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Multi-Fluids Discontinuous Control Volume – Finite Element Methods(CVFEM) for Subsurface Geothermal Flows

Project Description

Immiscible displacement flows have been widely studied in contaminant dispersion in the subsurface (e.g., solute transport to aquifers, radionuclide’s diffusion in nuclear storage, etc) and oil & gas production (e.g., enhanced oil recovery, heavy oil production, etc) applications. Equations that represent such fluid displacement are mostly hyperbolic and nonlinear, and the solutions are often discontinuous. Several computational methods have been developed over the past 50 years to improve our understanding of mmultiphase fluid flows in complex geometries. More recently, families of stable mixing finite element formulation have been used to consistently represent mass conservation whereas improving numerical accuracy.

This project will extend the current mixed control volume finite element method (CVFEM) formulation for multi-fluids flow to numerically investigate shock-capturing schemes for multicomponent multiphase thermal flows in porous media. The project will exploit the existing state-of-the-art opensource flow simulator model to develop high-order accurate methods. This will involve conducting high-fidelity numerical simulations with high-order flux-limiters and assessing model computational scalability (HPC).

The successful candidate should have (or expect to achieve) a minimum of a UK Honours degree at 2.1 or above (or equivalent) Mathematics, Physics or Mechanical/Chemical/Civil/Petroleum Engineering.

Essential Background in Advanced mathematics, fluid dynamics and programming.
Knowledge of: Fluid dynamics; Numerical methods; Computational linear algebra; Fortran or Python or C languages.


Formal applications can be completed online: You should apply for Degree of Doctor of Philosophy in Engineering, to ensure that your application is passed to the correct person for processing.


Informal inquiries can be made to Dr J Gomes () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ().

Funding Notes

There is no funding attached to this project. It is for self-funded students only.


J. Gomes et al. (2016) “Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling”, Intl. J. Num. Meth.Fluids, 83:431-445;

D. Pavlidis et al. (2016) “'Compressive advection and multi-component methods for interface-capturing”, Intl. J. Num. Meth. Fluids. 80:256-282;

J. Gomes et al. (2013) “Reservoir Modeling for Flow Simulation Using Surfaces, Adaptive Unstructured Meshes, and Control-Volume-Finite-Element Methods”, SPE Reservoir Simulation Symposium, SPE-163633-MS;

E. Wendland, D. Flensberg (2005) “Numerical Solution of Two-Phase Flow for the Advection-Dominated and Non-Linear Case”, Adv. Water Res. 28:643-660.

How good is research at Aberdeen University in General Engineering?

FTE Category A staff submitted: 38.60

Research output data provided by the Research Excellence Framework (REF)

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