Timothy Reis

Dr Timothy Reis BSc, MSc, PhD

Associate Professor in Mathematics

Dr Reis joined the University of Greenwich in 2016 after three years as a Lecturer in Applied Mathematics at Plymouth  University.  Before this he held the position of Junior Research Fellow at the Oxford Centre for Collaborative Applied Mathematics, University of Oxford, and earlier still enjoyed postdoctoral research at UCL ("Instabilities in Polymer Processing") and the University of Oxford ("Multiphase Lattice Boltzmann Models").

He 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.

Dr Reis has taught various branches of mathematics to undergraduate and postgraduate students including Partial Differential Equations, Optimisation and Operational Research, Foundations of Mathematics, and Fluid Mechanics.

Responsibilities within the university

Module Leader

  • Research Methods and Mathematics Projects
  • Partial Differential Equations
  • Operational Research: Linear Programming
  • Simulation and Modelling


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)


Editor of the International journal of Computer Mathematics

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

Reviewer for Mathematical Reviews (MathSciNet)

Visiting Research Fellow at the Isaac Newton Institute (Partial Differential Equations in Kinetic Theories Programme, 2010)

Fellow of the Institute of Mathematics and its Applications

Member of the London Mathematical Society

Research / Scholarly interests

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.

Recent publications


Reis, Timothy and , (2022), A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Elsevier - Academic Press. In: , , , . Elsevier - Academic Press, Journal of Computational Physics, 453: 110962 ISSN: 0021-9991 (Print), 1090-2716 (Online) (doi: https://doi.org/10.1016/j.jcp.2022.110962).

Mohammed, S. and , Reis, T. (2021), A Lattice Boltzmann method with moment-based boundary conditions for rarefied flow in the slip regime. American Physical Society. In: , , , . American Physical Society, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 104: 45309 (4) ISSN: 1539-3755 (Print), 1550-2376 (Online) (doi: https://doi.org/10.1103/PhysRevE.104.045309).

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.


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 CONFERENCE. 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).