Professor Timothy Phillips
(he/him)

Chair in Applied Mathematics

: Available for postgraduate supervision

Research interests

My research interests are in non-Newtonian fluid mechanics and computational fluid dynamics and involves the mathematical modelling of complex fluids and the development of computational techniques for predicting complex flows. My research has been funded by the Engineering and Physical Sciences Research Council since 1985 and I have also received funding from the Leverhulme Trust, the Royal Society, EU and Industry. My most recent substantial EPSRC grant was a Portfolio Partnership Award in the area of Complex Fluids and Complex Flows in collaboration with the School of Engineering at Swansea. This award allowed me to develop mathematical modelling and numerical simulation tools for applications including lubrication and cavitation bubble dynamics. I am currently participating in the UK Consortium on Mesoscale Engineering Sciences (UKCOMES) funded by EPSRC.

My most recent work has been concerned with the development of mathematical models for compressible viscoelastic fluids. This has required an understanding of thermodynamics of complex systems. I also work on the immersed boundary method for fluid-structure interaction problems, numerical methods for multiphase flows, biomedical applications of bubble dynamics, modelling of groundwater flow using stochastic finite elements, proper generalized decomposition for elliptic systems and a range of numerical techniques for solving the Fokker-Planck equation. I have a particular interest in spectral element methods and the lattice Boltzmann method.

Research group

Applied and Computational Mathematics Research Group

Administrative duties

Head of Applied and Computational Mathematics Research Group
Member of School Research Committee
Co-chair School Athena SWAN Self-Assessment Team

2024

Hergibo, P., Phillips, T. N. and Xie, Z. 2024. Resolving subgrid-scale structures for multiphase flows using a filament moment-of-fluid method. Computers & Fluids 285, article number: 106455. (10.1016/j.compfluid.2024.106455)
Doherty, W., Phillips, T. N. and Xie, Z. 2024. The log-conformation formulation for single- and multi-phase axisymmetric viscoelastic flows. Journal of Computational Physics 508, article number: 113014. (10.1016/j.jcp.2024.113014)
Gómez-López, A., Vargas, R. O., Mil-Martínez, A. and Phillips, T. N. 2024. Multiscale simulations of viscoelastic fluids in complex geometries using a finitely extensible nonlinear elastic transient network model. Physics of Fluids 36(4), article number: 43117. (10.1063/5.0203787)
Mackay, A. and Phillips, T. 2024. Computational modelling of compressible nonisothermal viscoelastic fluids. Computers and Fluids 272, article number: 106189. (10.1016/j.compfluid.2024.106189)
Hergibo, P., Liang, Q., Phillips, T. N. and Xie, Z. 2024. A quadtree-based adaptive moment-of-fluid method for interface reconstruction with filaments. Journal of Computational Physics 499, article number: 112719. (10.1016/j.jcp.2023.112719)

2023

Mavron, V. C. and Phillips, T. N. 2023. Elements of mathematics for economics and finance. Springer. (10.1007/978-3-031-43910-0)
O'Brien, E. N., Mahmud, M., Smith, W. R., Wang, Q. X. and Phillips, T. N. 2023. The evolution of a three-dimensional microbubble at a corner in a Maxwell fluid. Physics of Fluids 35(10), article number: 103120. (10.1063/5.0170820)
Hergibo, P., Phillips, T. N. and Xie, Z. 2023. A moment-of-fluid method for resolving filamentary structures using a symmetric multi-material approach. Journal of Computational Physics 491, article number: 112401. (10.1016/j.jcp.2023.112401)
Leonenko, G. and Phillips, T. N. 2023. Transient numerical approximation of hyperbolic diffusions and beyond. Journal of Computational and Applied Mathematics 422, article number: 114893. (10.1016/j.cam.2022.114893)
Doherty, W., Phillips, T. N. and Xie, Z. 2023. A stabilised finite element framework for viscoelastic multiphase flows using a conservative level-set method. Journal of Computational Physics 477, article number: 111936. (10.1016/j.jcp.2023.111936)
Vargas, R. O., Gómez-López, A., Escandón, J. P., Mil-Martı́nez, R. and Phillips, T. 2023. Multiscale modeling of complex fluids under SAOS and LAOS using a combined FENE transient network model. Physica Scripta 98(2), article number: 25213. (10.1088/1402-4896/acb23b)

2022

Fanelli, C., Kaouri, K., Phillips, T. N., Myers, T. G. and Font, F. 2022. Magnetic nanodrug delivery in non-Newtonian blood flows. Microfluidics and Nanofluidics 26(10), article number: 74. (10.1007/s10404-022-02576-6)

2021

Mackay, A. T. and Phillips, T. N. 2021. Compressible and nonisothermal viscoelastic flow between eccentrically rotating cylinders. Theoretical and Computational Fluid Dynamics 35, pp. 735-756. (10.1007/s00162-021-00582-y)

2020

Traverso, L. and Phillips, T. N. 2020. Efficient stochastic finite element methods for flow in heterogeneous porous media. Part 2: random lognormal permeability. International Journal for Numerical Methods in Fluids 92(11), pp. 1626-1652. (10.1002/fld.4842)
Cracco, M., Davies, C. and Phillips, T. N. 2020. Linear stability of the flow of a second order fluid past a wedge. Physics of Fluids 32, article number: 84102. (10.1063/5.0018300)

2019

MacKay, A. T. and Phillips, T. N. 2019. On the derivation of macroscopic models for compressible viscoelastic fluids using the generalized bracket framework. Journal of Non-Newtonian Fluid Mechanics 266, pp. 59-71. (10.1016/j.jnnfm.2019.02.006)
Phillips, T. N., Oldham, D. and Davies, J. H. 2019. Towards global SEM mantle convection simulations on Polyhedral-based grids. Journal of Computational and Applied Mathematics 348, pp. 48-57. (10.1016/j.cam.2018.08.042)

2018

Jafari, A., Chitsaz, A., Nouri, R. and Phillips, T. N. 2018. Property preserving reformulation of constitutive laws for the conformation tensor. Theoretical and Computational Fluid Dynamics 32, pp. 789-803. (10.1007/s00162-018-0476-y)

2012

Lind, S. and Phillips, T. N. 2012. Bubble collapse in compressible fluids using a spectral element marker particle method. Part 1. Newtonian fluids. International Journal for Numerical Methods in Fluids 70(9), pp. 1167-1187. (10.1002/fld.2737)
Lind, S. and Phillips, T. N. 2012. The effect of viscoelasticity on the dynamics of two gas bubbles near a rigid boundary. IMA Journal of Applied Mathematics 77(5), pp. 652-677. (10.1093/imamat/hxs041)
Leonenko, G. M. and Phillips, T. N. 2012. High-order approximation of Pearson diffusion processes. Journal of Computational and Applied Mathematics 236(11), pp. 2853-2868. (10.1016/j.cam.2012.01.022)
Oldham, D. N., Davies, J. H. and Phillips, T. N. 2012. Generic polyhedron grid generation for solving partial differential equations on spherical surfaces. Computers & Geosciences 39, pp. 11-17. (10.1016/j.cageo.2011.06.004)
Bollada, P. C. and Phillips, T. N. 2012. On the mathematical modelling of a compressible viscoelastic fluid. Archive for Rational Mechanics and Analysis 205(1), pp. 1-26. (10.1007/s00205-012-0496-5)

2011

Russo, G. and Phillips, T. N. 2011. Spectral element predictions of die-swell for Oldroyd-B fluids. Computers & Fluids 43(1), pp. 107-118. (10.1016/j.compfluid.2010.09.028)
Phillips, T. N. and Roberts, G. W. 2011. Lattice Boltzmann models for non-Newtonian flows. IMA Journal of Applied Mathematics 76(5), pp. 790-816. (10.1093/imamat/hxr003)
Lind, S. and Phillips, T. N. 2011. The influence of viscoelasticity on the collapse of cavitation bubbles near a rigid boundary. Theoretical and Computational Fluid Dynamics 26(1-4), pp. 245-277. (10.1007/s00162-011-0227-9)
Lozinski, A., Owens, R. G. and Phillips, T. N. 2011. The Langevin and Fokker-Planck equations in polymer rheology. In: Glowinski, R. and Xu, J. eds. Handbook of Numerical Analysis - Special volume: Numerical Methods for Non-Newtonian Fluids., Vol. 16. Amsterdam: Elsevier, pp. 211-303., (10.1016/B978-0-444-53047-9.00002-2)
Leonenko, G. M. and Phillips, T. N. 2011. The prediction of plane Couette flow for a FENE fluid using a reduced basis approximation of the Fokker-Planck equation. International Journal for Multiscale Computational Engineering 9(1), pp. 73-88. (10.1615/IntJMultCompEng.v9.i1.60)

2010

Russo, G. and Phillips, T. N. 2010. Numerical prediction of extrudate swell of branched polymer melts. Rheologica Acta 49(6), pp. 657-676. (10.1007/s00397-009-0426-0)
Lind, S. and Phillips, T. N. 2010. Spherical bubble collapse in viscoelastic fluids. Journal of non-Newtonian fluid mechanics 165(1-2), pp. 56-64. (10.1016/j.jnnfm.2009.09.002)
Lind, S. and Phillips, T. N. 2010. The effect of viscoelasticity on a rising gas bubble. Journal of non-Newtonian fluid mechanics 165(15-16), pp. 852-865. (10.1016/j.jnnfm.2010.04.002)
Russo, G. and Phillips, T. N. 2010. Numerical simulation of steady planar die swell for a Newtonian fluid using the spectral element method. Computers & Fluids 39(5), pp. 780-792. (10.1016/j.compfluid.2009.12.006)
Yokoi, K., Kay, P. J., Bowen, P. J. and Phillips, T. N. 2010. Numerical Studies of Multiple Drop Impacts onto a Flat Substrate. Presented at: 23rd European Conference on Liquid Atomisation and Spray Systems (ILASS), Brno, Czech Republic.

2009

Bollada, P. C. and Phillips, T. N. 2009. A modified deformation field method for integral constitutive models. Journal of Non-Newtonian Fluid Mechanics 163(1-3), pp. 78-87. (10.1016/j.jnnfm.2009.07.001)
Inkson, N., Phillips, T. N. and van Os, R. G. M. 2009. Numerical simulation of flow past a cylinder using models of XPP type. Journal of non-Newtonian fluid mechanics 156(1-2), pp. 7-20. (10.1016/j.jnnfm.2008.06.004)
Vargas, R. O., Manero, O. and Phillips, T. N. 2009. Viscoelastic flow past confined objects using a micro-macro approach. Rheologica Acta 48(4), pp. 373-395. (10.1007/s00397-008-0323-y)
Bierbrauer, F., Bollada, P. C. and Phillips, T. N. 2009. A consistent reflected image particle approach to the treatment of boundary conditions in smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering 198(41-44), pp. 3400-3410. (10.1016/j.cma.2009.06.014)
Leonenko, G. M. and Phillips, T. N. 2009. On the solution of the Fokker-Planck equation using a high-order reduced basis approximation. Computer Methods in Applied Mechanics and Engineering 199(1-4), pp. 158-168. (10.1016/j.cma.2009.09.028)

2008

Bierbrauer, F. and Phillips, T. N. 2008. Modelling spray impingement onto flat, rigid walls using an Eulerian-Lagrangian method. Proceedings of the 22nd European Confrerence on Liquid Atomisation and Spray Systems, Como, Italy, 2008 Paper ILASS08-030
Bierbrauer, F. and Phillips, T. N. 2008. Secondary atomisation: simulation of droplet break-up in disturbed flow fields. Proceedings of the 22nd European Conference on Liquid Atomisation and Spray Systems, Como, Italy, 2008, Paper ILASS08-A029
Bollada, P. C. and Phillips, T. 2008. An anisothermal, compressible, piezoviscous model for journal-bearing lubrication. International Journal for Numerical Methods in Fluids 58(1), pp. 27-55. (10.1002/fld.1705)
Gerritsma, M. I. and Phillips, T. N. 2008. On the characteristics and compatibility equations for the UCM model fluid. Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM) 88(7), pp. 523-539. (10.1002/zamm.200700058)
Reis, T. and Phillips, T. N. 2008. Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation. Physical Review -Series e- 77(2), article number: 26702. (10.1103/PhysRevE.77.026702)
Reis, T. and Phillips, T. N. 2008. Numerical validation of a consistent axisymmetric lattice Boltzmann model. Physical Review E 77(2), article number: 26703. (10.1103/PhysRevE.77.026703)
Bierbrauer, F. and Phillips, T. N. 2008. The numerical prediction of droplet deformation and break-up using the Godunov marker-particle projection scheme. International Journal for Numerical Methods in Fluids 56(8), pp. 1155-1160. (10.1002/fld.1710)
Gwynllyw, D. R. and Phillips, T. N. 2008. The influence of Oldroyd-B and PTT lubricants on moving journal bearing systems. Journal of Non-Newtonian Fluid Mechanics 150(2-3), pp. 196-210. (10.1016/j.jnnfm.2007.10.014)
Leonenko, G. M. and Phillips, T. N. 2008. Reduced basis function method for solving the 2D Fokker-Planck equation. Presented at: SASOR 2008: 2nd Southern African Conference of Rheology, Cape Town, South Africa, 6-8 October 2008.
Bollada, P. C. and Phillips, T. N. 2008. A physical decomposition of the stress tensor for complex flows. Rheologica Acta 47(7), pp. 719-725. (10.1007/s00397-007-0256-x)

2007

Bollada, P. C. and Phillips, T. N. 2007. On the effects of a compressible viscous lubricant on the load-bearing capacity of a journal bearing. International Journal for Numerical Methods in Fluids 55(11), pp. 1091-1120. (10.1002/fld.1545)
Reis, T. and Phillips, T. N. 2007. Modified lattice Boltzmann model for axisymmetric flows. Physical Review E 75(5), article number: 56703. (10.1103/PhysRevE.75.056703)
van Os, R. G. M. and Phillips, T. N. 2007. The choice of spectral element basis functions in domains with an axis of symmetry. Journal of computational and applied mathematics 201(1), pp. 217-229. (10.1016/j.cam.2006.02.016)
Aguayo, J. P., Phillips, P. M., Phillips, T. N., Tamaddon-Jahromi, H. R., Snigerev, B. A. and Webster, M. F. 2007. The numerical prediction of planar viscoelastic contraction flows using the pom-pom model and higher-order finite volume schemes. Journal of Computational Physics 220(2), pp. 586-611. (10.1016/j.jcp.2006.05.039)
Reis, T. and Phillips, T. N. 2007. Lattice Boltzmann model for simulating immiscible two-phase flows. Journal of Physics A: Mathematical and Theoretical 40(14), article number: 4033. (10.1088/1751-8113/40/14/018)
Mavron, V. C. and Phillips, T. N. 2007. Elements of mathematics for economics and finance. London: Springer.
Inkson, N. and Phillips, T. N. 2007. Unphysical phenomena associated with the extended pom-pom model in steady flow. Journal of non-Newtonian fluid mechanics 145(2-3), pp. 92-101. (10.1016/j.jnnfm.2007.05.002)

2006

Binding, D. M., Phillips, P. M. and Phillips, T. N. 2006. Contraction/expansion flows: the pressure drop and related issues. Journal of non-Newtonian fluid mechanics 137(1-3), pp. 31-38. (10.1016/j.jnnfm.2006.03.006)
Ervin, V. J. and Phillips, T. N. 2006. Residual a posteriori error estimator for a three-field model of a generalized Stokes problem. Computer Methods in Applied Mechanics and Engineering 195(19-22), pp. 2599-2610. (10.1016/j.cma.2005.05.019)
Phillips, T. N. and Rh, G. D. 2006. On the enforcement of the zero mean pressure condition in the spectral element approximation of the Stokes problem. Computer Methods in Applied Mechanics and Engineering 195(9-12), pp. 1027-1049. (10.1016/j.cma.2005.04.004)
Bowen, P. J., Phillips, T. N. and Zheng, Y. 2006. Direct numerical simulation of non-Newtonian droplet deformation. Presented at: 10th International Conference on Liquid Atomization and Spray Systems (ICLASS-2006), Kyoto, Japan, 27 August - 1 September 2006.

2005

van Os, R. G. M. and Phillips, T. N. 2005. Efficient and stable spectral element methods for predicting the flow of an XPP fluid past a cylinder. Journal of non-Newtonian fluid mechanics 129(3), pp. 143-162. (10.1016/j.jnnfm.2005.06.004)
Gwynllyw, D. R. and Phillips, T. N. 2005. Some issues regarding spectral element meshes for moving journal bearing systems. International Journal for Numerical Methods in Fluids 48(4), pp. 423-454. (10.1002/fld.932)

2004

Van Os, R. G. M. and Phillips, T. 2004. Spectral element methods for transient viscoelastic flow problems. Journal of Computational Physics 201(1), pp. 286-314. (10.1016/j.jcp.2004.05.016)
Aboubacar, M., Phillips, T. N., Tamaddon-Jahromi, H. R., Snigerev, B. A. and Webster, M. F. 2004. High-order finite volume methods for viscoelastic flow problems. Journal of Computational Physics 199(1), pp. 16-40. (10.1016/j.jcp.2004.01.033)
Momeni-Masuleh, S. H. and Phillips, T. N. 2004. Viscoelastic flow in an undulating tube using spectral methods. Computers & Fluids 33(8), pp. 1075-1095. (10.1016/j.compfluid.2003.09.002)
van Os, R. G. M. and Phillips, T. N. 2004. The prediction of complex flows of polymer melts using spectral elements. Journal of non-Newtonian fluid mechanics 122(1-3), pp. 287-301. (10.1016/j.jnnfm.2003.12.009)

2003

Zheng, Y., Phillips, T. N. and Bowen, P. J. 2003. Development of DNS Spectral Element Methods for Study of Newtonian Droplet-Gas Systems. Presented at: 9th International Conference on Liquid Atomisation and Spray Systems (ICLASS), Sorrento, Italy.

2002

Phillips, T. N. and Williams, A. J. 2002. Comparison of creeping and inertial flow of an Oldroyd B fluid through planar and axisymmetric contractions. Journal of non-Newtonian fluid mechanics 108(1-3), pp. 25-47. (10.1016/S0377-0257(02)00123-4)
Owens, R. G. and Phillips, T. N. 2002. Computational rheology. London: Imperial College Press.

2001

Phillips, T. N. and Williams, A. J. 2001. Conservative semi-Lagrangian finite volume schemes. Numerical Methods for Partial Differential Equations 17(4), pp. 403-425. (10.1002/num.1019)
Gerritsma, M. I. and Phillips, T. N. 2001. On the use of characteristic variables in viscoelastic flow problems. IMA Journal of Applied Mathematics 66(2), pp. 127-147. (10.1093/imamat/66.2.127)
Phillips, T. N. and Williams, A. J. 2001. A semi-Lagrangian finite volume method for Newtonian contraction flows. SIAM Journal on Scientific Computing 22(6), pp. 2152-2177. (10.1137/S1064827599365288)

External funding since 2000

Type-Dependent Computations for Viscoelastic Flows. EPSRC £179,104.
Masters Training Package in Complex Fluids: Modelling, Computation and Industrial Applications. EPSRC £424,542.
Direct Numerical Simulation of Droplet-Gas Systems for Power Generation Applications. EPSRC £74,597.
The Prediction and Validation of Contraction Flows of Complex Fluids. EPSRC £148,161 (with D. M. Binding).
Portfolio Partnership in Complex Fluids and Complex Flows. EPSRC £3.1M (with UW Swansea).
Modelling of Mantle Convection. Leverhulme Trust £108,726 (with J. H. Davies).
UK Consortium On Mesoscale Engineering Sciences (UKCOMES). EPSRC £397,424.

Major conference talks since 2013

Modelling the dynamics of gas bubbles near free surfaces. BSR Annual Award Lecture. Advances in Non-Newtonian Fluid Mechanics, Royal Society International Conference Centre, Chicheley Hall, March 2013.
A least-squares proper generalised decomposition algorithm for the Stokes problem, Second International Workshop on “Reduced Basis, POD and PGD model Reduction Techniques”, Blois, France, November 2013.
A non-singular boundary element method for modelling the dynamics of cavitation bubbles, INNFM Conference on Rheology of Structured Fluids, Ruthin, Wales, March 2015.
The immersed boundary method for fluid structure interaction (FSI) problems with an Oldroyd-B fluid. Annual European Rheology Conference, Nantes, France, April 2015.
The immersed boundary method for fluid-structure interaction (FSI) problems with an Oldroyd-B fluid. XVIIth International Congress on Rheology, Kyoto, Japan, August 2016.
The extended spectral element method for the approximation of discontinuous functions and fluid-structure interaction problems. 20th IMACS World Congress, Xiamen, China, December 2016.
Large amplitude oscillatory shear flow simulation of complex fluids using micro-macro approach with transient network dynamics. XXth International Workshop on Numerical Methods for Non-Newtonian Flows, Oaxaca, Mexico (online), June 2021.
A conservative level set method for the numerical prediction of multiphase flows, INNFM-BSR Meeting on Non-Newtonian Fluid Mechanics, Lake Vyrnwy, Wales, April 2023.
A conservative level-set method for multiphase viscoelastic flows, XXIth International Workshop on Numerical Methods for Non-Newtonian Flows, Loch Lomond, Scotland, May 2023.
A conservative level-set method for multiphase viscoelastic flows, Annual European Rheology Conference, Leeds, April 2024.
An introduction to computational methods for complex fluids. Invited speaker at 'Joint Challenges in Non-Newtonian and BioActive Fluids', UCL, June 2024.

Conferences organized

INNFM/BSR Conference on Complex Flows of Complex Fluids, Liverpool, March 2008.
Annual European Rheology Conference, Cardiff, April 2009.
Advances in Non-Newtonian Fluid Mechanics, Kavli Royal Society International Centre, Chicheley Hall, March 2013.
British Applied Mathematics Colloquium, Cardiff, April 2014.

Professional responsibilities

President, British Society of Rheology, 2017-19
Council Member, British Society of Rheology.
Editorial Board Member. Theoretical and Computational Fluid Mechanics, 2012-2024
Editorial Board Member. Journal of Non-Newtonian Fluid Mechanics, 2017-
External examiner for the undergraduate degree schemes in Mathematics at University of Reading, 2016-2020.
External examiner for the undergraduate degree schemes in Mathematics at University of Lincoln, 2023-.
Member, EPSRC College, 2000-
Chair, MAGIC Programme Committee, 2017-
Council Member, Learned Society of Wales, 2017-2020

Undergraduate

MA3304 Methods of Applied Mathematics

Biography

BA – Mathematics, University of Oxford, 1979.
MSc – Mathematics (mathematical modelling and numerical analysis), University of Oxford, 1980.
DPhil – Mathematics, University of Oxford, 1983.
MA – University of Oxford, 1987.
DSc – University of Oxford, 2004.

After graduating from the University of Oxford, I was appointed to a research fellowship at ICASE (NASA Langley, USA), prior to taking up an academic position at Aberystwyth in 1984. I was appointed to a Professorial Fellowship at Cardiff University in 2004. I have held visiting professorships at the University of Delaware (Chemical Engineering) and the Ecole Polytechnique Fédérale de Lausanne (Mechanical Engineering).

I have published over 100 papers in international journals and over 30 papers in peer-reviewed conference proceedings. I co-authored one of the leading research monographs in my field - Computational Rheology - which was published by Imperial College Press in 2002. I have also published an undergraduate text – Elements of Mathematics for Economics and Finance – which was published by Springer in 2007. A second edtion of this book was published in November 2023. I have considerable experience in supervising young researchers (15 PDRAs and 28 PhD students).

Honours and awards

DSc University of Oxford, 2004
Fellow, Learned Society of Wales, Elected 2012
Annual Award, British Society of Rheology, 2012
Fellow, Institute of Mathematics and its Applications, Elected 2010

Professional memberships

Fellow of the Institute of Mathematics and its Applications (IMA)
Fellow of the Learned Society of Wales
Member of the Society for Industrial and Applied Mathematics (SIAM)
Member of the British Society of Rheology

Academic positions

2004 - present: Professor, School of Mathematics, Cardiff University
2000 - 2004: Professor, Department of Mathematics, University of Wales, Aberystwyth
1996 - 2000: Reader, Department of Mathematics, University of Wales, Aberystwyth
1992 - 1996: Senior Lecturer, Department of Mathematics, University of Wales, Aberystwyth
1984 - 1992: New Blood Lecturer in Computational Fluid Dynamics, Department of Applied Mathematics, University College of Wales, Aberystwyth
1982 - 1984: Research Scientist, Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Virginia, USA

Committees and reviewing

External committees

Chair of MAGIC Programme Committee
Member of MAGIC Management Committee
Member of MAGIC Academic Steering Committee
Council member, Institute of Mathematics and its Applications, June 2022 -
External examiner for undergraduate degree programmes at University of Lincoln, 2023 - 2027.
Member of the Royal Society’s Research Grants Board: Physical Sciences, January 2024 - December 2026.

MAGIC is one of 6 EPSRC funded Taught Course Centres (TCC). The MAGIC group runs a wide range of postgraduate-level lecture courses in mathematics:

http://maths-magic.ac.uk/index.php

Editorial Board, Theoretical and Computational Fluid Dynamics

Editorial Board, Journal of Non-Newtonian Fluid Mechanics

I am interested in supervising PhD students in the areas of:

numerical methods for non-Newtonian flows
dynamics of cavitation bubbles
multiphase flows
extended spectral element method
immersed boundary method
lattice Boltzmann method

Current supervision

Abhishek Chakraborty

Research student

Will Doherty

Research student

Layla Sadeghi Namaghi

Research student

Philippe Hergibo

Graduate Demonstrator

Ahlam Alghamdi

Research student

Past projects

Susanne Claus. Numerical Simulation of Complex Viscoelastic Flows using Discontinuous Galerkin Spectral/hp Element Methods. 2013.
Ross Kynch. Numerical Investigation of Sedimentation in Viscoelastic Fluids using Spectral Element Methods. 2013.
Chris Rowlatt. Modelling Flows of Complex Fluids using the Immersed Boundary Method. 2014.
Mike Walters. An Investigation into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine. 2015.
Tom Croft. Proper Generalised Decompositions: Theory and Applications. 2015.
Edward Lewis. Lattice Boltzmann Models for Complex Fluids. 2017.
Alex Mackay. Nonisothermal Compressible Viscoelastic Modelling. 2018.
Ahmed Alshehri. Efficient Spectral Element Methods for Elliptic Partial Differential Equations. 2020.
Martina Cracco. Linear Stability and Transient Behaviour of Viscoelastic Fluids in Boundary Layers. 2020.
Abhishek Chakraborty. Incorporating Calcium Signalling in Vertex Models of Neural Tube Closure. 2024.
William Doherty. Finite Element Methods for Viscoelastic Multiphase Flows using a Conservative Level Set Approach. 2024.

Contact Details

PhillipsTN@cardiff.ac.uk
+44 29208 74194
Abacws, Room 5.04, Senghennydd Road, Cathays, Cardiff, CF24 4AG

Research themes

Specialisms

Numerical and computational mathematics
Non-Newtonian fluid flows
Computational fluid dynamics

School of Mathematics has highest satisfaction among Russell Group universities

Professor Timothy Phillips (he/him)

Overview

Research interests

Research group

Administrative duties

Publication

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

Articles

Book sections

Books

Conferences

Research

External funding since 2000

Major conference talks since 2013

Conferences organized

Teaching

Undergraduate

Biography

Biography

Honours and awards

Professional memberships

Academic positions

Committees and reviewing

Supervisions

Current supervision

Abhishek Chakraborty

Will Doherty

Layla Sadeghi Namaghi

Philippe Hergibo

Ahlam Alghamdi

Past projects

Contact Details

Research themes

Specialisms

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School of Mathematics has highest satisfaction among Russell Group universities

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External profiles

Professor Timothy Phillips
(he/him)