Research and teaching of computational applied mathematics. Dr Chappell teaches on the modules Numerical Methods for Ordinary Differential Equations and Mathematical Recipes. He conducts research in computational applied mathematics with applications in industry.
In 2007 Dr Chappell completed his PhD at the University of Brighton on modelling transient acoustic fields radiated by vibrating elastic structures with application to modelling sound fields from loudspeakers.
He continued to work at the University of Brighton until 2009, conducting research in the numerical analysis and solution of the wave equation in unbounded domains and on numerical approaches for nearfield acoustic holography, a process whereby the acoustic intensity field may be studied on a structure from measurements of the exterior acoustic field.
In 2009 Dr Chappell moved to the University of Nottingham to work as a postdoc researching high frequency wave energy transport in built up systems. This work lead to a knowledge transfer secondment position with Jaguar Land Rover in January 2012 on modelling high frequency wave energy flow in large moulded aluminium car body components. In September 2012 he started work as a lecturer in numerical analysis at Nottingham Trent University. In September 2017 he was promoted to his present Associate Professor role.
Dr Chappell's research interests surround Industrial mathematics, mathematical modelling and numerical analysis including:
- Time-dependent wave propagation problems
- Boundary integral and boundary element methods
- Convolution quadrature methods
- Inverse problems in acoustics, electromagnetics and applications in medical imaging
- Fluid-structure interaction problems
- High frequency wave modelling
- Wave energy flow in complex industrial and engineering structures
- Numerical methods for phase space flow equations
- Uncertainty modelling
- Multiscale methods
If you are considering applying for an MRes or PhD in any of the areas above, please email Dr Chappell for further information. Some available PhD titles include:
- Wave energy transport through composite built-up structures
- Modelling dynamic interfaces driven by fluid flow
Predicting the vibrational energy distribution throughout complex built-up structures, such as cars, trains or aircraft is highly challenging. For large structures the problem becomes multi-scale, since the wavelengths will be short in comparison with the overall structure size, yet the structure will often contain fine details on the scale of the wavelength such as spot welds, rib-like stiffeners or inhomogeneities within a composite material. Such features often appear in a regular and repeated fashion, and hence characterising the wave dynamics within a periodic medium is an important step towards understanding the vibrational behaviour.
The aim of this project is to develop a library of energy transmission/ reflection models. Simple test cases will be considered initially, and both analytic and asymptotic solution methods will be investigated. Finite element techniques will be employed when analytic methods are no longer feasible in complex geometric or higher dimensional settings. Interesting wave phenomena including cloaking, stop-bands of periodic media and the acoustic black hole effect could also be considered. The propagation characteristics of different wave-types will then be implemented into a novel high frequency energy propagation method called dynamical energy analysis, making it possible to compute the vibrational response of complex built-up structures at high-frequencies.
The manipulation of liquid-air and liquid-liquid interfaces due to fluid flow is of interest for applications throughout the natural sciences including in liquid optics, chemical analysis, thin film deposition and drying. Modelling and simulation tools are not only used to verify experimental findings, but to quickly and efficiently study the fluid’s behaviour beyond the limits of the experimental set-up. In this way, the project will help to inform the design of future experiments and shape the direction of cutting-edge science.
The aim of this project is to make breakthroughs in linking fluid properties, such as local variations in the surface tension, to their effects on the motion of the corresponding interface. A combination of numerical and asymptotic methods will be explored for this purpose. For example, boundary integral approaches provide a unique advantage of reducing the fluid modelling to the interface alone, meaning that the fluid velocities driving the interface motion can be rapidly computed. In addition, level set formulations have the advantage of being able to include topological change and can therefore naturally handle contact line singularities where the interface intersects a bounding surface.
- A noisy flow model for uncertain wave dynamics in built-up vibroacoustic systems
Computer aided engineering tools for predicting noise and vibration are indispensable in many industries since they lead to huge savings in cost and development time, and their results impact comfort, safety, health and the environment. However, uncertainties arising during manufacturing processes (for example, in material properties or physical dimensions) can lead to large variations in the levels of noise and vibration of supposedly identical structures at high frequencies. In this case, the mean response (and variance) of an ensemble of “identical” structures is of more importance for engineering design than the deterministic response of any individual structure.
The aim of this project is to develop a computational model for predicting noise and vibration levels in built-up structures (examples include cars, ships and aircraft), where uncertainties in the manufacturing process and the sheer scales involved render standard techniques unviable. The work will be driven by problems from industry and underpinned by rigorous mathematical foundations drawing from numerical analysis, dynamical systems and operator theory.
Opportunities arise to carry out postgraduate research towards an MPhil / PhD in the areas identified above. Further information may be obtained on the NTU Research Degrees website https://www.ntu.ac.uk/research/research-degrees-at-ntu
Current and recent postgraduate supervisory experience:
- Dr Janis Bajars worked on the EU project "Mid-to-high frequency modelling of vehicle noise and vibration" (2015 to 2016) and subsequently the EPSRC project "Stochastic transfer operator methods for modelling the vibroacoustic properties of newly emerging transport structures" (2016 to 2017).
- Dr Martin Richter is working on the EPSRC project "Transfer operator methods for modelling high-frequency wave fields - advancements through modern functional and numerical analysis" (2018 to present).
- Thomas Dutton is working on the KTP project "Analysis, testing and optimisation of joint design for lightweight automotive structures" (2019 to present).
PhD - Director of Studies (Main Supervisor)
- Jacob Rowbottom (in progress) - A hybrid convolution quadrature method for modelling time-dependent waves with broadband frequency content.
- Nadia Abusag (in progress) - Numerical techniques for near-field acoustic holography.
PhD - Co-Supervisor (Second Supervisor)
- Rebecca Martin (completed 2018) - Collocation techniques for solving neural field models on complex cortical geometries. Director of Studies: Dr Jonathan Crofts.
- Jacob Rowbottom (Completed 2017) - The boundary element method for elliptic PDEs.
- Thomas Dutton (completed 2018) - Modelling wave scattering from an infinite quasi-periodic array.
Refereeing for scientific journals:
- Journal of the Acoustical Society of America
- International Journal for Numerical Methods in Engineering
- Journal of Mathematical Analysis and Applications
- IMA Journal of Numerical Analysis
- IMA Journal of Applied Mathematics
- Journal of Sound and Vibration
- Journal of Vibration and Acoustics
- Numerische Mathematik
- Wave Motion
Sponsors and collaborators
Current and recent research is being conducted in collaboration with:
- Paul Harris, University of Brighton
- Gregor Tanner, University of Nottingham
- Jamil Renno, Qatar University
- Brian Mace, University of Auckland, NZ
- Niels Sondergaard, inuTech Gmbh, Nuremberg
- Dominik Loechel, inuTech Gmbh
- Dmitrii Maksimov, LV Kirensky Institute of Physics
- Stefano Giani, Durham University
- Oscar Bandtlow, Queen Mary University of London