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 (small pockets of turbulence in an otherwise laminar flow) may be created in a cylindrical pipe of gradually increasing radius. After moving to Imperial College London my research focused on the development of efficient implementations of spectral/hp element methods, applied to modelling of cardiac electrophysiology. I have since transitioned to investigating biomedical challenges in the clinical treatment of atrial arrhythmias.
I have developed a high-order spectral/hp element solver for the monodomain and bidomain equations, built on the Nektar++ framework, allowing the simulation of action potential propagation in anatomically accurate models of the heart. I have also developed an novel manifold discretisation for high-order finite element methods and applied it to modelling conduction in patient-specific left atrial geometries (JCP, 2014). This significantly improves the efficiency and reduces the runtime of the model over conventional finite element techniques. Current work includes integrating imaging and intracardiac electrogram data gathered during clinical procedures into the model. It is hoped the model can soon be used to simulate patient-specific electrophysiological activity, improve understanding of the mechanistic drivers of atrial arrhythmias and guide clinical intervention to improve patient outcomes.
Spectral/hp element methods
Spectral/hp element methods combine the geometric flexibility of widely-used finite element techniques with the exponential solution convergence of pure spectral approaches for smooth solutions. These methods have been implemented in the open-source software framework Nektar++, for which I am a lead developer.
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 using the Spectral/hp-Fourier method implemented in SEMTEX, written by Dr. Hugh Blackburn.