# School of Mathematics

## Prof Mark A Kelmanson

Professor of Applied Mathematics

Applied Mathematics

### Contact details

Room: Satellite 10.07

Tel: +44 (0)113 3435150

Email: M.Kelmanson @ leeds.ac.uk

### Keywords

Thin-film fluid mechanics

Coating flows

Ophthalmic flows

Asymptotics

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)

## Publications

**Fairbairn AI; Kelmanson MA ** *An exponentially convergent Volterra-Fredholm method for 1-D integro-differential equations*Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11) 2017

View abstract

**Salwa TJ; Bokhove O; Kelmanson MA ** *Variational Coupling of Wave Slamming against Elastic Masts*Proceedings 31st International Workshop on Water Waves and Floating Bodies, 149-152 2016

View abstract

**Salwa T; Bokhove O; Kelmanson MA ** *Variational modelling of wave-structure interactions for offshore wind turbines*Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE 2016

DOI:10.1115/OMAE2016-54897

View abstract

**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

DOI:10.1007/978-3-319-25454-8_20

View abstract

**Fairbairn AI; Kelmanson MA ** *Computable theoretical error bounds for Nyström methods for 1-D Fredholm integral equations of the second kind*Proceedings 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 Flows*11th 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

DOI:10.1017/jfm.2014.432

View abstract

**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

DOI:10.1002/fld.2458

**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

DOI:10.1063/1.3231847

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

DOI:10.1017/S0022112009006703

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

DOI:10.1017/S0022112009005989

**Kelmanson MA; Tenwick MC ** *A modified orthogonal-polynomial Nyström method for Fredholm integral equations of the second kind*7th 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

DOI:10.1103/PhysRevE.74.011404

**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

DOI:10.1122/1.2167487

View abstract

**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

DOI:10.1007/s10915-004-4611-0

**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

DOI:10.1002/fld.839

**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

DOI:10.1098/rspa.2004.1327

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

DOI:10.1017/S0022112004000515

**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

DOI:10.1002/cnm.677

View abstract

**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

DOI:10.1098/rspa.2002.1069

**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

View abstract

**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

View abstract

**Peterson RC; Jimack PK; Kelmanson MA ** *Automatic generation of finite-element meshes for evolving gas-liquid interfaces with arbitrary geometry*ICFD 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 PDEs*11th 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

View abstract

**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

DOI:10.1016/0893-9659(93)90005-8

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

**Fairbairn AI, Kelmanson MA** Spectrally accurate Nyström-solver error bounds for 1-D Fredholm integral equations of the second kind *Applied Mathematics and Computation*

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