Post-doctoral Research Associate (Cardiff University)

Mathematical modelling and smart coatings: fighting the COVID-19 pandemic with Smart Separations Ltd (SSL). The project was funded by the Welsh Government (Sêr Cymru “Tackling COVID-19” call).

I worked as part of a team, developing mathematical models of the transmission of COVID-19 in indoor spaces, with a focus on airborne transmission. The novel modelling framework involved numerical and analytical solutions of the advection-diffusion-reaction equation governing the transport of viral particles, coupled with Computational Fluid Dynamics (CFD) simulations to model indoor air flows.

My contribution was to extend the modelling framework to incorporate a simple air purifier model, which removes viral particles from the room while also modifying the flow in the room. This framework was then used to investigate an air sanitising product developed by SSL to help understand the efficiency and effectiveness of this product. 

In addition to writting a report for SSL, I also contributed a report on air purifiers for the Welsh Government TAG (Technical Advisory Group) on the pandemic, reviewing existing research on air cleaning devices.

The team:

Post-doctoral Research Associate (Swansea University)

On completion of my PhD, I began a 3 year post-doctoral position at Swansea University (Feb 2017 to Oct 2020) studying electromagnetics. The aim of this project was to use a finite-difference time-domain (FDTD) method for solving Maxwell's equations on complex geometries, and to apply a reduced order model to facilitate a fast and cheap design process for a thermal solar panel coating.

This work was conducted in partnership with the Luxembourg Institude of Science and Technology (LIST) with the aim being a means of selecting geometric properties of a nano-scale unit cell with a metallic omega-shaped inclusion that promoted desired electromagnetic scattering effects (i.e. absorption at some frequencies and reflection at others).

My contributions included the incorporation of periodic boundary conditions in an existing FDTD code to simulate the behaviour of a single unit cell when it is part of a larger array. Additional modifications to this code were also attempted such as a co-ordinate transformation to convert geometric parameters (such as radius and length) into material parameters (such as electric permittivity and magnetic permeability) and a proper generalised decompostion (PGD) iterative process so that these parameters could be treated as additional co-ordinates without making the problem prohibitively large.

Regrettably, the co-ordinate transform and PGD never fully worked. In order to get a useable solution within the available timeframe we instead implemented a proper orthogonal decomposition (POD) of design space to provide the necessary reduced order model to aid in the design process.

The team:

PhD (Cardiff Univeristy)

I studied a PhD at Cardiff University in the School of Mathematics. I worked in the field of hydrodynamic stability theory (fluid mechanics) and completed the course in 2017 with a thesis entitled Linear disturbance evolution in the semi-infinite Stokes layer and related flows.

By studying linear stability equations such as the Orr-Sommerfeld equation, the behaviour of small disturbances to known hydrodynamic flows (such as the Blasius boundary layer, Poiseuille flow, Couette flow etc) can be studied, with unstable disturbances leading to a significant change in the flow behaviour such as transition to turbulence. In this project, we applied these well-established methods to the semi-infinite Stokes layer, being the flow generated in a semi-infinite region of fluid by the oscillatory motion of a bounding wall, with the temporally periodic nature of this flow accounted for using Floquet theory.

Complimenting this stability analysis (performed numerically using Matlab) was direct numerical simulation (DNS) of the linearised Navier-Stokes equations which provided a phenomenological account of the predicted behaviour. Furthermore, the stability problem was modified to determine the absolute or convective nature of instabilities (i.e. whether they grow or decay at fixed spatial locations).

In this work, it was demonstrated that the Stokes layer is subject to an absolute form of instability with an onset Reynolds number corresponding to the onset of linear instability. Furthermore, by demonstrating that the pointwise behaviour is characterised by several absolutely unstable modes, insight was provided into the formation of the family-tree structure of the impulse response that had previously been reported for this flow.

Finally, a modification of the Stokes layer was considered, in which the wall motion was modified by low-amplitude, high-frequency harmonic oscillations to crudely immitate the noise associated with the mechanical movement of the wall in experiments (while retaining periodicity). It was demonstrated that in addition to a dramatic destabilisation of the flow, even at modest noise levels, the family-tree structure was significantly disrupted and the nature of the absolute instability changed.

This work was carried out with the help and support of