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Prof Mark A Kelmanson

Professor of Applied Mathematics
Applied Mathematics

Contact details

Room: Satellite 10.07
Tel: +44 (0)113 3435150
Email: M.Kelmanson @


Thin-film fluid mechanics
Coating flows
Ophthalmic flows
Multiple timescales
Algebraic manipulators
Fredholm integral equations
Error analysis

Research interests

As a member of the Polymers and Industrial Mathematics (PIM) group, my main current research interests are in the field of thin-fim viscous fluid mechanics, with particular emphasis on the development of (possibly automated) asymptotic methods for both deriving and solving the spatio-temporal evolution equations arising in both industrial coating flows and ophthalmic flows.

Other industrially related research has been done under funded collaborations with: Dr Daniel Read (Maths, PIM) on computational linear rheology; Professor Peter Jimack (Computing) on fully adaptive finite-element methods for free-surface viscous flows; PPG Protective and Marine Coatings (industrial sponsors) on the modelling of fire-resistant properties of reactive intumescent protective coatings, and; Defence Research Agency (Fort Halstead) on the modelling of high-velocity impact phenomena.

As a former member of the now-disbanded Computational PDEs group, my other current research interests involve error analyses of numerical methods for solving Fredholm integral equations of the second kind, because many examples of these arise when modelling industrial problems. A full understanding of the errors incurred in such methods may enable improved techniques to be developed and implemented. For example, recent research on problems involving boundary singularities can provide an better insight into crack formation in elastostatics.

Useful links

Personal homepage
PIM group page
Industrial placement page

Current postgraduate students

Abigail Fairbairn (2014)
Tomasz Salwa (2014)


Fairbairn AI, Kelmanson MA Spectrally accurate Nyström-solver error bounds for 1-D Fredholm integral equations of the second kind Applied Mathematics and Computation, 315, 211-223, 2017
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Fairbairn AI; Kelmanson MA An exponentially convergent Volterra-Fredholm method for 1-D integro-differential equationsProceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11) 2017
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Salwa TJ; Bokhove O; Kelmanson MA Variational Coupling of Wave Slamming against Elastic MastsProceedings 31st International Workshop on Water Waves and Floating Bodies, 149-152 2016
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Salwa T; Bokhove O; Kelmanson MA Variational modelling of wave-structure interactions for offshore wind turbinesProceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE 2016
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Cullis IG, Kelmanson MA Cost-effective simulation and prediction of explosions for military and public safety, and for improved oil extraction In UK Success Stories in Industrial Mathematics, 155-161, 2016
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Fairbairn AI; Kelmanson MA Computable theoretical error bounds for Nyström methods for 1-D Fredholm integral equations of the second kindProceedings of the 10th UK Conference on Boundary Integral Methods 2015
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Groh CM; Kelmanson MA Inertially Induced Cyclic Solutions in Thin-Film Free-Surface Flows11th US National Congress on Computational Mechanics 2014

Groh CM, Kelmanson MA Inertially induced cyclic solutions in thin-film free-surface flows Journal of Fluid Mechanics, 755, 628-653, 2014
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Groh CM, Kelmanson MA Computer-algebra multiple-timescale method for spatially periodic thin-film viscous-flow problems Int. J. Num. Meth. Fluids, 68, 1457-1470, 2012

Kelmanson MA, Tenwick MC Error Reduction in Gauss-Jacobi-Nystrom Quadrature for Fredholm Integral Equations of the Second Kind CMES-COMP MODEL ENG, 55, 191-210, 2010

Groh CM, Kelmanson MA Multiple-timescale asymptotic analysis of transient coating flows PHYS FLUIDS, 21, 2009

Kelmanson MA On inertial effects in the Moffatt-Pukhnachov coating-flow problem J FLUID MECH, 633, 327-353, 2009

Kelmanson MA Pseudo-three-timescale approximation of exponentially modulated free-surface waves J FLUID MECH, 625, 435-443, 2009

Kelmanson MA; Tenwick MC A modified orthogonal-polynomial Nyström method for Fredholm integral equations of the second kind7th UK Conference on Boundary-Integral Methods, 181-192 2009

Groh CM, Kelmanson MA Closed-form error estimates for the numerical solution of Fredholm integral equations of the second kind J. Integral Equations and Applics.,, 20, 481-505, 2008

Das C, Read DJ, Kelmanson MA, McLeish TCB Dynamic scaling in entangled mean-field gelation polymers PHYS REV E, 74, 2006

Das C, Inkson NJ, Read DJ, Kelmanson MA, McLeish TCB Computational linear rheology of general branch-on-branch polymers Journal of Rheology, 50, 207-235, 2006
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Walkley MA, Gaskell PH, Jimack PK, Kelmanson MA, Summers JL Finite element simulation of three-dimensional free-surface flow problems JOURNAL OF SCIENTIFIC COMPUTING, 24, 147-162, 2005

Walkley MA, Gaskell PH, Jimack PK, Kelmanson MA, Summers JL Finite element simulation of three-dimensional free-surface flow problems with dynamic contact lines INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 47, 1353-1359, 2005

Walkley MA, Gaskell PH, Jimack PK, Kelmanson MA, Summers JL Adaptive finite element simulation of three-dimensional surface-tension-dominated free-surface flow problems Australian&New Zealand Industrial and Applied Mathematics Journal, 46, C558-C571, 2005

Hinch EJ, Kelmanson MA, Metcalfe PD Shock-like free-surface perturbations in low-surface-tension, viscous, thin-film flow exterior to a rotating cylinder Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 460, 2975-2991, 2004

Kelmanson MA Hypersingular boundary integrals in cusped two-dimensional free-surface Stokes flow Journal of Fluid Mechanics, 514, 313-325, 2004

Walkley MA, Gaskell PH, Jimack PK, Kelmanson MA, Summers JL, Wilson MCT On the calculation of normals in free-surface flow problems Communications in Numerical Methods in Engineering, 20, 343-352, 2004
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Hinch EJ, Kelmanson MA On the decay and drift of free-surface perturbations in viscous thin-film flow exterior to a rotating cylinder Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 459, 1193-1213, 2003

Peterson RC, Jimack PK, Kelmanson MA On the stability of viscous free-surface flow supported by a rotating cylinder P ROY SOC LOND A MAT, 457, 1427-1445, 2001

Kelmanson MA A Rapid Zonal Algorithm for Polyelliptic PDEs in Domains with High Aspect Ratio Mathematical and Computer Modelling, 31, 45-59, 2000
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Peterson RC, Jimack PK, Kelmanson MA The solution of two-dimensional free-surface problems using automatic mesh generation International Journal for Numerical Methods in Fluids, 31, 937-960, 1999

Bateson LE, Kelmanson MA, Knudsen C Solution of a non-linear transcendental eigenvalue equation via interval analysis Computers&Mathematics with Applications, 38, 133-142, 1999

Kelmanson MA, Maunder SB Modelling High-Velocity Impact Phenomena Using Unstructured Dynamically-Adaptive Eulerian Meshes Journal of the Mechanics and Physics of Solids, 47, 731-762, 1999
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Peterson RC; Jimack PK; Kelmanson MA Automatic generation of finite-element meshes for evolving gas-liquid interfaces with arbitrary geometryICFD 1998, Oxford, UK, 467-473 1998

Decorps SAM, Kelmanson MA A zonal boundary-element method for analysing heat exchangers with thin extended surfaces Computers&Mathematics with Applications, 33, 103-107, 1997

Kelmanson MA Truncation errors in a 2-D hyperbolic PDE integration scheme Mathematical Engineering in Industry, 6, 171-183, 1997

Lonsdale B; Bloor MIG; Kelmanson MA An iterative integral-equation method for 6th-order inhomogeneous PDEs11th International Conference on Boundary Element Technology (Hawaii), 369-378 1996

Kelmanson MA, Lonsdale B Eddy Genesis in the Double-Lid-Driven Cavity Quarterly Journal of Mechanics and Applied Mathematics, 49, 635-655, 1996
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Kelmanson MA Theoretical and experimental analyses of the maximum-supportable fluid load on a rotating cylinder Journal of Engineering Mathematics, 29, 271-285, 1995

Kelmanson MA, Lonsdale B Annihilation of boundary singularities via suitable Green's functions Computers&Mathematics with Applications, 29, 1-7, 1995

Kelmanson MA Unstructured rectangular mesh generation for adaptive two-dimensional conservative schemes. Applied Mathematics Letters, 6, 17-21, 1993

Kelmanson MA Error analysis of a 2-D Eulerian impact codeDefence Research Agency Working Paper 1993