Burnett stress

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2019) Burnett order stress and spatially-dependent boundary conditions for the lattice Boltzmann method. Communications in Computational Physics, 27 (1). pp. 167-197. ISSN 1815-2406 (Print), 1991-7120 (Online) (doi:10.4208/cicp.OA-2018-0229)

CFD

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2022) A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Journal of Computational Physics, 453:110962. ISSN 0021-9991 (Print), 1090-2716 (Online) (doi:10.1016/j.jcp.2022.110962)

D3Q19

Krastins, Ivars, Kao, Andrew ORCID: https://orcid.org/0000-0002-6430-2134, Pericleous, Koulis ORCID: https://orcid.org/0000-0002-7426-9999 and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2020) Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations. International Journal for Numerical Methods in Fluids, 92 (12). pp. 1948-1974. ISSN 0271-2091 (Print), 1097-0363 (Online) (doi:10.1002/fld.4856)

Dipole-wall collision

Mohammed, Seemaa, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions. Computers and Fluids, 176 (C). pp. 79-96. ISSN 0045-7930 (Print), 1879-0747 (Online) (doi:10.1016/j.compfluid.2018.08.025)

dispersion relation

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X and Phillips, Timothy (2008) Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 77 (2):026702. ISSN 1539-3755 (Print), 1550-2376 (Online) (doi:10.1103/PhysRevE.77.026702)

Engineering mathematics

James, Glyn, Dyke, Phil, Craven, Matthew, Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X and Stander, Julian (2018) Advanced Modern Engineering Mathematics. Pearson Education, Harlow, UK. ISBN 978-1292174341

fluid mechanics

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2022) A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Journal of Computational Physics, 453:110962. ISSN 0021-9991 (Print), 1090-2716 (Online) (doi:10.1016/j.jcp.2022.110962)

lattice Boltzmann

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2022) A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Journal of Computational Physics, 453:110962. ISSN 0021-9991 (Print), 1090-2716 (Online) (doi:10.1016/j.jcp.2022.110962)

Krastins, Ivars, Kao, Andrew ORCID: https://orcid.org/0000-0002-6430-2134, Pericleous, Koulis ORCID: https://orcid.org/0000-0002-7426-9999 and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2020) Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations. International Journal for Numerical Methods in Fluids, 92 (12). pp. 1948-1974. ISSN 0271-2091 (Print), 1097-0363 (Online) (doi:10.1002/fld.4856)

Bu Sinnah, Zainab A., Graham, David I. and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Lattice Boltzmann modelling of pulsatile flow using moment boundary conditions. In: 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7). ECCOMAS, Glasgow.

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X and Phillips, Timothy (2008) Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 77 (2):026702. ISSN 1539-3755 (Print), 1550-2376 (Online) (doi:10.1103/PhysRevE.77.026702)

Lattice Boltzmann equation

Mohammed, Seemaa, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions. Computers and Fluids, 176 (C). pp. 79-96. ISSN 0045-7930 (Print), 1879-0747 (Online) (doi:10.1016/j.compfluid.2018.08.025)

lattice Boltzmann method

bu Sinnah, Zainab, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2025) Imposing Navier-slip boundary conditions on the lattice Boltzmann equation in three dimensions. International Journal of Computer Mathematics. ISSN 0020-7160 (Print), 1029-0265 (Online) (doi:10.1080/00207160.2025.2542488)

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2019) Burnett order stress and spatially-dependent boundary conditions for the lattice Boltzmann method. Communications in Computational Physics, 27 (1). pp. 167-197. ISSN 1815-2406 (Print), 1991-7120 (Online) (doi:10.4208/cicp.OA-2018-0229)

moment based boundary conditions

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2019) Burnett order stress and spatially-dependent boundary conditions for the lattice Boltzmann method. Communications in Computational Physics, 27 (1). pp. 167-197. ISSN 1815-2406 (Print), 1991-7120 (Online) (doi:10.4208/cicp.OA-2018-0229)

Bu Sinnah, Zainab A., Graham, David I. and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Lattice Boltzmann modelling of pulsatile flow using moment boundary conditions. In: 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7). ECCOMAS, Glasgow.

moment-based boundary conditions

bu Sinnah, Zainab, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2025) Imposing Navier-slip boundary conditions on the lattice Boltzmann equation in three dimensions. International Journal of Computer Mathematics. ISSN 0020-7160 (Print), 1029-0265 (Online) (doi:10.1080/00207160.2025.2542488)

Krastins, Ivars, Kao, Andrew ORCID: https://orcid.org/0000-0002-6430-2134, Pericleous, Koulis ORCID: https://orcid.org/0000-0002-7426-9999 and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2020) Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations. International Journal for Numerical Methods in Fluids, 92 (12). pp. 1948-1974. ISSN 0271-2091 (Print), 1097-0363 (Online) (doi:10.1002/fld.4856)

Mohammed, Seemaa, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions. Computers and Fluids, 176 (C). pp. 79-96. ISSN 0045-7930 (Print), 1879-0747 (Online) (doi:10.1016/j.compfluid.2018.08.025)

multiphase flow

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2022) A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Journal of Computational Physics, 453:110962. ISSN 0021-9991 (Print), 1090-2716 (Online) (doi:10.1016/j.jcp.2022.110962)

multiple relaxation time

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X and Phillips, Timothy (2008) Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 77 (2):026702. ISSN 1539-3755 (Print), 1550-2376 (Online) (doi:10.1103/PhysRevE.77.026702)

Navier slip

Bu Sinnah, Zainab A., Graham, David I. and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Lattice Boltzmann modelling of pulsatile flow using moment boundary conditions. In: 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7). ECCOMAS, Glasgow.

Navier-slip

bu Sinnah, Zainab, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2025) Imposing Navier-slip boundary conditions on the lattice Boltzmann equation in three dimensions. International Journal of Computer Mathematics. ISSN 0020-7160 (Print), 1029-0265 (Online) (doi:10.1080/00207160.2025.2542488)

pulsatile flow

Bu Sinnah, Zainab A., Graham, David I. and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Lattice Boltzmann modelling of pulsatile flow using moment boundary conditions. In: 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7). ECCOMAS, Glasgow.

regularized cavity

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2019) Burnett order stress and spatially-dependent boundary conditions for the lattice Boltzmann method. Communications in Computational Physics, 27 (1). pp. 167-197. ISSN 1815-2406 (Print), 1991-7120 (Online) (doi:10.4208/cicp.OA-2018-0229)

surface tension

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2022) A lattice Boltzmann formulation of the one-fluid model for multiphase flow. Journal of Computational Physics, 453:110962. ISSN 0021-9991 (Print), 1090-2716 (Online) (doi:10.1016/j.jcp.2022.110962)

two relaxation times

Krastins, Ivars, Kao, Andrew ORCID: https://orcid.org/0000-0002-6430-2134, Pericleous, Koulis ORCID: https://orcid.org/0000-0002-7426-9999 and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2020) Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations. International Journal for Numerical Methods in Fluids, 92 (12). pp. 1948-1974. ISSN 0271-2091 (Print), 1097-0363 (Online) (doi:10.1002/fld.4856)

Mohammed, Seemaa, Graham, David and Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X (2018) Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions. Computers and Fluids, 176 (C). pp. 79-96. ISSN 0045-7930 (Print), 1879-0747 (Online) (doi:10.1016/j.compfluid.2018.08.025)