Dr Timothy Reis

Dr Timothy Reis

Discretionary Member


Lecturer in Applied Mathematics

Outreach Activities 

Butlins Astonishing Science Weekends

Let Maths Take you Further


Research Fellow, University of Oxford

Research Associate, University of Oxford
(project: numerical modelling of carbon sequestration, with Dr Paul Dellar)

Research Associate, University College London
(project: instabilities in polymer processing, with Dr Helen Wilson)

PhD, Applied Mathematics, Cardiff University
(thesis title: The lattice Boltzmann method for complex flows)

MSc, applied mathematics/complex fluids, University of Wales Aberystwyth

BSc, Mathematics, University of Wales Aberystwyth

Postgraduate Certificate in Academic Practice, Plymouth University 


Vernon Harrison doctoral award of the British Society of Rheology for the most distinguished thesis, 2007

Plymouth University Faculty of Science and Engineering  SSTAR Award for "Most Innovative Use Of Teaching Methods", 2016

Professional membership

Society of Industrial and Applied Mathematics (SIAM)

British Society of Rheology (BSR)

UK Consortium on Mesoscopic Engineering Science (UKCOMES)

UK Carbon Capture and Storage Research Centre (UKCCSRC)

Roles on external bodies

Co-chairman, International Conference of Mesocopic Methods in Engineering and Science (ICMMES-2013)

Guest editor, Computers and Fluids, and Computers and Mathematics with Applications (2016)

Guest editor, Communications in Computational Physics (2014)

Teaching interests

Applied mathematics, mathematical modelling, fluid mechanics, numerical analysis

Courses (Plymouth)

MATH3609: Optimisation, Graphs, and Networks 

MATH3605: Partial Differential Equations

MATH1606: Numerical and Computational Methods

MATH055:   Mathematics 1

Previous courses

InFoMM Graduate Mathematics Modelling Camp, University of Oxford (2016)

Case Studies in Mathematical Modelling, University of Oxford (2012)

Mathematical Modelling (part of the European Summer School for Industrial Mathematics, Dresden, 2012)

Boundary Conditions for the Lattice Boltzmann Equation (part of the Lattice Boltzmann Summer School, Beijing 2012)

Fluid Dynamics and Waves (tutor), Keble College, University of Oxford (2009-2013)

Viscous Flow (tutor), University of Oxford (2011-2013)

Research interests

My research interests include the theory and application of the lattice Boltzmann equation, fluid mechanics, and rheology. More generally, I am interested in mathematical modelling and computational fluid dynamics. 

Current PhD Students

Seemaa Mohammed, "Lattice Boltzmann models in the slip-flow regime" (DoS)
Norjan Jumaa, "Lattice Boltzmann methods for free surface problems" 
Zainab Bu Sinnah, "Multiphase flow in porous media" (DoS)
Oleg Wagner, "Large eddy simulation using lattice Boltzmann methods" (DoS)
Ebtesam Alousta, "Modelling fatigue crack closure" 

Previous Supervision

Andreas Hantsch, "Liquid film flow modelling with lattice Boltzmann methods" (visiting scholarship, University of Oxford, 2011 and 2012)
Rebecca Allen, "Numerical models for natural convection" (visiting scholarship, University of Oxford, 2012 and 2013)
Stuart Thomson, ``Frederick's transition in liquid crystals" (summer internship, University of Oxford, July-September 2012) 

Journal Articles

C Pang, R Alcock, N Pilkington, T Reis, and C. Roobottom, Determing the haemodynamic significance of arterial stenosis: the relationship between CT angiography, computational fluid dynamics, and non-invasive fractional flow reserve, Clinical Radiology, In press (2016)

R. Allen and T. Reis,  Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities, Prog. Comp. Fluid Dyn.: An Int. J., In press (2015)

A .Hantsch, T. Reis and U. Gross,  Moment method boundary conditions for multiphase lattice Boltzmann simulations with partially-wetted walls, J.Comp. Multiphase Flow, 7(1):1-14 (2015)

T. Reis and H. Wilson, Rolie-Poly fluid flowing through constrictions: Two distinct instabilities, J.Non-Newt. Fluid Mech., 195 (2013), 77-87

T. Reis and P. Dellar,Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier-Maxwell slip boundary conditions, Phys.Fluids, 24 (2012), 112001

T. Reis and P. Dellar, A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations ,Computers and Fluids, 46 (2011), 417-421

T. Reis and T. Phillips, Numerical validation of a consistent axisymmetric lattice Boltzmann model, Phys.Rev. E, 77 (2008), 026703

T. Reis and T. Phillips, An alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation, Phys.Rev. E, 77 (2008), 026702

T. Reis and T. Phillips, Lattice Boltzmann model for simulating immiscible two-phase flows, J.Phys. A: Math. Theor, 40 (2007) 4033-4053

T. Reis and T. Phillips, Modified lattice Boltzmann model for axisymmetric flows, Phys.Rev. E, 75 (2007), 056703

Proceedings and Technical Reports

K Langfeld, D Graham, D Greeves, A Mehmood, and T Reis, The virtual source approach to non-linear potential flow simulation , Proceedings of the International Offshore and Polar Engineering (ISOPE) Conference, 2016

R Allen, T Reis and S Sun, A lattice Boltzmann Eeuation to simulate density-driven convection of carbon dioxide , Proceedings of the Society for Petroleum Engineering (SPE) Reservoir Simulation Symposium, 2013

T Reis and P J Dellar, A random projection method for sharp phase boundaries in lattice Boltzmann simulations, Proceedings of the 12th European Conference on the Mathematics of Oil Recovery (ECMOR), 2010

Study Group Report, Reaction-diffusion models of decontamination, 68th ESGI, Southampton 30/3/2009 - 3/4/2009

Study Group Report, Reacting flows and vortices , 3rd Montreal Industrial Problem Solving Workshop, CRM, Montreal, August 2009

T Reis and T N Phillips, Reply to comment on `Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation', Phys.Rev. E, 78 (2008), 068702

T Reis, M Sahin and H J Wilson, Co-extrusion instabilities modeled with a single fluid , AIP Conf. Proc, 1027 (2008), 150

T Reis, Rheology:The Science of Deformation and Flow , iSquared Magazine, Issue 4

The Lattice Boltzmann Equation for Complex Flows, PhD thesis, Cardiff University, 2007. Supervised by Professor T.N. Phillips

Reports & invited lectures

Invited seminars and lectures

A lattice Boltzmann implementation of the Fokker-Plank equation for polymeric fluids, British Applied Mathematics Colloquium (Mathematics of Complex Fluids symposium) , University of Oxford, April 2016

Lattice Boltzmann methodologies and their applications , Centre for Scientific Computing, Warwick University, 12 May 2014

Burnett stress and discrete velocity Boltzmann equations: numerical or physical phenomena?, Oxford Conference on Challenges in Applied Mathematics, University of Oxford, July 2012

2012 Summer School on the Lattice Boltzmann Method (instructor), Beijing Computational Science Research Center, Beijing, 9-13 July 2012

Boundary conditions for the lattice Boltzmann equation, PREM seminar, Department of Mechanical Engineering, City College New York, 15 June 2012

An introduction to the lattice Boltzmann equation, Applied maths and computational science seminar, KAUST, Jeddah, 27May 2012

Instabilities in Polymer Processing, Fluids Seminar Series, School of Mathematics, Cardiff University,11 November 2008

Selected Conference Presentations

Burentt stress and the implementation of lattice Boltzmnan boundary conditions, ICMMES 2015, Beijing Computational Science Research Centre , China, 20-24 July 2015

Moment-based formulation of Navier--Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels, ICMMES 2012, Taipei, Taiwan, 23-27 July 2012

A multiphase lattice Boltzmann model with sharp interfaces, ICNMMF 2012, Penn State University, Pennsylvania, 12-14 August 2012

A volume-conserving stochastic sharpening approach for the pinning and facetting of sharp phase boundaries in multiphase lattice Boltzmann simulations, DSFD 2011, Fargo, North Dakota, 8-12 August 2011

A conservative stochastic sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations, ICFD conference on Numerical Methods for Fluid Dynamics, University of Reading, 12-15 April 2010.

Instabilities modelled with a single fluid, The XVth International Congress on Rheology, Monterey, California, 3-8 August 2008

Study groups

European Summer School in Industrial Mathematics and Modelling Week (Instructor), Technische Universität Dresden, 12-26 August 2012

Fourth Montreal Industrial Problem Solving Workshop, Centre de Recherches Mathèmatiques, Universitè de Montrèal,15-19 August 2011

First Euroasia Study Group with Industry, Karadeniz Technical University 4-8 October 2010

Third Montreal Industrial Problem Solving Workshop, Centre de Recherches Matèmatiques, Universitè de Montrèal,17-21 August 2009

68th European Study Group with Industry, University of Southampton, 30 March - 3 April 2009

More information can about study groups can be found here and here.


UK Consortium on Mesoscopic Engineering Science (UKCOMES)

Applied Maths Research at Plymouth

Previous webpage

Mathematics in industry

Mathematical modelling summer schools