Department of Mathematics

MSc Courses in Mathematical Sciences

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Contaminents, Oil and Water: two phase flow and uncertainty

Flow through porous media is a particularly important problem. It may model, for example, the flow of oil and gas in an oil field, spread of contaminents in ground water, or strage of C02 in reservoirs. This project will examine the phyical derivation of the equations, examine numerical computations of two-phase flow. Of particular interest is when the porosity of the media is taken to be a random field. The aim is to develop efficient numerical methods for the problem and techniques for evaluating the uncertainty.

Simulation of granular flow and growing sandpiles

The p--Laplacian is a variation on the standard Laplacian and allows for fast and slow diffusion for large p values and has been proposed as a model for granular flow. This project will investigate the numerical simualtion of the problem using novel basis functions and compare to standard finite element, finite difference and Galerkin techniques. We will examine the efficiency of the algorithms and explore the numerical approximations numerically as well as perform some analysis. We will numerically grow sand piles in one and two dimenions.