Dr Timothy Reis BSc (Hons), MSc, PhD, PGCAP

Senior Lecturer

Key details

Dr Timothy Reis
BSc (Hons), MSc, PhD, PGCAP

Senior Lecturer

Dr Reis obtained his BSc in Mathematics and MSc with Distinction in the Mathematical Theory of Complex Fluids from the University of Wales Aberystwyth. He was awarded his PhD in 2007 from Cardiff University's School of Mathematics and his doctoral work  on "The Lattice Boltzmann Equation for Complex Flows" won the Vernon Harrison Prize from the British Society of Rheology for the most distinguished thesis. After postdoctoral research at UCL ("Instabilities in Polymer Processing") and the University of Oxford ("Multiphase Lattice Boltzmann Models") he held the position of Junior Research Fellow at the Oxford Centre for Collaborative Applied Mathematics, University of Oxford. His first faculty position was as a lecturer in Applied Mathematics at Plymouth University and in September 2016 he joined the Department of Mathematical Sciences at the University of Greenwich. Find out more here https://timreis.org/.

Dr Reis's primary research interests combine fluid mechanics, mathematical modelling, and numerical analysis. He is particularly interested in the theory of the lattice Boltzmann method and its application to rheology, microfluidics and multiphase flow problems. He is an associate editor of the International Journal of Computer Mathematics and has been a guest editor of several other international journals.   

Dr Reis is a fellow of the Institute of Mathematics and its Applications (IMA) and of the Higher Education Academy (HEA).

Responsibilities within the university

Module Leader 2018/19 

  • Research Methods and Mathematics Projects
  • Partial Differential Equations
  • Operational Research for Industry
  • Mathematics Foundation Projects


Vernon Harrison Annual Doctoral Prize of the British Society of Rheology (2007)

Plymouth University Faculty of Science and Engineering award for Most Innovative use of Teaching Methods (2016)


Fellow of the Institute of Mathematics and its Applications (IMA)

Fellow of the Higher Education Academy (HEA)

Member of the UK Consortium on Mesoscopic Engineering Science (UKCOMES)

Reviewer for Mathematical Reviews (MathSciNet)

Associate Editor of the International journal of Computer Mathematics

Research / Scholarly interests

Lattice Boltzmann Models, Fluid Mechanics, Computational Fluid Dynamics, Rheology

Recent publications


Krastins, Ivars , Kao, Andrew, Pericleous, Koulis, Reis, Timothy (2020), Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations. Wiley. In: , , , . Wiley, International Journal for Numerical Methods in Fluids, 92 (12) . pp. 1948-1974 ISSN: 0271-2091 (Print), 1097-0363 (Online) (doi: https://doi.org/10.1002/fld.4856).

Reis, T. and , (2020), On the lattice Boltzmann deviatoric stress: analysis, boundary conditions, and optimal relaxation times. Society for Industrial and Applied Mathematics. In: , , , . Society for Industrial and Applied Mathematics, SIAM Journal on Scientific Computing, 42 (2) . pp. B397-B424 ISSN: 1064-8275 (Print), 1095-7197 (Online) (doi: https://doi.org/10.1137/19M1244846).

Mohammed, S. , Graham, D. I., Reis, T. (2020), Modelling the effects of slip on dipole-wall collision problems using a lattice Boltzmann equation method. AIP Publishing. In: , , , . AIP Publishing, Physics of Fluids, 32: 25104 (2) ISSN: 1070-6631 (Print), 1089-7666 (Online) (doi: https://doi.org/10.1063/1.5131865).

Reis, Timothy and , (2019), Burnett order stress and spatially-dependent boundary conditions for the lattice Boltzmann method. Global Science Press. In: , , , . Global Science Press, Communications in Computational Physics, 27 (1) . pp. 167-197 ISSN: 1815-2406 (Print), 1991-7120 (Online) (doi: https://doi.org/10.4208/cicp.OA-2018-0229) NB Item availability restricted.

Reis, T. and , (2018), A conservative interface sharpening Lattice Boltzmann Model. Society for Industrial and Applied Mathematics. In: , , , . Society for Industrial and Applied Mathematics, SIAM Journal on Scientific Computing, 40 (6) . pp. B1495-B1516 ISSN: 1064-8275 (Print), 1095-7197 (Online) (doi: https://doi.org/10.1137/18M1184928).

Mohammed, Seemaa , Graham, David, Reis, Timothy (2018), Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions. Elsevier. In: , , , . Elsevier, Computers and Fluids, 176 (C) . pp. 79-96 ISSN: 0045-7930 (Print), 1879-0747 (Online) (doi: https://doi.org/10.1016/j.compfluid.2018.08.025).

Mohammed, Seemaa and , Reis, Tim (2017), Using the lid-driven cavity flow to validate moment-based boundary conditions for the Lattice Boltzmann Equation. De Gruyter Open. In: , , , . De Gruyter Open, Archive of Mechanical Engineering, 64 (1) ISSN: 2300-1895 (Print), (doi: https://doi.org/10.1515/meceng-2017-0004).

Allen, Rebecca and , Reis, Tim (2016), Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities. Inderscience. In: , , , . Inderscience, Progress in Computational Fluid Dynamics, An International Journal (PFCD), 16 (4) . pp. 216 ISSN: 1468-4349 (Print), 1741-5233 (Online) (doi: https://doi.org/10.1504/PCFD.2016.077296).

Pang, C.L. , Alcock, R., Pilkington, N., Reis, T. , Roobottom, C. (2016), Determining the haemodynamic significance of arterial stenosis: the relationship between CT angiography, computational fluid dynamics, and non-invasive fractional flow reserve. Elsevier. In: , , , . Elsevier, Clinical Radiology, 71 (8) . pp. 750-757 ISSN: 0009-9260 (Print), 1365-229X (Online) (doi: http://dx.doi.org/10.1016/j.crad.2016.03.001) NB Item availability restricted.

Hantsch, Andreas , Reis, Tim, Gross, Ulrich (2015), Moment method boundary conditions for multiphase Lattice Boltzmann simulations with partially-wetted walls. SAGE Publications. In: , , , . SAGE Publications, The Journal of Computational Multiphase Flows, 7 (1) . pp. 1-14 ISSN: 1757-482X (Print), 1757-4838 (Online) (doi: https://doi.org/10.1260/1757-482X.7.1.1).

Reis, T. and , Wilson, H. J. (2013), Rolie-Poly fluid flowing through constrictions: Two distinct instabilities. Elsevier. In: , , , . Elsevier, Journal of Non-Newtonian Fluid Mechanics, 195 . pp. 77-87 ISSN: 0377-0257 (Print), 1873-2631 (Online) (doi: https://doi.org/10.1016/j.jnnfm.2013.01.002).

Reis, Tim and , Dellar, Paul J. (2012), Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier-Maxwell slip boundary conditions. AIP Publishing. In: , , , . AIP Publishing, Physics of Fluids, 24: 112001 ISSN: 1070-6631 (Print), 1089-7666 (Online) (doi: https://doi.org/10.1063/1.4764514).

Reis, T. and , Dellar, P. J. (2010), A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations. Elsevier. In: , , , . Elsevier, Computers and Fluids, 46 . pp. 417-421 ISSN: 0045-7930 (Print), 1879-0747 (Online) (doi: https://doi.org/10.1016/j.compfluid.2010.12.005).


James, Glyn , Dyke, Phil, Craven, Matthew, Reis, Timothy , Stander, Julian (2018), Advanced Modern Engineering Mathematics. Pearson Education. In: , , In: Glyn James, Phil Dyke (eds.), . Pearson Education, Harlow, UK (5th) . ISBN: 9781292174341 (doi: ).

Conference proceedings

Bu Sinnah, Zainab A. , Graham, David I., Reis, Timothy (2018), Lattice Boltzmann modelling of pulsatile flow using moment boundary condiitons. ECCOMAS. In: , , , 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7. ECCOMAS, Glasgow (doi: ) NB Item availability restricted.

Langfeld, Kurt , Graham, David I., Greaves, Deborah M., Mehmood, Arshad , Reis, Tim (2016), The virtual source approach to non-linear potential flow simulations. ISOPE. In: , , , The Proceedings of The Twenty-sixth (2016) International OCEAN AND POLAR ENGINEERING CONFERENC. ISOPE, California, USA Proceedings of the International Offshore and Polar Engineering Conference, 3 . pp. 242-249 . ISBN: 9781880653883ISSN: 1098-6189 (Print), (doi: http://legacy.isope.org/publications/proceedings/ISOPE/ISOPE%202016/index.htm).

Allen, Rebecca , Reis, Tim, Sun, Shuyu (2013), A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide. Society of Petroleum Engineers. In: , , , Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 201. Society of Petroleum Engineers, Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 2013 . ISBN: 9781613992333 (doi: https://doi.org/10.2118/163658-MS).