Study level

Master of Philosophy


Vacation research experience scheme


Topic status

We're looking for students to study this topic.


Dr Michael Dallaston
Lecturer in Applied and Computational Mathematics
Division / Faculty
Faculty of Science


When liquids of different densities mix, they can produce complex fingering patterns. This is particularly important in the flow of liquid in underground porous aquifers, where the density of the groundwater can be influenced by salinity or heat, as well as the insulation properties of porous materials. Another important application is the still-prototypical use of aquifers for carbon sequestration; the dissolution of CO2 into groundwater has a complex effect on its density, and convective mixing is crucial for accelerating the dissolution/storage process.

This project will involve the modelling, and analytical or semi-analytical study of the onset of convection in porous media, including the prediction of key parameters such as the onset time and the critical wavelength. The project may also involve the development of a numerical (e.g. finite volume) scheme to solve the full nonlinear system, more advanced methods to improve the stability analysis, and exploration of the effect of inclination on porous convection.

Further reading

  • D.A. Nield and A. Bejan. Convection in Porous Media. Springer, New York, NY, 2013.
  • H.E. Huppert and J.A. Neufeld. The fluid mechanics of Carbon Dioxide sequestration. Ann. Rev. Fluid Mech., 46: 255-272. 2013.

Research activities

In this project you may expect to do some or all of the following:

  • mathematical modelling (PDEs)
  • development of numerical code to simulate PDEs from fluid dynamics
  • analytical methods such as linear stability analysis to provide insight into numerical observations
  • exploration of the effect of parameters, such as the angle of inclination of a system
  • academic writing/communication.


This project aims to produce a robust and efficient numerical code (in Matlab, say), verified against linear stability and previous results in the literature, for computing solutions of the equations that govern convection in porous media.

Another ambitious aim is to build up a comprehensive picture of the effect of angle on porous convection by using such a numerical method to build a bifurcation diagram of steady convection patterns.

Skills and experience

Experience in programming (e.g. Matlab) and numerical solution of PDEs essential. Knowledge of fluid mechanics principles advantageous but not essential.


You may be eligible to apply for a research scholarship.

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Contact the supervisor for more information.