Richard Purvis


  • 1.18 Sciences

Accepting PhD Students

Personal profile


My research interests are in fluid dynamics and mathematical modelling, in particular using mathematics to model, understand and make predictions about practical problems arising from industry and other scientific disciplines.  My research uses combined asymptotic and numerical techniques, exploiting small parameters to reduce the complexity of the models studied.  

One long-term research interest is in droplet (and solid) impacts into water, and subsequent splashing. Originally motivated by predicting ice formation on aircraft during flight in clouds, my research has tried to improve predictions of splashing and water entry.  Recently, I have been interested in the influence of air effects, such as pre-impact air cushioning and how air influences the post-impact splash development.

Other ongoing research includes boundary-layer flow past multiple aerofoils and ground effects, the fluid mechanics of digestion and the stomach, and flow in elastic channels. 

I am actively involved in the UK Industrial Mathematics community.  I regularly attend Mathematical Study Groups with Industry, and organised the 85th European Study group with Industry at UEA in 2012.  I am also on the Scientific Committee of the Industrial Mathematics Knowledge Transfer Network.

Follow this link for details of current PhD opportunities in Mathematics. But feel free to email me to discuss projects outside these areas and alternative sources of funding.


  • Senior Lecturer, School of Mathematics, UEA. 2013-Present.
  • Lecturer, School of Mathematics, UEA. 2005-2013.
  • Research Associate, Rotorcraft and Aircraft Icing team, QinetiQ, Farnborough.  Under EPSRC RAIS Scheme, 2004-2005
  • Postdoc Researcher, University College London, 2003-2004Temporary Lecturer, University College London, 2002-2003
  • PhD, Rotor blades and ground effects, UCL, 2002

Key Research Interests

Impacts, violent flows and splashing: Using local asymptotic models to predict small-time behaviour just before and just after droplet/solid impacts.  A particular focus is on the influence of air on splashing; how does it cushion the impact before touchdown and how does air trigger splashing post impact?  Experimental evidence suggests that bubble trapping before impact, and air effects after impact, are vital in understanding the mechanisms present during splashing. Trying to answer these questions using 2D and 3D asymptotic models, coupled to numerical solutions. 

Aircraft Icing: How do droplet impacts and splashing influence ice growth on an aircraft during flight?  Experimentally it is known that splashing changes amount of ice formed and, more seriously, can cause ice to form in different (maybe unprotected) places.  Also trying to understand how rivulets form in runback ice on a wing, and how local conditions influence the structure and strength of the ice formed. 

High Reynolds-number flow past multiple aerofoils and ground effects:  Although flow past one aerofoil is well studied and understood, flow past several sequential aerofoils is less understood.  This work uses coupled viscous-inviscid models to investigate sheltering effects and upstream influence.  With multiple aerofoils, the viscous boundary layer part of the solution is coupled to the outer inviscid flow.  For 2D planar flows this has been investigated and solved, but an open problem remains to solve this coupled viscous-inviscid problem for a rotor blade. 

Mathematical Modelling: Other ongoing research includes the fluid mechanics of digestion in the stomach (joint work with Institute of Food Research), effects of pinching on explosives (joint with industry, motivated by safe handling of explosives), and fluid flow in elastic channels.

Research Keywords:

Droplet impacts and splashing

Air cushioning

High Reynolds number flows

Aircraft Icing

Asymptotic analysis

Mathematical Biology

Mathematical modelling

Industrial Mathematics

PGR Supervision:

Air cushioning in violent impacts


Flow past multiple aerofoils

Aircraft Icing

Mathematical modelling/industrial mathematics

Rivulet formation in runback ice

Key Responsibilities

  • Director of Equality, Diversity and Inclusivity.
  • IMA Departmental Representative for UEA
  • Previously: Director of Admissions, Director of Enterprise, CIMR research coordinator, Senior Advisor, Disability Liaison Officer,  Chair of MTH Extenuating Circumstances Panel,  Staff-Student Liaison Officer, London Technology Network Business Fellow.

Teaching Interests

Richard has taught a wide-range of undergraduate courses across all years of the degree programme.  These include lecturing:

Level 4: Calculus, and Multivariable Calculus, and introductions to Latex, Maple, Matlab and programming

Level 5: Differential Equations, Mathematical modelling, Fluid Mechanics, and Maths for Scientists

Level 6: Electricity and Magnetism, and Fluid Dynamics (plus level 7 versions of both with advanced topics)

Richard has also supervised several BSc projects, and many MMTH projects.


Areas of Expertise

Industrial mathematics; aircraft icing; mathematical modelling and fluid mechanics.

Collaborations and top research areas from the last five years

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