Multiscale computational modelling of heterogeneous transport processes

Study level


Master of Philosophy


Topic status

We're looking for students to study this topic.


Dr Elliot Carr
Senior Lecturer
Division / Faculty
Science and Engineering Faculty
Professor Ian Turner
Division / Faculty
Science and Engineering Faculty


Computational models of a multiscale nature, whether they involve partial differential equations with fine-scale variation in coefficients or distinct processes at multiple scales, are ubiquitous across engineering and scientific disciplines. For such problems, direct numerical solution of the governing equations is infeasible due to the huge amount of computational resources required to resolve the smaller scale.

Such numerical issues motivate the need for either spatial-averaged models that aim to efficiently and accurately approximate the averaged fine-scale solution on a coarser scale or multiscale models that aim to resolve both the fine and coarse scales simultaneously in a computationally-efficient way.

This project aims to contribute fundamental results to the field of multiscale modelling and develop new computational multiscale models for simulating processes governed by general transport equations (e.g. fluid flow and heat transfer).

Research activities

You will meet regularly with the supervisory team to acquire new knowledge, brainstorm ideas, discuss your progress and receive feedback and direction on your work. This project will involve pen and paper derivations and calculations, developing code in MATLAB and communicating your work in written form.


You will develop new skills in:
  • multiscale modelling
  • partial differential equations
  • computational mathematics
  • programming (MATLAB)
  • mathematical writing
  • LaTeX typesetting.
New techniques/knowledge/results generated during your project will be published in leading mathematical/scientific journals.

Skills and experience

This project can be tailored to your study level whether you are an Honours, Masters or PhD student. This topic can also be personalised to suit your individual interests and skills. Ideally, the successful student will have some prior experience with solving partial differential equations in MATLAB.


You may be able to apply for a research scholarship in our annual scholarship round.

Annual scholarship round



Contact the supervisor for more information.