In this edition, we profile Dr. David Moxey, Postdoctoral Research Associate, Imperial College, London, who focuses in the area of high-order spectral element methods.
I studied at University of Warwick between 2003 - 2007 completing an M.Math and PhD in Mathematics. I have been a Postdoctoral Research Associate at Imperial College London since 2011. Recently, I accepted a lectureship at Exeter University commencing in March 2017, focused on the area of research that I specialise in - developing the next generation of numerical methods for computational engineering. My interest in this area began while studying for my undergraduate degree, where I was involved in a project focused on finite element methods. During my PhD, I participated in a really interesting CFD project where we used the spectral element method (SEM) to understand the transition to turbulence in a pipe flow, an important problem in fundamental flow dynamics. This led quite naturally to my position at Imperial College, where my current research group specialises in this kind of numerical method and how they apply to fluids problems. My area of research has afforded me the opportunity to work with many different and very talented people, investigating the possibilities that this method holds in a much broader scope of engineering problems.
Essentially my goal is to develop the next generation of numerical methods for computational engineering problems, which I believe lie in the realm of high-order spectral element methods. These methods have been well developed in academia across the last 20 years, but, more recently, they are viewed as one of the ways that we can make efficient use of a very challenging hardware landscape, utilising different types of computational hardware from GPU’s, CPU’s to more exotic technologies. Although they are more difficult to use and implement than the more traditionally-used methods, these advanced methods being developed by academia look very promising in fluids and other areas, and are already being applied to solve industrial problems. Right now, I’m looking at how we can use this technology to more efficiently model unsteady flow problems, which presently lie outside the scope of current industry-standard CFD tools.
I was a little bit unsure about what I wanted to do until I got to university, but after being involved in a fantastic undergraduate research project, I really got a taste for academia and research. Looking back, my mum and aunt are teachers and my dad has always been quite technical and into computers, so this career has been quite a natural one for me. Their influence motivated me from a very early age to have a technical and learning aspect to my career, which has guided me down the academic career path. I think that they have also helped me in focusing my research. Explaining what I do to my family and friends has firmly cemented the belief that it’s really important for academic work to not only be an academic exercise but to have real, practical applications, and my intention is to develop my work with industry while in an academic role.
Probably my biggest contribution to fluid dynamics is from my PhD, where I investigated the transition to turbulence in pipe flow. This was first investigated by Reynolds about 130 years ago and where the infamous ‘Reynolds number’ made its first appearance. This parameter determines whether a flow remains laminar (steady and ordered) or turbulent (unsteady and chaotic), but for pipes, an unsolved problem has been finding the ‘critical’ number that determines the transition from laminar to turbulent flow. I was lucky and fortunate to work with a very talented PhD supervisor on the project and we identified some of the mechanisms that lie underneath that transition process, obtaining a very good understanding of this new insight into the problem and, with a strong collaboration with another experimental group, figured out the critical Reynolds number.
In terms of numerical methods research, one area I am really interested in is perhaps something that isn’t so popular amongst the community but is still vitally important. Generally in high-order methods, we – myself included -- spend a lot of time developing a really complicated solver that does all the fluid dynamics modelling. To have practical applications, we’d like investigate these problems over planes or cars, which have a lot of complex geometrical features – for a good example of this, have a look at the front wing of a Formula 1 car. However the thing that’s often overlooked is that you need to have a mesh of your geometry to run your simulation. In high-order methods this turns out to be very hard, since you need to be able to curve elements where they meet the body of the plane or the car or whatever you are trying to model. One of my biggest projects over the last couple of years has been investigating ways we can really robustly generate meshes for these kind of geometries so that we can actually do the simulations. I think it is a quite under appreciated area of research but as these methods are becoming more popular and we want to investigate more complex geometries, people are picking up on this as being a really important problem to solve.
It is a difficult question to answer, since my area of research is clearly very reliant on computing and we have this really difficult problem, which is how we use the maths to align to the kinds of hardware that we are looking at. All these different types of hardware including GPU’s and CPU’s are being introduced but we don’t really know what is coming in the next 10 years. The really big problem is how we use the hardware to its fullest potential. Some of this is about writing lots of operations every second and a larger part of it is about how much memory your algorithms are using. I think the next big challenge is how we use the next generation of computing hardware and how we match our algorithms to that.
If you ask me on different days I’m sure I’ll give you different answers! I’ve always been a big space geek, reading about all the NASA missions and programs since I was little. Naturally then, one of my big heroes over the last couple of years has been Elon Musk, founder of a whole bunch of companies including Tesla and PayPal, but in particular SpaceX. I remember reading about them in the early 2000’s and it’s amazing that in a matter of years they’ve done what others have taken decades to do. One of the reasons I really admire Musk is because of his ethos and philosophy. He has a vision of ‘I want to do this’: be that ‘I want to reduce our carbon emissions’, ‘I want to explore space’, or ‘I want to make electric cars’. He comes up with ideas that are a bit crazy and timelines that people might think are unattainable, but over the course of a couple of years he has the right set of people around him, and has got the ball rolling in the right direction to achieve his goal. I think that, from an academic perspective, we can learn a lot from this philosophy and it’s something I hope to take forward in my own career.
I am one of the project leaders of an open-source software package called Nektar++, which is being developed by myself and a number of other collaborators and colleagues. Nektar++ is a framework for the SEM and aims to help overcome some of the difficulties in practically using this method, making it easier to write solvers for it. An overview of Nektar++ has been published in Computer Physics Communications, covering our strategy and the use of the software to solve problems in various fields. We also have a recent publication in Computer Methods in Applied Mechanics and Engineering that focuses on how different mathematical formulations translate to computational efficiency.
On mesh generation, I have been supervising some exciting work, recently published in Procedia Engineering, that looks at how we can encompass a number of different high-order mesh generation techniques from the literature to form a robust and very efficient method to generated curved meshes.
Finally, on the application side, our group has a recent publication in AIAA Journal, which looks at the modelling capabilities of the SEM in industrial flow problems with collaborators in industry. In particular, we have been investigating the dynamics of wingtip vortices, which you might often see being shed from the wingtips of commercial aircraft as they take off. These have very strong dynamics that generates a lot of turbulence, and are one of the main reasons that aircraft have to be spaced widely apart when they take off. In motorsport applications too, these vortices are important in generating downforce, which determines the performance of a car. This is one of the reasons that the front wing of an F1 car looks so complex: vortices are generated at the front wing, then tracked onto the rear surfaces of the car in order to generate downforce. Our work demonstrates how unsteady simulations using the SEM can yield accurate results for predicting the strength and position of these vortices.
Publications relating to text above:
Lots more listed on website: https://davidmoxey.uk/publications.html
I am interested in connecting with anyone who is looking at unsteady flow problems in industrial settings, as this is a big part of my research. These methods are specifically designed to look at unsteady flow that evolves in time, so that we can capture a full range of the structures that are being generated. These methods have lots of potential outside of fluid dynamics too, so I’d definitely be interested to talk to anyone that thinks the SEM could be useful for them. Finally, it would be great to connect with people that are having issues generating curved meshes for high-order simulations, to see if our recent developments might help in this area.