Discontinuous-Galerkin Methods for Two-phase Flows in Porous Media

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 multiphase 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 flow in porous media. The project will exploit the existing state-of-the-art open-source 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 have, an Honours Degree at 2.1 or above (or equivalent) in mathematics, physics, mechanical or chemical engineering, and have a strong interest in mathematical modelling, numerical analysis and computer programming. It is essential that candidates have experience using Linux. It is desirable, but not essential, that candidates have experience using HPC platform, programming (in Python and Fortran or C) and have strong interest in CFD.