I completed my PhD thesis in 2009, under the supervision of Professor Dwight Barkley. I examined, through numerical techniques, the evolution of small disturbances to a steady flow in an expanding pipe and in flow past a uniform circular cylinder. I also explored how turbulent puffs may be created in a cylindrical pipe of gradually increasing radius.

More generally, my research interests extend to the numerical solution of PDEs, Numerical Linear Algebra, High Performance Computing and Parallel Computing. Below is a summary of my current research interests.

I am currently developing numerical models for simulating action potentials in atrial myocardium. The approach taken is to use the mono domain model, rather than fully resolving the detailed changes of the various cell ion channels in the bidomain model, to simplify computation. It is hoped this model can be used to simulate atrial fibrillation to aid clinical understanding and improve treatments.

Spectral/hp element methods combine the geometric flexibility of widely-used finite element techniques with the exponential error convergence of spectral approaches. I am currently developing support for three-dimensional solvers in Nektar++.

My PhD thesis examined the transient growth of perturbations to a steady flow in an expanding pipe - that is, the how slight disturbances to the flow entering the pipe develop as they move downstream. This research was conducted via a Spectral/hp-Fourier method using SEMTEX written by Dr. Hugh Blackburn.