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David Chappell

David Chappell

Associate Professor

School of Science & Technology

Staff Group(s)
Physics and Mathematics


David Chappell is an Associate Professor in Applied Mathematics within the School of Science and Technology.  He leads research in computational mathematical modelling with application areas including acoustics, fluid mechanics, neuroscience and structural vibrations. The underlying motivation for his research is often to develop improved virtual design, analysis and optimisation tools for industry. He has published over 20 peer-reviewed papers and has attracted grant funding as PI or Co-I in excess of £2.1M, including from the EU, the UK EPSRC, Innovate UK and from industry. Dr Chappell teaches on the undergraduate modules MATH20441 Numerical Methods for Ordinary Differential Equations and MATH30461 Partial Differential Equations. He also leads the M-level module MATH44051 Mathematical Recipes and supervises both Bachelors and Masters projects in Mathematics.

Career overview

Nottingham Trent University, School of Science and Technology

Associate Professor in Applied Mathematics (2017-present), previously Senior Lecturer in Numerical Analysis (2015-2017), Lecturer (2012-2015).

University of Nottingham, School of Mathematical Sciences

Knowledge Transfer Associate seconded to Jaguar Land Rover Ltd. (2012), previously Postdoctoral Research Associate in modelling high-frequency wave energy transport (2009-2011).

University of Brighton, School of Computing, Mathematical and Information Sciences

Postdoctoral Research Officer in computational acoustics (2007-2009).

Research areas

Dr Chappell is a member of the Computation and Simulation ( and the Acoustics and Vibrometry ( research groups.

Current research is being carried out in the following areas:

  • Wave energy transport through composite built-up structures
  • 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. Interesting wave phenomena including cloaking, stop-bands of periodic media and the acoustic black hole effect could also be investigated. This work is funded by Innovate UK (KTP grant number 11548) and is a collaboration between NottinghamTrent University and Far UK Ltd.

  • Noisy flow and data driven models 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 research is to develop computational models for predicting high-frequency 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. This ongoing research area has been funded by the EPSRC (grant EP/M027201/1) and the EU (FP7 Marie-Curie Action IAPP Grant Agreement ID: 612237).

  • Direction preserving discrete flow mapping for modelling vibrational energy transport on thin shells
  • Modelling high-frequency wave transport on thin shells is important for simulating vibrational energy transport in automotive and aerospace structures such as a car body or an aeroplane fuselage. The aim of this research is to develop computational models that can accurately predict the flow of energy around thin and curved complex structures described by meshes. To correctly model wave barrier effects caused by the curvature of the shell or changes of material, then it is important that the correct flow direction is maintained when moving between different mesh cells (or elements). This research is funded by the EPSRC (grant EP/R012008/1) and is a collaboration between Nottingham Trent University, the University of Nottingham and Queen Mary University of London.

  • Convolution quadrature methods for transient and broadband wave modelling  
  • Fully time-dependent wave models are essential when the wave sources themselves undergo fundamental changes. Examples include linear vibrations induced by a structural shock (such as in vehicle crash testing) and acoustic emissions in the presence of structural fatigue (such as in condition monitoring). The broadband frequency content typically present in such models makes them highly challenging for mathematical modelling via numerical simulation methods, due to large computational overheads. This research aims to develop novel hybrid methodologies for time-dependent waves by combining popular numerical wave simulation methods that are most efficient at low frequencies and asymptotic models for high frequencies. The coupling of these approaches will take place within the framework of the so-called Convolution Quadrature method. This work has previously been supported by a centrally funded PhD studentship at Nottingham Trent University.

  • Modelling dynamic interfaces driven by fluid flow
  • 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. This research aims to better understand how fluid properties, such as local variations in the surface tension, influence the motion of the corresponding interface. A combination of numerical and asymptotic methods are being developed 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. This is collaborative work between Nottingham Trent University and the University of Nottingham.

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

Current and recent postgraduate supervisory experience:

Research fellows:

  • 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 2021).
  • Thomas Dutton is working on the KTP project "Analysis, testing and optimisation of joint design for lightweight automotive structures" (2019 to 2021).

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 (completed 2020) - Numerical techniques for near-field acoustic holography.

PhD - Co-Supervisor (Second Supervisor)

  • David Jenkins (in progress) - Revolutionising landslide-tsunami prediction with advanced machine learning techniques. Director of Studies: Dr Archontis Giannakidis.
  • Rebecca Martin (completed 2018) - Collocation techniques for solving neural field models on complex cortical geometries. Director of Studies: Dr Jonathan Crofts.

MRes students

  • Jacob Rowbottom (completed 2017) - The boundary element method for elliptic PDEs.
  • Thomas Dutton  (completed 2018) - Modelling wave scattering from an infinite quasi-periodic array.
  • Robert Lockett (in progress) - Modelling structural damage using finite element methods.

External activity

Editorial roles:

  • Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11),  Edited by David J. Chappell, Nottingham Trent University, July 2017.
  • Innovations in Wave Modelling II, Edited by David J. Chappell, Brian Mace, Gregor Tanner, Wave Motion, Volume 87, April 2019.

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
  • PLOS One
  • 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
  • Niels Sondergaard, inuTech Gmbh, Nuremberg
  • Dmitrii Maksimov, LV Kirensky Institute of Physics
  • Stefano Giani, Durham University
  • Oscar Bandtlow, Wolfram Just and Julia Slipantschuk, Queen Mary University of London
  • Drew Smith, Far UK Ltd

Recent funding has included:

  • Analysis, testing and optimisation of joint design for lightweight automotive structures, Innovate UK KTP 11548 (2019 to 2021)
  • Transfer operator methods for modelling high-frequency wave fields - advancements through modern functional and numerical analysis, EPSRC EP/R012008/1 (2018 to 2021)
  • Stochastic transfer operator methods for modelling emerging transport structures, EPSRC EP/M027201/1 (2016 to 2017)
  • Mid-to-high frequency modelling of vehicle noise and vibration, EU FP7, Marie-Curie Action IAPP Grant Agreement ID: 612237 (2013-2017)


CHAPPELL, D.J. and O'DEA, R.D., 2020. Numerical-asymptotic models for the manipulation of viscous films via dielectrophoresis. Journal of Fluid Mechanics, 901: A35. ISSN 0022-1120, DOI:

BAJARS, J. and CHAPPELL, D.J., 2020. Modelling uncertainties in phase-space boundary integral models of ray propagation. Communications in Nonlinear Science and Numerical Simulation, 80: 104973. ISSN 1007-5704, DOI:

HARTMANN, T., MORITA, S., TANNER, G. and CHAPPELL, D.J., 2019. High-frequency structure- and air-borne sound transmission for a tractor model using Dynamical Energy Analysis. Wave Motion, 87, pp. 132-150. ISSN 0165-2125, DOI:

BAJARS, J. and CHAPPELL, D.J., 2018. A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures. Journal of Computational Physics, 373, pp. 130-147. ISSN 0021-9991, DOI:

MARTIN, R., CHAPPELL, D.J., CHUZHANOVA, N. and CROFTS, J.J., 2018. A numerical simulation of neural fields on curved geometries. Journal of Computational Neuroscience, 45, pp. 133-145. ISSN 0929-5313,DOI:

BAJARS, J., CHAPPELL, D.J., SØNDERGAARD, N. and TANNER, G., 2017. Transport of phase space densities through tetrahedral meshes using discrete flow mapping. Journal of Computational Physics, 328, pp. 95-108. ISSN 0021-9991 DOI:

CHAPPELL, D.J., LÖCHEL, D., SØNDERGAARD, N. and TANNER, G., 2014. Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures. Wave Motion, 51 (4), pp. 589-597. ISSN 0165-2125, DOI:

See all of David Chappell's publications...