. Methodology: types of data to be used, approach to data collection, and data analysis methods.
4. List of references.

The outline must be created solely by the applicant. Supervisors can only offer general discussions about the project idea without providing any additional support.

• Statement no longer than 1 page describing your motivations and fit with the project.
• Evidence of proficiency in English (if appropriate)

To be considered, the application must use

• the advertised title as project title

PhD Start Date: October 2026

Application link: https://evision.napier.ac.uk/si/sits.urd/run/siw_sso.go?mP9MDnTs1Rwm8ftb3WVhDhXtraMQwXSUMdHC9wIc34es5bJqXf

Funding Notes

International applicants should note that visa application costs and the NHS health surcharge are additional costs to be taken into consideration, and successful applicants will need to cover these expenses themselves.

References

1. Z-Q. Qu, Model Order Reduction Techniques with applications in Finite Element Analysis, Spinger-Verlag, London, 2004. 
2. P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. Schilders, L. M. Silveira. Model Order Reduction, Volume 1: System- and Data-Driven Methods and Algorithms, De Gruyter, 2021. 
3. C. Kadapa and M. Hossain, A linearized consistent mixed displacement-pressure formulation for hyperelasticity, Mechanics of Advanced Materials and Structures, 29:267-284, 2020. 
4. C. Kadapa and M. Hossain, A unified numerical approach for soft to hard magneto-viscoelastically coupled polymers, Mechanics of Materials, 166:104207, 2022. 
5. M. Li, T. Thurnher, Z. Xu, S. Jain, Data-free non-intrusive model reduction for nonlinear finite element models via spectral submanifolds, Computer Methos in Applied Mechanics and Engineering, 434:117590, 2025.