Professor Timothy Phillips
(he/him)
Chair in Applied Mathematics
 Available for postgraduate supervision
Overview
Research interests
My research interests are in nonNewtonian 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 fluidstructure 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 FokkerPlanck equation. I have a particular interest in spectral element methods and the lattice Boltzmann method.
Research group
Administrative duties
 Head of Applied and Computational Mathematics Research Group
 Member of School Research Committee
 Cochair School Athena SWAN SelfAssessment Team
Publication
2024
 Hergibo, P., Phillips, T. N. and Xie, Z. 2024. Resolving subgridscale structures for multiphase flows using a filament momentoffluid method. Computers & Fluids 285, article number: 106455. (10.1016/j.compfluid.2024.106455)
 Doherty, W., Phillips, T. N. and Xie, Z. 2024. The logconformation formulation for single and multiphase axisymmetric viscoelastic flows. Journal of Computational Physics 508, article number: 113014. (10.1016/j.jcp.2024.113014)
 GómezLópez, A., Vargas, R. O., MilMartínez, 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 quadtreebased adaptive momentoffluid 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. (10.1007/9783031439100)
 O'Brien, E. N., Mahmud, M., Smith, W. R., Wang, Q. X. and Phillips, T. N. 2023. The evolution of a threedimensional 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 momentoffluid method for resolving filamentary structures using a symmetric multimaterial 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 levelset method. Journal of Computational Physics 477, article number: 111936. (10.1016/j.jcp.2023.111936)
 Vargas, R. O., GómezLópez, A., Escandón, J. P., MilMartı́nez, 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. (10.1088/14024896/acb23b)
2022
 Fanelli, C., Kaouri, K., Phillips, T. N., Myers, T. G. and Font, F. 2022. Magnetic nanodrug delivery in nonNewtonian blood flows. Microfluidics and Nanofluidics 26(10), article number: 74. (10.1007/s10404022025766)
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. 735756. (10.1007/s0016202100582y)
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. 16261652. (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 NonNewtonian Fluid Mechanics 266, pp. 5971. (10.1016/j.jnnfm.2019.02.006)
 Phillips, T. N., Oldham, D. and Davies, J. H. 2019. Towards global SEM mantle convection simulations on Polyhedralbased grids. Journal of Computational and Applied Mathematics 348, pp. 4857. (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. 789803. (10.1007/s001620180476y)
2017
 Croft, T. L. D. and Phillips, T. N. 2017. Leastsquares proper generalized decompositions for weakly coercive elliptic problems. SIAM Journal on Scientific Computing 39(4), pp. A1366A1388. (10.1137/15M1049269)
 Kynch, R. and Phillips, T. N. 2017. A high resolution spectral element approximation of viscoelastic flows in axisymmetric geometries using a DEVSSG/DG formulation. Journal of NonNewtonian Fluid Mechanics 240, pp. 1533. (10.1016/j.jnnfm.2016.12.008)
2016
 Walters, M. J. and Phillips, T. N. 2016. A nonsingular boundary element method for modelling bubble dynamics in viscoelastic fluids. Journal of NonNewtonian Fluid Mechanics 235, pp. 109124. (10.1016/j.jnnfm.2016.07.012)
 Rowlatt, C. F. and Phillips, T. N. 2016. A spectral element formulation of the immersed boundary method for Newtonian fluids. Computer Methods in Applied Mechanics and Engineering 298, pp. 2957. (10.1016/j.cma.2015.08.010)
2015
 Claus, S., Cantwell, C. D. and Phillips, T. N. 2015. Spectral/hp element methods for plane Newtonian extrudate swell. Computers & Fluids 116, pp. 105117. (10.1016/j.compfluid.2015.04.002)
 Leonenko, G. M. and Phillips, T. N. 2015. Numerical approximation of highdimensional FokkerPlanck equations with polynomial coefficients. Journal of computational and applied mathematics 273, pp. 296312. (10.1016/j.cam.2014.05.024)
2014
 Traverso, L., Phillips, T. N. and Yang, Y. 2014. Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients. International Journal for Numerical Methods in Fluids 74(5), pp. 359385. (10.1002/fld.3854)
 Phillips, T. N. and Rowlatt, C. F. 2014. The extended spectral element method for the approximation of discontinuous functions. Siam Journal on Numerical Analysis
2013
 Claus, S. and Phillips, T. N. 2013. Viscoelastic flow around a confined cylinder using spectral/hp element methods. Journal of NonNewtonian Fluid Mechanics 200, pp. 131146. (10.1016/j.jnnfm.2013.03.004)
 Lind, S. and Phillips, T. N. 2013. Bubble collapse in compressible fluids using a spectral element marker particle method. Part 2. Viscoelastic fluids. International Journal for Numerical Methods in Fluids 71(9), pp. 11031130. (10.1002/fld.3701)
 Lind, S. and Phillips, T. N. 2013. The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces. Physics of Fluids 25(2), pp. 022104022135. (10.1063/1.4790512)
 Traverso, L., Phillips, T. N. and Yang, Y. 2013. Mixed finite element methods for groundwater flow in heterogeneous aquifers. Computers and Fluids 88, pp. 6080. (10.1016/j.compfluid.2013.08.018)
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. 11671187. (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. 652677. (10.1093/imamat/hxs041)
 Leonenko, G. M. and Phillips, T. N. 2012. Highorder approximation of Pearson diffusion processes. Journal of Computational and Applied Mathematics 236(11), pp. 28532868. (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. 1117. (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. 126. (10.1007/s0020501204965)
2011
 Russo, G. and Phillips, T. N. 2011. Spectral element predictions of dieswell for OldroydB fluids. Computers & Fluids 43(1), pp. 107118. (10.1016/j.compfluid.2010.09.028)
 Phillips, T. N. and Roberts, G. W. 2011. Lattice Boltzmann models for nonNewtonian flows. IMA Journal of Applied Mathematics 76(5), pp. 790816. (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(14), pp. 245277. (10.1007/s0016201102279)
 Lozinski, A., Owens, R. G. and Phillips, T. N. 2011. The Langevin and FokkerPlanck equations in polymer rheology. In: Glowinski, R. and Xu, J. eds. Handbook of Numerical Analysis  Special volume: Numerical Methods for NonNewtonian Fluids., Vol. 16. Amsterdam: Elsevier, pp. 211303., (10.1016/B9780444530479.000022)
 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 FokkerPlanck equation. International Journal for Multiscale Computational Engineering 9(1), pp. 7388. (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. 657676. (10.1007/s0039700904260)
 Lind, S. and Phillips, T. N. 2010. Spherical bubble collapse in viscoelastic fluids. Journal of nonNewtonian fluid mechanics 165(12), pp. 5664. (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 nonNewtonian fluid mechanics 165(1516), pp. 852865. (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. 780792. (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 NonNewtonian Fluid Mechanics 163(13), pp. 7887. (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 nonNewtonian fluid mechanics 156(12), pp. 720. (10.1016/j.jnnfm.2008.06.004)
 Vargas, R. O., Manero, O. and Phillips, T. N. 2009. Viscoelastic flow past confined objects using a micromacro approach. Rheologica Acta 48(4), pp. 373395. (10.1007/s003970080323y)
 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(4144), pp. 34003410. (10.1016/j.cma.2009.06.014)
 Leonenko, G. M. and Phillips, T. N. 2009. On the solution of the FokkerPlanck equation using a highorder reduced basis approximation. Computer Methods in Applied Mechanics and Engineering 199(14), pp. 158168. (10.1016/j.cma.2009.09.028)
2008
 Bierbrauer, F. and Phillips, T. N. 2008. Modelling spray impingement onto flat, rigid walls using an EulerianLagrangian method. Proceedings of the 22nd European Confrerence on Liquid Atomisation and Spray Systems, Como, Italy, 2008 Paper ILASS08030
 Bierbrauer, F. and Phillips, T. N. 2008. Secondary atomisation: simulation of droplet breakup in disturbed flow fields. Proceedings of the 22nd European Conference on Liquid Atomisation and Spray Systems, Como, Italy, 2008, Paper ILASS08A029
 Bollada, P. C. and Phillips, T. 2008. An anisothermal, compressible, piezoviscous model for journalbearing lubrication. International Journal for Numerical Methods in Fluids 58(1), pp. 2755. (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. 523539. (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 breakup using the Godunov markerparticle projection scheme. International Journal for Numerical Methods in Fluids 56(8), pp. 11551160. (10.1002/fld.1710)
 Gwynllyw, D. R. and Phillips, T. N. 2008. The influence of OldroydB and PTT lubricants on moving journal bearing systems. Journal of NonNewtonian Fluid Mechanics 150(23), pp. 196210. (10.1016/j.jnnfm.2007.10.014)
 Leonenko, G. M. and Phillips, T. N. 2008. Reduced basis function method for solving the 2D FokkerPlanck equation. Presented at: SASOR 2008: 2nd Southern African Conference of Rheology, Cape Town, South Africa, 68 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. 719725. (10.1007/s003970070256x)
2007
 Bollada, P. C. and Phillips, T. N. 2007. On the effects of a compressible viscous lubricant on the loadbearing capacity of a journal bearing. International Journal for Numerical Methods in Fluids 55(11), pp. 10911120. (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. 217229. (10.1016/j.cam.2006.02.016)
 Aguayo, J. P., Phillips, P. M., Phillips, T. N., TamaddonJahromi, H. R., Snigerev, B. A. and Webster, M. F. 2007. The numerical prediction of planar viscoelastic contraction flows using the pompom model and higherorder finite volume schemes. Journal of Computational Physics 220(2), pp. 586611. (10.1016/j.jcp.2006.05.039)
 Reis, T. and Phillips, T. N. 2007. Lattice Boltzmann model for simulating immiscible twophase flows. Journal of Physics A: Mathematical and Theoretical 40(14), article number: 4033. (10.1088/17518113/40/14/018)
 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 pompom model in steady flow. Journal of nonNewtonian fluid mechanics 145(23), pp. 92101. (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 nonNewtonian fluid mechanics 137(13), pp. 3138. (10.1016/j.jnnfm.2006.03.006)
 Ervin, V. J. and Phillips, T. N. 2006. Residual a posteriori error estimator for a threefield model of a generalized Stokes problem. Computer Methods in Applied Mechanics and Engineering 195(1922), pp. 25992610. (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(912), pp. 10271049. (10.1016/j.cma.2005.04.004)
 Bowen, P. J., Phillips, T. N. and Zheng, Y. 2006. Direct numerical simulation of nonNewtonian droplet deformation. Presented at: 10th International Conference on Liquid Atomization and Spray Systems (ICLASS2006), 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 nonNewtonian fluid mechanics 129(3), pp. 143162. (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. 423454. (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. 286314. (10.1016/j.jcp.2004.05.016)
 Aboubacar, M., Phillips, T. N., TamaddonJahromi, H. R., Snigerev, B. A. and Webster, M. F. 2004. Highorder finite volume methods for viscoelastic flow problems. Journal of Computational Physics 199(1), pp. 1640. (10.1016/j.jcp.2004.01.033)
 MomeniMasuleh, S. H. and Phillips, T. N. 2004. Viscoelastic flow in an undulating tube using spectral methods. Computers & Fluids 33(8), pp. 10751095. (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 nonNewtonian fluid mechanics 122(13), pp. 287301. (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 DropletGas 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 nonNewtonian fluid mechanics 108(13), pp. 2547. (10.1016/S03770257(02)001234)
 Owens, R. G. and Phillips, T. N. 2002. Computational rheology. London: Imperial College Press.
2001
 Phillips, T. N. and Williams, A. J. 2001. Conservative semiLagrangian finite volume schemes. Numerical Methods for Partial Differential Equations 17(4), pp. 403425. (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. 127147. (10.1093/imamat/66.2.127)
 Phillips, T. N. and Williams, A. J. 2001. A semiLagrangian finite volume method for Newtonian contraction flows. SIAM Journal on Scientific Computing 22(6), pp. 21522177. (10.1137/S1064827599365288)
Adrannau llyfrau
 Lozinski, A., Owens, R. G. and Phillips, T. N. 2011. The Langevin and FokkerPlanck equations in polymer rheology. In: Glowinski, R. and Xu, J. eds. Handbook of Numerical Analysis  Special volume: Numerical Methods for NonNewtonian Fluids., Vol. 16. Amsterdam: Elsevier, pp. 211303., (10.1016/B9780444530479.000022)
Cynadleddau
 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.
 Leonenko, G. M. and Phillips, T. N. 2008. Reduced basis function method for solving the 2D FokkerPlanck equation. Presented at: SASOR 2008: 2nd Southern African Conference of Rheology, Cape Town, South Africa, 68 October 2008.
 Bowen, P. J., Phillips, T. N. and Zheng, Y. 2006. Direct numerical simulation of nonNewtonian droplet deformation. Presented at: 10th International Conference on Liquid Atomization and Spray Systems (ICLASS2006), Kyoto, Japan, 27 August  1 September 2006.
 Zheng, Y., Phillips, T. N. and Bowen, P. J. 2003. Development of DNS Spectral Element Methods for Study of Newtonian DropletGas Systems. Presented at: 9th International Conference on Liquid Atomisation and Spray Systems (ICLASS), Sorrento, Italy.
Erthyglau
 Hergibo, P., Phillips, T. N. and Xie, Z. 2024. Resolving subgridscale structures for multiphase flows using a filament momentoffluid method. Computers & Fluids 285, article number: 106455. (10.1016/j.compfluid.2024.106455)
 Doherty, W., Phillips, T. N. and Xie, Z. 2024. The logconformation formulation for single and multiphase axisymmetric viscoelastic flows. Journal of Computational Physics 508, article number: 113014. (10.1016/j.jcp.2024.113014)
 GómezLópez, A., Vargas, R. O., MilMartínez, 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 quadtreebased adaptive momentoffluid method for interface reconstruction with filaments. Journal of Computational Physics 499, article number: 112719. (10.1016/j.jcp.2023.112719)
 O'Brien, E. N., Mahmud, M., Smith, W. R., Wang, Q. X. and Phillips, T. N. 2023. The evolution of a threedimensional 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 momentoffluid method for resolving filamentary structures using a symmetric multimaterial 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 levelset method. Journal of Computational Physics 477, article number: 111936. (10.1016/j.jcp.2023.111936)
 Vargas, R. O., GómezLópez, A., Escandón, J. P., MilMartı́nez, 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. (10.1088/14024896/acb23b)
 Fanelli, C., Kaouri, K., Phillips, T. N., Myers, T. G. and Font, F. 2022. Magnetic nanodrug delivery in nonNewtonian blood flows. Microfluidics and Nanofluidics 26(10), article number: 74. (10.1007/s10404022025766)
 Mackay, A. T. and Phillips, T. N. 2021. Compressible and nonisothermal viscoelastic flow between eccentrically rotating cylinders. Theoretical and Computational Fluid Dynamics 35, pp. 735756. (10.1007/s0016202100582y)
 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. 16261652. (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)
 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 NonNewtonian Fluid Mechanics 266, pp. 5971. (10.1016/j.jnnfm.2019.02.006)
 Phillips, T. N., Oldham, D. and Davies, J. H. 2019. Towards global SEM mantle convection simulations on Polyhedralbased grids. Journal of Computational and Applied Mathematics 348, pp. 4857. (10.1016/j.cam.2018.08.042)
 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. 789803. (10.1007/s001620180476y)
 Croft, T. L. D. and Phillips, T. N. 2017. Leastsquares proper generalized decompositions for weakly coercive elliptic problems. SIAM Journal on Scientific Computing 39(4), pp. A1366A1388. (10.1137/15M1049269)
 Kynch, R. and Phillips, T. N. 2017. A high resolution spectral element approximation of viscoelastic flows in axisymmetric geometries using a DEVSSG/DG formulation. Journal of NonNewtonian Fluid Mechanics 240, pp. 1533. (10.1016/j.jnnfm.2016.12.008)
 Walters, M. J. and Phillips, T. N. 2016. A nonsingular boundary element method for modelling bubble dynamics in viscoelastic fluids. Journal of NonNewtonian Fluid Mechanics 235, pp. 109124. (10.1016/j.jnnfm.2016.07.012)
 Rowlatt, C. F. and Phillips, T. N. 2016. A spectral element formulation of the immersed boundary method for Newtonian fluids. Computer Methods in Applied Mechanics and Engineering 298, pp. 2957. (10.1016/j.cma.2015.08.010)
 Claus, S., Cantwell, C. D. and Phillips, T. N. 2015. Spectral/hp element methods for plane Newtonian extrudate swell. Computers & Fluids 116, pp. 105117. (10.1016/j.compfluid.2015.04.002)
 Leonenko, G. M. and Phillips, T. N. 2015. Numerical approximation of highdimensional FokkerPlanck equations with polynomial coefficients. Journal of computational and applied mathematics 273, pp. 296312. (10.1016/j.cam.2014.05.024)
 Traverso, L., Phillips, T. N. and Yang, Y. 2014. Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients. International Journal for Numerical Methods in Fluids 74(5), pp. 359385. (10.1002/fld.3854)
 Phillips, T. N. and Rowlatt, C. F. 2014. The extended spectral element method for the approximation of discontinuous functions. Siam Journal on Numerical Analysis
 Claus, S. and Phillips, T. N. 2013. Viscoelastic flow around a confined cylinder using spectral/hp element methods. Journal of NonNewtonian Fluid Mechanics 200, pp. 131146. (10.1016/j.jnnfm.2013.03.004)
 Lind, S. and Phillips, T. N. 2013. Bubble collapse in compressible fluids using a spectral element marker particle method. Part 2. Viscoelastic fluids. International Journal for Numerical Methods in Fluids 71(9), pp. 11031130. (10.1002/fld.3701)
 Lind, S. and Phillips, T. N. 2013. The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces. Physics of Fluids 25(2), pp. 022104022135. (10.1063/1.4790512)
 Traverso, L., Phillips, T. N. and Yang, Y. 2013. Mixed finite element methods for groundwater flow in heterogeneous aquifers. Computers and Fluids 88, pp. 6080. (10.1016/j.compfluid.2013.08.018)
 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. 11671187. (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. 652677. (10.1093/imamat/hxs041)
 Leonenko, G. M. and Phillips, T. N. 2012. Highorder approximation of Pearson diffusion processes. Journal of Computational and Applied Mathematics 236(11), pp. 28532868. (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. 1117. (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. 126. (10.1007/s0020501204965)
 Russo, G. and Phillips, T. N. 2011. Spectral element predictions of dieswell for OldroydB fluids. Computers & Fluids 43(1), pp. 107118. (10.1016/j.compfluid.2010.09.028)
 Phillips, T. N. and Roberts, G. W. 2011. Lattice Boltzmann models for nonNewtonian flows. IMA Journal of Applied Mathematics 76(5), pp. 790816. (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(14), pp. 245277. (10.1007/s0016201102279)
 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 FokkerPlanck equation. International Journal for Multiscale Computational Engineering 9(1), pp. 7388. (10.1615/IntJMultCompEng.v9.i1.60)
 Russo, G. and Phillips, T. N. 2010. Numerical prediction of extrudate swell of branched polymer melts. Rheologica Acta 49(6), pp. 657676. (10.1007/s0039700904260)
 Lind, S. and Phillips, T. N. 2010. Spherical bubble collapse in viscoelastic fluids. Journal of nonNewtonian fluid mechanics 165(12), pp. 5664. (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 nonNewtonian fluid mechanics 165(1516), pp. 852865. (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. 780792. (10.1016/j.compfluid.2009.12.006)
 Bollada, P. C. and Phillips, T. N. 2009. A modified deformation field method for integral constitutive models. Journal of NonNewtonian Fluid Mechanics 163(13), pp. 7887. (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 nonNewtonian fluid mechanics 156(12), pp. 720. (10.1016/j.jnnfm.2008.06.004)
 Vargas, R. O., Manero, O. and Phillips, T. N. 2009. Viscoelastic flow past confined objects using a micromacro approach. Rheologica Acta 48(4), pp. 373395. (10.1007/s003970080323y)
 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(4144), pp. 34003410. (10.1016/j.cma.2009.06.014)
 Leonenko, G. M. and Phillips, T. N. 2009. On the solution of the FokkerPlanck equation using a highorder reduced basis approximation. Computer Methods in Applied Mechanics and Engineering 199(14), pp. 158168. (10.1016/j.cma.2009.09.028)
 Bierbrauer, F. and Phillips, T. N. 2008. Modelling spray impingement onto flat, rigid walls using an EulerianLagrangian method. Proceedings of the 22nd European Confrerence on Liquid Atomisation and Spray Systems, Como, Italy, 2008 Paper ILASS08030
 Bierbrauer, F. and Phillips, T. N. 2008. Secondary atomisation: simulation of droplet breakup in disturbed flow fields. Proceedings of the 22nd European Conference on Liquid Atomisation and Spray Systems, Como, Italy, 2008, Paper ILASS08A029
 Bollada, P. C. and Phillips, T. 2008. An anisothermal, compressible, piezoviscous model for journalbearing lubrication. International Journal for Numerical Methods in Fluids 58(1), pp. 2755. (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. 523539. (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 breakup using the Godunov markerparticle projection scheme. International Journal for Numerical Methods in Fluids 56(8), pp. 11551160. (10.1002/fld.1710)
 Gwynllyw, D. R. and Phillips, T. N. 2008. The influence of OldroydB and PTT lubricants on moving journal bearing systems. Journal of NonNewtonian Fluid Mechanics 150(23), pp. 196210. (10.1016/j.jnnfm.2007.10.014)
 Bollada, P. C. and Phillips, T. N. 2008. A physical decomposition of the stress tensor for complex flows. Rheologica Acta 47(7), pp. 719725. (10.1007/s003970070256x)
 Bollada, P. C. and Phillips, T. N. 2007. On the effects of a compressible viscous lubricant on the loadbearing capacity of a journal bearing. International Journal for Numerical Methods in Fluids 55(11), pp. 10911120. (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. 217229. (10.1016/j.cam.2006.02.016)
 Aguayo, J. P., Phillips, P. M., Phillips, T. N., TamaddonJahromi, H. R., Snigerev, B. A. and Webster, M. F. 2007. The numerical prediction of planar viscoelastic contraction flows using the pompom model and higherorder finite volume schemes. Journal of Computational Physics 220(2), pp. 586611. (10.1016/j.jcp.2006.05.039)
 Reis, T. and Phillips, T. N. 2007. Lattice Boltzmann model for simulating immiscible twophase flows. Journal of Physics A: Mathematical and Theoretical 40(14), article number: 4033. (10.1088/17518113/40/14/018)
 Inkson, N. and Phillips, T. N. 2007. Unphysical phenomena associated with the extended pompom model in steady flow. Journal of nonNewtonian fluid mechanics 145(23), pp. 92101. (10.1016/j.jnnfm.2007.05.002)
 Binding, D. M., Phillips, P. M. and Phillips, T. N. 2006. Contraction/expansion flows: the pressure drop and related issues. Journal of nonNewtonian fluid mechanics 137(13), pp. 3138. (10.1016/j.jnnfm.2006.03.006)
 Ervin, V. J. and Phillips, T. N. 2006. Residual a posteriori error estimator for a threefield model of a generalized Stokes problem. Computer Methods in Applied Mechanics and Engineering 195(1922), pp. 25992610. (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(912), pp. 10271049. (10.1016/j.cma.2005.04.004)
 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 nonNewtonian fluid mechanics 129(3), pp. 143162. (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. 423454. (10.1002/fld.932)
 Van Os, R. G. M. and Phillips, T. 2004. Spectral element methods for transient viscoelastic flow problems. Journal of Computational Physics 201(1), pp. 286314. (10.1016/j.jcp.2004.05.016)
 Aboubacar, M., Phillips, T. N., TamaddonJahromi, H. R., Snigerev, B. A. and Webster, M. F. 2004. Highorder finite volume methods for viscoelastic flow problems. Journal of Computational Physics 199(1), pp. 1640. (10.1016/j.jcp.2004.01.033)
 MomeniMasuleh, S. H. and Phillips, T. N. 2004. Viscoelastic flow in an undulating tube using spectral methods. Computers & Fluids 33(8), pp. 10751095. (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 nonNewtonian fluid mechanics 122(13), pp. 287301. (10.1016/j.jnnfm.2003.12.009)
 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 nonNewtonian fluid mechanics 108(13), pp. 2547. (10.1016/S03770257(02)001234)
 Phillips, T. N. and Williams, A. J. 2001. Conservative semiLagrangian finite volume schemes. Numerical Methods for Partial Differential Equations 17(4), pp. 403425. (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. 127147. (10.1093/imamat/66.2.127)
 Phillips, T. N. and Williams, A. J. 2001. A semiLagrangian finite volume method for Newtonian contraction flows. SIAM Journal on Scientific Computing 22(6), pp. 21522177. (10.1137/S1064827599365288)
Llyfrau
 Mavron, V. C. and Phillips, T. N. 2023. Elements of mathematics for economics and finance. Springer. (10.1007/9783031439100)
 Mavron, V. C. and Phillips, T. N. 2007. Elements of mathematics for economics and finance. London: Springer.
 Owens, R. G. and Phillips, T. N. 2002. Computational rheology. London: Imperial College Press.
 Lind, S. and Phillips, T. N. 2013. The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces. Physics of Fluids 25(2), pp. 022104022135. (10.1063/1.4790512)
 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. 126. (10.1007/s0020501204965)
 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. 523539. (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)
Research
External funding since 2000
 TypeDependent 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 DropletGas 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 NonNewtonian Fluid Mechanics, Royal Society International Conference Centre, Chicheley Hall, March 2013.
 A leastsquares 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 nonsingular 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 OldroydB fluid. Annual European Rheology Conference, Nantes, France, April 2015.
 The immersed boundary method for fluidstructure interaction (FSI) problems with an OldroydB fluid. XVIIth International Congress on Rheology, Kyoto, Japan, August 2016.

The extended spectral element method for the approximation of discontinuous functions and fluidstructure interaction problems. 20th IMACS World Congress, Xiamen, China, December 2016.

Large amplitude oscillatory shear flow simulation of complex fluids using micromacro approach with transient network dynamics. XXth International Workshop on Numerical Methods for NonNewtonian Flows, Oaxaca, Mexico (online), June 2021.

A conservative level set method for the numerical prediction of multiphase flows, INNFMBSR Meeting on NonNewtonian Fluid Mechanics, Lake Vyrnwy, Wales, April 2023.

A conservative levelset method for multiphase viscoelastic flows, XXIth International Workshop on Numerical Methods for NonNewtonian Flows, Loch Lomond, Scotland, May 2023.

A conservative levelset 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 NonNewtonian 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 NonNewtonian 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, 201719
 Council Member, British Society of Rheology.
 Editorial Board Member. Theoretical and Computational Fluid Mechanics, 20122024
 Editorial Board Member. Journal of NonNewtonian Fluid Mechanics, 2017
 External examiner for the undergraduate degree schemes in Mathematics at University of Reading, 20162020.
 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, 20172020
Teaching
Undergraduate
 MA3304 Methods of Applied Mathematics
Biography
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 peerreviewed conference proceedings. I coauthored 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 postgraduatelevel lecture courses in mathematics:
http://mathsmagic.ac.uk/index.php
Editorial Board, Theoretical and Computational Fluid Dynamics
Editorial Board, Journal of NonNewtonian Fluid Mechanics
Supervisions
I am interested in supervising PhD students in the areas of:
 numerical methods for nonNewtonian flows
 dynamics of cavitation bubbles
 multiphase flows
 extended spectral element method
 immersed boundary method
 lattice Boltzmann method
Current supervision
Abhishek Chakraborty
Research student
Layla Sadeghi Namaghi
Research student
Philippe Hergibo
Research student
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.
Contact Details
+44 29208 74194
Abacws, Room 5.04, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Research themes
Specialisms
 Numerical and computational mathematics
 NonNewtonian fluid flows
 Computational fluid dynamics