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Timothy Phillips

Professor Timothy Phillips


Chair in Applied Mathematics

School of Mathematics

+44 29208 74194
Abacws, Room 5.04, Senghennydd Road, Cathays, Cardiff, CF24 4AG
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

Administrative duties

  • Member of School Research Committee
  • Director of EDI
  • Chair of School EDI Committee


























Book sections




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 2010

  • High-order approximations of viscoelastic flow problems. Invited speaker at Symposium on High Accuracy Flow Simulations, Lausanne, Switzerland, February 2010.
  • Mathematical and computational modelling of compressible viscoelastic fluids. 6th Annual European Rheology Conference, Goteborg, Sweden, April 2010.
  • Mathematical and computational modelling of compressible viscoelastic fluids. Invited speaker at Computational Challenges in Partial Differential Equations. INI/WIMCS Meeting, Swansea, April 2011.
  • High-order approximations of viscoelastic flows. Invited plenary speaker at the Institute of Non-Newtonian Fluid Mechanics Spring Meeting, Portmeirion, April 2011.
  • The influence of viscoelasticity on cavitation bubble dynamics. Invited speaker at Bubble Dynamics Workshop, Birmingham, July 2011.
  • Bubble collapse in compressible viscoelastic fluids using a spectral element marker particle method. 17th International Workshop on Numerical Methods for Non-Newtonian Flows, Blois, France, March 2012.
  • The effect of viscoelasticity on the dynamics of bubbles near rigid and free surfaces. Invited speaker at Bubble Dynamics Workshop, Birmingham, April 2012.
  • The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces.  XVIth International Congress on Rheology, Lisbon, Portugal, August 2012.
  • Bubble collapse in compressible viscoelastic fluids using a spectral element marker particle method. BSR Midwinter Meeting, Aberystwyth, December 2012.
  • 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.

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-
  • Editorial Board Member. Journal of Non-Newtonian Fluid Mechanics, 2017-
  • External examiner for the undergraduate degree schemes in Mathematics at University of Reading, 2016-.
  • Member, EPSRC College, 2000-
  • Chair, MAGIC Programme Committee, 2017-
  • Council Member, Learned Society of Wales, 2017-2020



  • MA3304 Methods of Applied Mathematics



  • 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. I am in the process of producing a second edtion of this book which is due towards the end of 2023. I have considerable experience in supervising young researchers (15 PDRAs and 24 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

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:

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

Abhishek Chakraborty

Research student

William Doherty

William Doherty

Graduate Tutor

Layla Sadeghi Namaghi

Layla Sadeghi Namaghi

Research student

Philippe Hergibo

Philippe Hergibo

Graduate Demonstrator

Ahlam Alghamdi

Ahlam Alghamdi

Research student