## Professor Tim Phillips

### Overview

Telephone: +44(0)29 208 74194

Fax: +44(0)29 208 74199

Extension: 74194

Location: M/2.41

#### Research Interests

Professor Phillips’s research interests include numerical analysis, spectral methods, computational fluid dynamics and rheology. He is an international authority on high-order discretization methods for solving problems in computational fluid dynamics, especially with respect to problems in rheology. He has written over one hundred research articles and contributions to conference proceedings. His first book, Computational Rheology, was published by Imperial College Press in 2002. His research activities have generated substantial funding from EPSRC, EU and Industry. He is one of the principal investigators in an EPSRC funded Portfolio Partnership in the area of Complex Fluids and Complex Flows, which is an interdisciplinary research network involving chemical engineers and computer scientists at Swansea University. He is a member of the EPSRC College and Membership Secretary of the British Society of Rheology.

#### Research Group

#### Recent Significant Publications

**Russo G and Phillips T N**, Numerical prediction of extrudate swell behaviour of branched polymer melts.* Rheologica Acta* 49 (2010), 657-676.

**Lind S J and Phillips T N**, The effect of viscoelasticity on a rising gas bubble. *Journal of Non-Newtonian Fluid Mechanics* 165 (2010), 852-865.

**Inkson N J, Phillips T N and van Os R G M**, Numerical simulation of flow past a cylinder using models of XPP type. *Journal of Non-Newtonian Fluid Mechanics* 156 (2009), 7-20.

**Gerritsma M I and Phillips T N**, On the characteristics and compatibility equations for
the UCM model fluid. *Zeitschrift fur Angewandte Mathematik und Mechanik* 8 (2008), 523-539.

#### Teaching

**Undergraduate**

MA0379 Numerical Solution of Elliptic Differential Equations

MA4008 Computational Fluid Dynamics

**Postgraduate**

#### Administrative Duties

Director of Research

Chair of School Research Committee

Chair of School IT Committee

Chair of School REF Committee

Member of School Management Board

Member of School Learning and Teaching Committee

Member of MAGIC Academic Steering Committee

Member of ARCCA Operational and User Group

### Publications

#### 2012

**Oldham D, Davies J H and Phillips T N**, Generic polyhedron grid generation for solving partial differential equations on spherical surfaces. Computers and Geosciences 39 (2012), 11-17.

(doi:10.1016/j.cageo.2011.06.004)

**Leonenko G and Phillips T N**, High order approximation of Pearson diffusion processes. Journal of Computational and Applied Mathematics 236 (2012),

2853-2868. (doi:10.1016/j.cam.2012.01.022)

**Lind S J and Phillips T N**, The influence of viscoelasticity on the collapse of cavitation bubbles near a rigid boundary. *Theoretical and Computational Fluid Dynamic *26 (2012), 245-277.

**Lind S J and Phillips T N**, Bubble collapse in compressible fluids using a spectral element marker particle method. Part 1. Newtonian fluids. *International Journal for Numerical Methods in Fluids* (DOI: 10.1002/fld.2737).

**2011**

**Russo G and Phillips T N**, Numerical prediction of extrudate swell behaviour of branched polymer melts.* Rheologica Acta* 49 (2010), 657-676.

**Leonenko G M and Phillips T N**, The prediction of plane Couette flow for a FENE fluid using a reduced basis approximation of the Fokker-Planck equation. *International Journal of Multiscale Computational Engineering* 9 (2011), 73-88.

**Russo G and Phillips T N** , Spectral element predictions of die-swell for Oldroyd B fluids. *Computers and Fluids* 43 (2011), 107-118.

**Lozinski A, Owens R G and Phillips T N**, The Langevin and Fokker-Planck equations in polymer rheology. In Handbook of Numerical Analysis (P. G. Ciarlet, Ed.), Vol. XVI, Special Volume: Numerical Methods for Non-Newtonian Fluids (Guest Editors: R. Glowinski and J. Xu), North-Holland, The Netherlands, 2011, 211--303.

**Phillips T N and Roberts G W**, Lattice Boltzmann models for non-Newtonian flows. IMA *Journal of Applied Mathematics, 76* (2011), 790-816 (doi: 10.1093/imamat/hxr003).

**2010 **

**Lind S J and Phillips T N**, The effect of viscoelasticity on a rising gas bubble. *Journal of Non-Newtonian Fluid Mechanics* 165 (2010), 852-865.

**Lind S J and Phillips T N**, Spherical bubble collapse in viscoelastic fluids. *Journal of Non-Newtonian Fluid Mechanics* 165 (2010), 56-64.

**Russo G and Phillips T N**, Numerical simulation of unsteady plane die swell for a Newtonian fluid using the spectral element method. *Computers and Fluids* 39 (2010), 780-792.

**2009 **

**Vargas R O, Manero O and Phillips T N**, Viscoelastic flow past confined objects using a micro-macro approach. *Rheologica Acta* 48 (2009), 373-395.

**Inkson N J, Phillips T N and van Os R G M**, Numerical simulation of flow past a cylinder using models of XPP type. *Journal of Non-Newtonian Fluid Mechanics* 156 (2009), 7-20.

**Bierbrauer F, Bollada P C and Phillips T N**, A consistent reflected image particle approach to the treatment of boundary conditions in smoothed particle hydrodynamics. *Computer Methods in Applied Mechanics and Engineering* 198 (2009), 3400-3410.

**Leonenko G M and Phillips T N**, On the solution of the Fokker-Planck equation using a high-order reduced basis function approximation. *Computer Methods in Applied Mechanics and Engineerin*g 199 (2009), 158-168.

**Bollada P C and Phillips T N**, A modified deformation field method for integral viscoelastic constitutive equations. *Journal of Non-Newtonian Fluid Mechanic*s 163 (2009), 78-87.

**2008 **

**Bollada P C and Phillips T N**, An anisothermal compressible piezoviscous model for journal
bearing lubrication. *International Journal for Numerical Methods in Fluids* 58 (2008), 27-55.

**Gerritsma M I and Phillips T N**, On the characteristics and compatibility equations for
the UCM model fluid. *Zeitschrift fur Angewandte Mathematik und Mechanik* 8 (2008), 523-539.

**Bollada, P C and Phillips T N**, A physical decomposition of the stress tensor for
complex flows. *Rheologica Acta* 47 (2008), 719-725.

**Bierbrauer F and Phillips T N**, Secondary atomisation: simulation of the droplet break-up in disturbed flow fields. Proceedings of the 22nd European Conference on Liquid Atomization and Spray Systems, Como, Italy, 2008, Paper ILASS08-A029.

**Bierbrauer F and Phillips T N**, Modelling spray impingement onto flat, rigid walls using an Eulerian-Lagrangian method. Proceedings of the 22nd European Conference on Liquid Atomization and Spray Systems, Como, Italy, 2008, Paper ILASS08-A030.

**Bierbrauer F and Phillips T N**, The numerical prediction of droplet
deformation and break-up using the Godunov marker-particle
projection scheme. International *Journal for Numerical Methods in Fluids* 56 (2008),
1155-1160.

**Reis T and Phillips T N**, An alternative approach to the solution to the dispersion equation
for a generalized lattice Boltzmann equation. *Physical Review *
E 77 (2008), 026702.

**Reis T and Phillips T N**, Numerical validation of a consistent axisymmetric
lattice Boltzmann model. *Physical Review* E 77 (2008), 026703 .

**Gwynllyw D Rh and Phillips T N**, The influence of Oldroyd-B and PTT lubricants on moving
journal bearing systems. *Journal of Non-Newtonian Fluid Mechanics *150
(2008), 196-210.

**2007 **

**Bollada P C and Phillips T N **, 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 (2007), 1091-1120.

**Inkson N J and Phillips T N** , Unphysical phenomena associated with the extended

pom-pom model in steady flow. *Journal of Non-Newtonian Fluid Mechanics* 145 (2007), 92-101.

**Aguayo J P, Phillips P M, Phillips T N, Tamaddon-Jahromi H R, Snigerev B A and Webster M F, **The numerical prediction of viscoelastic flows using the pom-pom model and high-order finite volume schemes. Journal of Computational Physics 220 (2007), 586-611.

**Van Os R G M and Phillips T N**, The choice of spectral element basis functions in domains with an axis of symmetry. Journal of Computational and Applied Mathematics 201 (2007), 217-229.

**Reis T and Phillips T N**, Lattice Boltzmann model for simulating immiscible two-phase flows. Journal of Physics A: Mathematical and Theoretical 40 (2007), 4033-4053.

**Reis T and Phillips T N**, A modified lattice Boltzmann model for axisymmetric flows. Physical Review E 75 (2007), 056703.

#### 2006

**Mavron V C and Phillips T N, **Elements of Mathematics for Economics and Finance. October 2006. Springer-Verlag, London. 312+x pages.

** Phillips T N and Smith K D, **A spectral element approach to the simulation of viscoelastic flows using Brownian configuration fields. Journal of Non-Newtonian Fluid Mechanics 138 (2006), 98-110.

** Gwynllyw D Rh and Phillips T N, **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 (2006), 1027-1049.

**Gwynllyw D Rh and Phillips T N,** The effect of viscoelasticity on the performance of journal bearings. In: Proceedings of the IUTAM Symposium on Elastohydrodynamics and Microelastohydrodynamics, R. W. Snidle and H. P. Evans (Eds), Springer, 175-186. 2006.

**Ervin V J and Phillips T N**, Residual a posteriori error estimator for a three-field model of a generalized Stokes problem. Computer Methods in Applied Mechanics and Engineering 195 (2006), 2599-2610.

** Binding D M, Phillips P M and Phillips T N**, Contraction/expansion flows: the pressure drop and related issues. Journal of Non-Newtonian Fluid Mechanics 137 (2006), 31-38.

#### 2005

**Aboubacar M, Aguayo J P, Phillips P M, Phillips T N, Tammaddon-Jahromi H R, Snigerev B A and Webster M F**, Modelling pom-pom type models with high-order finite volume schemes. Journal of Non-Newtonian Fluid Mechanics 126 (2005), 207-220

**Gwynllyw D Rh and Phillips T N**, Some issues regarding spectral element meshes for moving journal bearing systems. International Journal for Numerical Methods in Fluids 48 (2005), 423-454.

**Palmer A S and Phillips T N**, Linear stability analysis of plane Poiseuille flows of Phan-Thien Tanner liquids. Numerical Algorithms 38 (2005), 133-1547.

**van Os R G M and Phillips T N**, Efficient and stable spectral element methods for predicting the flow of an XPP fluid past a cylinder. Journal of Non-Newtonian Fluid Mechanics 129 (2005), 143-162.

**Palmer A S and Phillips T N**, Numerical approximation of the spectra of Poiseuille flow of two Phan-Thien Tanner liquids. In: Computational Fluid and Solid Mechanics 2005, K. J. Bathe (Ed.), Elsevier Science, 792-796, 2005.

#### 2004

**Aguayo J P, Phillips P M, Phillips T N, Snigerev B A, Tamaddon-Jahromi H R and Webster M F**. The numerical prediction of viscoelastic flows using the pom-pom model and high-order finite volume schemes. Proceedings of the XIVth International Congress on Rheology, Seoul, Korea, August, 2004.

**Aboubacar M, Phillips T N, Tammaddon-Jahromi H R, Snigerev B A and Webster M F**, High-order finite volume methods for viscoelastic flow problems. Journal of Computational Physics 199 (2004), 16-40.

**Momeni Masuleh S H and Phillips T N**, Viscoelastic flow in an undulating tube using spectral methods. Computers and Fluids 33 (2004), 1075-1095.

**van Os R G M and Phillips T N**, The prediction of complex flows of polymer melts using spectral elements. Journal of Non-Newtonian Fluid Mechanics 122 (2004), 336-350.

**van Os R G M and Phillips T N,** Spectral element methods for transient viscoelastic flow problems. Journal of Computational Physics **201** (2004), 286-314.

#### 2003

**Owens R G, Chauvière C and Phillips T N**, A locally-upwinded spectral technique (LUST) for viscoelastic flows, J of Non-Newtonian Fluid Mechanics 108, 49-71 (2003)

**Phillips T N and Williams A J**, Comparison of creeping and inertial flow of an Oldroyd B fluid through planar and axisymmetric contractions. Journal of Non-Newtonian Fluid Mechanics 108 (2003), 25-47.

#### 2002

**Aboubacar A, Phillips T N, Tammadon-Jahromi H T J, Webster M F and Williams A J**, Numerical simulation of contraction flows of Boger fluids using finite volume methods. Proceedings of the 6th European Conference on Rheology, H. Münstedt, J. Kaschta and A. Merten (Eds.), Erlangen, Germany, 2002, pages 279-280.

**Aboubacar M, Phillips T N, Snigerev B, Tammadon-Jahromi H T J and Webster M F**, Transient start-up of plane Poiuseuille flow. Proceedings of the 6th European Conference on Rheology, H. Münstedt, J. Kaschta and A. Merten (Eds.), Erlangen, Germany, 2002, pages 289-290.

**Escriva X, Leriche E and Phillips T N**, Preconditioned Uzawa algorithm for the velocity-pressure-stress formulation of viscoelastic flow problems. Journal of Scientific Computing 17 (2002), 219-229.

**Owens R G and Phillips T N**, Computational Rheology. Imperial College Press, London, May 2002. 417+xiv pages.

**Syed Mustapha S M F D and Phillips T N**, Rheometer advisory system - embedding mixed-initiative approach into its teaching and learning strategy. Journal of Applied Systems Studies 3 (2002) No.1.

#### 2001

**Gerritsma M I and Phillips T N**, On the use of characteristic variables in viscoelastic flow problems. IMA Journal of Applied Mathematics 66 (2001), 127-147.

**Phillips T N and Williams A J**, A semi-Lagrangian finite volume method for Newtonian contraction flows. SIAM Journal on Scientific Computing 22 (2001), 2152-2177.

**Phillips T N and Williams A J**, Conservative semi-Lagrangian finite volume schemes. Numerical Methods for Partial Differential Equations 17 (2001), 403-425.

**Phillips T N and Williams A J**, Semi-Lagrangian finite volume methods for viscoelastic planar and axisymmetric contraction flows. In: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference, Swansea, 2001, 20 pages.

### Research

#### 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).

#### Major Conference Talks Since 2004

The computation of flows of complex fluids using the spectral element method. Invited plenary speaker at the 6th International Conference on Spectral and High-Order Methods, Brown University, USA, June 2004.

The numerical prediction of flows of viscoelastic fluids. Invited plenary speaker at the Second Brazilian Rheology Conference, Rio de Janeiro, Brazil, July 2004.

Lattice Boltzmann model for simulating immiscible two-phase flows. Annual European Rheology Conference, Crete, April 2006.

Numerical simulation of flow past a cylinder using models of XPP type. Annual European Rheology Conference, Crete, April 2006.

Grid and particle based methods for complex fluids. Dynamics of Complex Fluids - 10 Years On, Cambridge, October 2006.

Whence and whither computational rheology? Invited plenary speaker at the Conference on `Whither Rheology?', Lake Vyrnwy, Wales, April 2007.

Numerical simulation of flow past a cylinder using models of XPP type. International Conference on Spectral and High Order Methods (ICOSAHOM), Beijing, China, June 2007.

The prediction of complex flows of complex fluids using spectral element approximations. Invited speaker at Workshop on Higher Order Methods in Computational Science and Engineering, Swansea, May 2008.

Macroscopic and micro/macro methods for viscoelastic flows. Invited speaker at 4th MIDNAG Meeting on Computational Methods for Non-Newtonian Flows, Birmingham, October 2008.

Reduced basis function method for solving the 2D Fokker-Planck equation. Invited plenary speaker at the Second Southern African Conference on Rheology, Cape Town, South Africa, October 2008.

Recent advances in the computational modelling of complex fluids. Computational Modelling Cluster Plenary Talk at WIMCS Annual Meeting, Aberystwyth, December 2008.

Numerical simulation of viscoelastic flows. Invited keynote speaker at New Trends in Complex Fluids Modelling, Bran, Romania, June 2009.

Lattice Boltzmann models for fluid flow. Invited speaker at @Part From the Atom to the Part: Models and Computational Methods, an ECCOMAS Thematic Conference on Multiscale Modelling and Simulation, Nantes, France, October 2009.

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.

### Postgraduate Students

#### Current

Susanne Claus - Filament Stretching Rheometry of Viscoelastic Liquids.

Tom Croft - Greedy Algorithms and the Proper Generalized Decomposition for Partial Differential Equations.

Ross Kynch - Sedimentation in Viscoelastic Fluids.

Chris Rowlatt - Mathematical and Computational Modelling of Blood Flow.

Mike Walters - Bubble Dynamics.

#### Graduated

List of graduated students with links to their homepages and theses

### 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.

#### Previous Positions

Oct. 1982 - Sept. 1984. Research Scientist, Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Virginia, U.S.A.

Oct. 1984 - Sept. 1992. New Blood Lecturer in Computational Fluid Dynamics, Department of Applied Mathematics, University College of Wales, Aberystwyth.

Oct. 1992 - May 1996. Senior Lecturer, Department of Mathematics, University of Wales, Aberystwyth.

June 1996 - Feb. 2000. Reader, Department of Mathematics, University of Wales, Aberystwyth.

March 2000 - August 2004. Professor, Department of Mathematics, University of Wales, Aberystwyth.